id	sid	tid	token	lemma	pos
ejpam-6202	1	1	european	european	PROPN
ejpam-6202	1	2	journal	journal	PROPN
ejpam-6202	1	3	of	of	ADP
ejpam-6202	1	4	pure	pure	ADJ
ejpam-6202	1	5	and	and	CCONJ
ejpam-6202	1	6	applied	applied	ADJ
ejpam-6202	1	7	mathematics	mathematic	NOUN
ejpam-6202	1	8	2025	2025	NUM
ejpam-6202	1	9	,	,	PUNCT
ejpam-6202	1	10	vol	vol	NOUN
ejpam-6202	1	11	.	.	PROPN
ejpam-6202	1	12	18	18	NUM
ejpam-6202	1	13	,	,	PUNCT
ejpam-6202	1	14	issue	issue	NOUN
ejpam-6202	1	15	2	2	NUM
ejpam-6202	1	16	,	,	PUNCT
ejpam-6202	1	17	article	article	NOUN
ejpam-6202	1	18	number	number	NOUN
ejpam-6202	1	19	6202	6202	NUM
ejpam-6202	1	20	issn	issn	PROPN
ejpam-6202	1	21	1307	1307	NUM
ejpam-6202	1	22	-	-	SYM
ejpam-6202	1	23	5543	5543	NUM
ejpam-6202	1	24	–	–	PUNCT
ejpam-6202	1	25	ejpam.com	ejpam.com	X
ejpam-6202	1	26	published	publish	VERB
ejpam-6202	1	27	by	by	ADP
ejpam-6202	1	28	new	new	PROPN
ejpam-6202	1	29	york	york	PROPN
ejpam-6202	1	30	business	business	PROPN
ejpam-6202	1	31	global	global	PROPN
ejpam-6202	1	32	the	the	DET
ejpam-6202	1	33	r	r	NOUN
ejpam-6202	1	34	-	-	PUNCT
ejpam-6202	1	35	stirling	stirling	NOUN
ejpam-6202	1	36	genocchi	genocchi	PROPN
ejpam-6202	1	37	numbers	number	NOUN
ejpam-6202	1	38	roberto	roberto	PROPN
ejpam-6202	1	39	b.	b.	PROPN
ejpam-6202	1	40	corcino1,2,∗	corcino1,2,∗	PROPN
ejpam-6202	1	41	,	,	PUNCT
ejpam-6202	1	42	vernard	vernard	NOUN
ejpam-6202	1	43	p.	p.	NOUN
ejpam-6202	1	44	dechosa2	dechosa2	PROPN
ejpam-6202	2	1	1	1	NUM
ejpam-6202	2	2	research	research	NOUN
ejpam-6202	2	3	institute	institute	NOUN
ejpam-6202	2	4	for	for	ADP
ejpam-6202	2	5	computational	computational	ADJ
ejpam-6202	2	6	mathematics	mathematic	NOUN
ejpam-6202	2	7	and	and	CCONJ
ejpam-6202	2	8	physics	physics	NOUN
ejpam-6202	2	9	,	,	PUNCT
ejpam-6202	2	10	cebu	cebu	NOUN
ejpam-6202	2	11	normal	normal	ADJ
ejpam-6202	2	12	university	university	NOUN
ejpam-6202	2	13	,	,	PUNCT
ejpam-6202	2	14	6000	6000	NUM
ejpam-6202	2	15	cebu	cebu	NOUN
ejpam-6202	2	16	city	city	NOUN
ejpam-6202	2	17	,	,	PUNCT
ejpam-6202	2	18	philippines	philippine	NOUN
ejpam-6202	2	19	2	2	NUM
ejpam-6202	2	20	mathematics	mathematics	NOUN
ejpam-6202	2	21	department	department	NOUN
ejpam-6202	2	22	,	,	PUNCT
ejpam-6202	2	23	cebu	cebu	NOUN
ejpam-6202	2	24	normal	normal	ADJ
ejpam-6202	2	25	university	university	NOUN
ejpam-6202	2	26	,	,	PUNCT
ejpam-6202	2	27	6000	6000	NUM
ejpam-6202	2	28	cebu	cebu	NOUN
ejpam-6202	2	29	city	city	NOUN
ejpam-6202	2	30	,	,	PUNCT
ejpam-6202	2	31	philippines	philippine	NOUN
ejpam-6202	2	32	abstract	abstract	ADJ
ejpam-6202	2	33	.	.	PUNCT
ejpam-6202	3	1	this	this	DET
ejpam-6202	3	2	paper	paper	NOUN
ejpam-6202	3	3	introduces	introduce	VERB
ejpam-6202	3	4	the	the	DET
ejpam-6202	3	5	r	r	NOUN
ejpam-6202	3	6	-	-	PUNCT
ejpam-6202	3	7	stirling	stirling	NOUN
ejpam-6202	3	8	genocchi	genocchi	PROPN
ejpam-6202	3	9	numbers	number	NOUN
ejpam-6202	3	10	,	,	PUNCT
ejpam-6202	3	11	a	a	DET
ejpam-6202	3	12	new	new	ADJ
ejpam-6202	3	13	sequence	sequence	NOUN
ejpam-6202	3	14	derived	derive	VERB
ejpam-6202	3	15	by	by	ADP
ejpam-6202	3	16	combining	combine	VERB
ejpam-6202	3	17	broder	broder	PROPN
ejpam-6202	3	18	’s	’s	PART
ejpam-6202	3	19	r	r	PROPN
ejpam-6202	3	20	-	-	PUNCT
ejpam-6202	3	21	stirling	stirling	NOUN
ejpam-6202	3	22	numbers	number	NOUN
ejpam-6202	3	23	with	with	ADP
ejpam-6202	3	24	the	the	DET
ejpam-6202	3	25	classical	classical	ADJ
ejpam-6202	3	26	genocchi	genocchi	NOUN
ejpam-6202	3	27	numbers	number	NOUN
ejpam-6202	3	28	,	,	PUNCT
ejpam-6202	3	29	which	which	PRON
ejpam-6202	3	30	are	be	AUX
ejpam-6202	3	31	closely	closely	ADV
ejpam-6202	3	32	related	relate	VERB
ejpam-6202	3	33	to	to	ADP
ejpam-6202	3	34	bernoulli	bernoulli	NOUN
ejpam-6202	3	35	numbers	number	NOUN
ejpam-6202	3	36	and	and	CCONJ
ejpam-6202	3	37	have	have	VERB
ejpam-6202	3	38	notable	notable	ADJ
ejpam-6202	3	39	applications	application	NOUN
ejpam-6202	3	40	in	in	ADP
ejpam-6202	3	41	algebraic	algebraic	ADJ
ejpam-6202	3	42	combinatorics	combinatoric	NOUN
ejpam-6202	3	43	.	.	PUNCT
ejpam-6202	4	1	while	while	SCONJ
ejpam-6202	4	2	the	the	DET
ejpam-6202	4	3	original	original	ADJ
ejpam-6202	4	4	r	r	NOUN
ejpam-6202	4	5	-	-	PUNCT
ejpam-6202	4	6	stirling	stirling	NOUN
ejpam-6202	4	7	numbers	number	NOUN
ejpam-6202	4	8	were	be	AUX
ejpam-6202	4	9	developed	develop	VERB
ejpam-6202	4	10	using	use	VERB
ejpam-6202	4	11	combinatorial	combinatorial	ADJ
ejpam-6202	4	12	methods	method	NOUN
ejpam-6202	4	13	to	to	PART
ejpam-6202	4	14	count	count	VERB
ejpam-6202	4	15	set	set	ADJ
ejpam-6202	4	16	partitions	partition	NOUN
ejpam-6202	4	17	,	,	PUNCT
ejpam-6202	4	18	this	this	DET
ejpam-6202	4	19	study	study	NOUN
ejpam-6202	4	20	adopts	adopt	VERB
ejpam-6202	4	21	an	an	DET
ejpam-6202	4	22	algebraic	algebraic	ADJ
ejpam-6202	4	23	approach	approach	NOUN
ejpam-6202	4	24	to	to	PART
ejpam-6202	4	25	explore	explore	VERB
ejpam-6202	4	26	the	the	DET
ejpam-6202	4	27	properties	property	NOUN
ejpam-6202	4	28	of	of	ADP
ejpam-6202	4	29	the	the	DET
ejpam-6202	4	30	new	new	ADJ
ejpam-6202	4	31	sequence	sequence	NOUN
ejpam-6202	4	32	.	.	PUNCT
ejpam-6202	5	1	through	through	ADP
ejpam-6202	5	2	tools	tool	NOUN
ejpam-6202	5	3	like	like	ADP
ejpam-6202	5	4	generating	generating	NOUN
ejpam-6202	5	5	functions	function	NOUN
ejpam-6202	5	6	,	,	PUNCT
ejpam-6202	5	7	recurrence	recurrence	NOUN
ejpam-6202	5	8	relations	relation	NOUN
ejpam-6202	5	9	,	,	PUNCT
ejpam-6202	5	10	and	and	CCONJ
ejpam-6202	5	11	algebraic	algebraic	ADJ
ejpam-6202	5	12	transformations	transformation	NOUN
ejpam-6202	5	13	,	,	PUNCT
ejpam-6202	5	14	the	the	DET
ejpam-6202	5	15	paper	paper	NOUN
ejpam-6202	5	16	uncovers	uncover	NOUN
ejpam-6202	5	17	deeper	deep	ADJ
ejpam-6202	5	18	structural	structural	ADJ
ejpam-6202	5	19	insights	insight	NOUN
ejpam-6202	5	20	and	and	CCONJ
ejpam-6202	5	21	highlights	highlight	NOUN
ejpam-6202	5	22	the	the	DET
ejpam-6202	5	23	broader	broad	ADJ
ejpam-6202	5	24	mathematical	mathematical	ADJ
ejpam-6202	5	25	connections	connection	NOUN
ejpam-6202	5	26	between	between	ADP
ejpam-6202	5	27	partition	partition	NOUN
ejpam-6202	5	28	theory	theory	NOUN
ejpam-6202	5	29	,	,	PUNCT
ejpam-6202	5	30	number	number	NOUN
ejpam-6202	5	31	theory	theory	NOUN
ejpam-6202	5	32	,	,	PUNCT
ejpam-6202	5	33	and	and	CCONJ
ejpam-6202	5	34	combinatorial	combinatorial	ADJ
ejpam-6202	5	35	analysis	analysis	NOUN
ejpam-6202	5	36	.	.	PUNCT
ejpam-6202	6	1	2020	2020	NUM
ejpam-6202	6	2	mathematics	mathematic	NOUN
ejpam-6202	6	3	subject	subject	NOUN
ejpam-6202	6	4	classifications	classification	NOUN
ejpam-6202	6	5	:	:	PUNCT
ejpam-6202	6	6	11b68	11b68	NUM
ejpam-6202	6	7	,	,	PUNCT
ejpam-6202	6	8	11b73	11b73	NUM
ejpam-6202	6	9	,	,	PUNCT
ejpam-6202	6	10	05a15	05a15	NOUN
ejpam-6202	6	11	key	key	ADJ
ejpam-6202	6	12	words	word	NOUN
ejpam-6202	6	13	and	and	CCONJ
ejpam-6202	6	14	phrases	phrase	NOUN
ejpam-6202	6	15	:	:	PUNCT
ejpam-6202	6	16	genocchi	genocchi	NOUN
ejpam-6202	6	17	numbers	number	NOUN
ejpam-6202	6	18	,	,	PUNCT
ejpam-6202	6	19	r	r	NOUN
ejpam-6202	6	20	-	-	PUNCT
ejpam-6202	6	21	stirling	stirling	NOUN
ejpam-6202	6	22	numbers	number	NOUN
ejpam-6202	6	23	,	,	PUNCT
ejpam-6202	6	24	recurrence	recurrence	NOUN
ejpam-6202	6	25	relations	relation	NOUN
ejpam-6202	6	26	,	,	PUNCT
ejpam-6202	6	27	generating	generate	VERB
ejpam-6202	6	28	function	function	NOUN
ejpam-6202	6	29	,	,	PUNCT
ejpam-6202	6	30	bernoulli	bernoulli	NOUN
ejpam-6202	6	31	numbers	number	NOUN
ejpam-6202	6	32	1	1	NUM
ejpam-6202	6	33	.	.	PUNCT
ejpam-6202	7	1	introduction	introduction	NOUN
ejpam-6202	7	2	stirling	stirling	NOUN
ejpam-6202	7	3	numbers	number	NOUN
ejpam-6202	7	4	were	be	AUX
ejpam-6202	7	5	first	first	ADV
ejpam-6202	7	6	introduced	introduce	VERB
ejpam-6202	7	7	by	by	ADP
ejpam-6202	7	8	james	james	PROPN
ejpam-6202	7	9	stirling	stirling	PROPN
ejpam-6202	7	10	with	with	ADP
ejpam-6202	7	11	pairs	pair	NOUN
ejpam-6202	7	12	of	of	ADP
ejpam-6202	7	13	numbers	number	NOUN
ejpam-6202	7	14	in	in	ADP
ejpam-6202	7	15	his	his	PRON
ejpam-6202	7	16	book	book	NOUN
ejpam-6202	7	17	methodus	methodus	NOUN
ejpam-6202	7	18	differentialis	differentialis	X
ejpam-6202	7	19	usually	usually	ADV
ejpam-6202	7	20	denoted	denote	VERB
ejpam-6202	7	21	by	by	ADP
ejpam-6202	7	22	s(n	s(n	PROPN
ejpam-6202	7	23	,	,	PUNCT
ejpam-6202	7	24	k	k	NOUN
ejpam-6202	7	25	)	)	PUNCT
ejpam-6202	7	26	and	and	CCONJ
ejpam-6202	7	27	s(n	s(n	PROPN
ejpam-6202	7	28	,	,	PUNCT
ejpam-6202	7	29	k	k	NOUN
ejpam-6202	7	30	)	)	PUNCT
ejpam-6202	7	31	where	where	SCONJ
ejpam-6202	7	32	s(n	s(n	PROPN
ejpam-6202	7	33	,	,	PUNCT
ejpam-6202	7	34	k	k	NOUN
ejpam-6202	7	35	)	)	PUNCT
ejpam-6202	7	36	referred	refer	VERB
ejpam-6202	7	37	to	to	ADP
ejpam-6202	7	38	as	as	SCONJ
ejpam-6202	7	39	stirling	stirling	NOUN
ejpam-6202	7	40	numbers	number	NOUN
ejpam-6202	7	41	of	of	ADP
ejpam-6202	7	42	the	the	DET
ejpam-6202	7	43	first	first	ADJ
ejpam-6202	7	44	kind	kind	NOUN
ejpam-6202	7	45	and	and	CCONJ
ejpam-6202	7	46	s(n	s(n	PROPN
ejpam-6202	7	47	,	,	PUNCT
ejpam-6202	7	48	k	k	NOUN
ejpam-6202	7	49	)	)	PUNCT
ejpam-6202	7	50	is	be	AUX
ejpam-6202	7	51	referred	refer	VERB
ejpam-6202	7	52	to	to	ADP
ejpam-6202	7	53	as	as	ADP
ejpam-6202	7	54	stirling	stirling	NOUN
ejpam-6202	7	55	numbers	number	NOUN
ejpam-6202	7	56	of	of	ADP
ejpam-6202	7	57	the	the	DET
ejpam-6202	7	58	second	second	ADJ
ejpam-6202	7	59	kind	kind	NOUN
ejpam-6202	7	60	.	.	PUNCT
ejpam-6202	8	1	[	[	X
ejpam-6202	8	2	1	1	X
ejpam-6202	8	3	]	]	PUNCT
ejpam-6202	8	4	over	over	ADP
ejpam-6202	8	5	the	the	DET
ejpam-6202	8	6	years	year	NOUN
ejpam-6202	8	7	,	,	PUNCT
ejpam-6202	8	8	many	many	ADJ
ejpam-6202	8	9	mathematics	mathematic	NOUN
ejpam-6202	8	10	enthusiasts	enthusiast	NOUN
ejpam-6202	8	11	have	have	AUX
ejpam-6202	8	12	investigated	investigate	VERB
ejpam-6202	8	13	and	and	CCONJ
ejpam-6202	8	14	expanded	expand	VERB
ejpam-6202	8	15	these	these	DET
ejpam-6202	8	16	two	two	NUM
ejpam-6202	8	17	special	special	ADJ
ejpam-6202	8	18	numbers	number	NOUN
ejpam-6202	8	19	.	.	PUNCT
ejpam-6202	9	1	one	one	NUM
ejpam-6202	9	2	of	of	ADP
ejpam-6202	9	3	them	they	PRON
ejpam-6202	9	4	is	be	AUX
ejpam-6202	9	5	broder	broder	NOUN
ejpam-6202	9	6	[	[	X
ejpam-6202	9	7	2	2	NUM
ejpam-6202	9	8	]	]	PUNCT
ejpam-6202	9	9	,	,	PUNCT
ejpam-6202	9	10	where	where	SCONJ
ejpam-6202	9	11	he	he	PRON
ejpam-6202	9	12	developed	develop	VERB
ejpam-6202	9	13	both	both	DET
ejpam-6202	9	14	types	type	NOUN
ejpam-6202	9	15	of	of	ADP
ejpam-6202	9	16	rstirling	rstirle	VERB
ejpam-6202	9	17	numbers	number	NOUN
ejpam-6202	9	18	and	and	CCONJ
ejpam-6202	9	19	imposed	impose	VERB
ejpam-6202	9	20	a	a	DET
ejpam-6202	9	21	constraint	constraint	NOUN
ejpam-6202	9	22	on	on	ADP
ejpam-6202	9	23	the	the	DET
ejpam-6202	9	24	first	first	ADJ
ejpam-6202	9	25	r	r	NOUN
ejpam-6202	9	26	elements	element	NOUN
ejpam-6202	9	27	,	,	PUNCT
ejpam-6202	9	28	requiring	require	VERB
ejpam-6202	9	29	them	they	PRON
ejpam-6202	9	30	to	to	PART
ejpam-6202	9	31	be	be	AUX
ejpam-6202	9	32	arranged	arrange	VERB
ejpam-6202	9	33	in	in	ADP
ejpam-6202	9	34	different	different	ADJ
ejpam-6202	9	35	cycles	cycle	NOUN
ejpam-6202	9	36	or	or	CCONJ
ejpam-6202	9	37	partition	partition	NOUN
ejpam-6202	9	38	in	in	ADP
ejpam-6202	9	39	different	different	ADJ
ejpam-6202	9	40	subsets	subset	NOUN
ejpam-6202	9	41	.	.	PUNCT
ejpam-6202	10	1	the	the	DET
ejpam-6202	10	2	r	r	NOUN
ejpam-6202	10	3	-	-	PUNCT
ejpam-6202	10	4	stirling	stirling	NOUN
ejpam-6202	10	5	numbers	number	NOUN
ejpam-6202	10	6	are	be	AUX
ejpam-6202	10	7	as	as	SCONJ
ejpam-6202	10	8	follows	follow	VERB
ejpam-6202	10	9	:	:	PUNCT
ejpam-6202	10	10	[	[	PUNCT
ejpam-6202	10	11	n	n	X
ejpam-6202	10	12	k	k	X
ejpam-6202	10	13	]	]	X
ejpam-6202	10	14	r	r	NOUN
ejpam-6202	10	15	∗corresponding	∗corresponde	VERB
ejpam-6202	10	16	author	author	NOUN
ejpam-6202	10	17	.	.	PUNCT
ejpam-6202	11	1	doi	doi	NOUN
ejpam-6202	11	2	:	:	PUNCT
ejpam-6202	11	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6202	https://doi.org/10.29020/nybg.ejpam.v18i2.6202	PROPN
ejpam-6202	11	4	email	email	NOUN
ejpam-6202	11	5	addresses	address	VERB
ejpam-6202	11	6	:	:	PUNCT
ejpam-6202	11	7	rcorcino@yahoo.com	rcorcino@yahoo.com	PROPN
ejpam-6202	11	8	(	(	PUNCT
ejpam-6202	11	9	r.	r.	PROPN
ejpam-6202	11	10	b.	b.	PROPN
ejpam-6202	11	11	corcino	corcino	PROPN
ejpam-6202	11	12	)	)	PUNCT
ejpam-6202	11	13	,	,	PUNCT
ejpam-6202	11	14	dechosav@cnu.edu.ph	dechosav@cnu.edu.ph	PROPN
ejpam-6202	11	15	(	(	PUNCT
ejpam-6202	11	16	v.	v.	ADP
ejpam-6202	11	17	p.	p.	PROPN
ejpam-6202	11	18	dechosa	dechosa	PROPN
ejpam-6202	11	19	)	)	PUNCT
ejpam-6202	11	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6202	12	1	1	1	NUM
ejpam-6202	12	2	copyright	copyright	NOUN
ejpam-6202	12	3	:	:	PUNCT
ejpam-6202	12	4	©	©	PROPN
ejpam-6202	12	5	2025	2025	NUM
ejpam-6202	12	6	the	the	DET
ejpam-6202	12	7	author(s	author(s	NOUN
ejpam-6202	12	8	)	)	PUNCT
ejpam-6202	12	9	.	.	PUNCT
ejpam-6202	13	1	(	(	PUNCT
ejpam-6202	13	2	cc	cc	NOUN
ejpam-6202	13	3	by	by	ADP
ejpam-6202	13	4	-	-	PUNCT
ejpam-6202	13	5	nc	nc	PROPN
ejpam-6202	13	6	4.0	4.0	NUM
ejpam-6202	13	7	)	)	PUNCT
ejpam-6202	13	8	2	2	NUM
ejpam-6202	13	9	of	of	ADP
ejpam-6202	13	10	26	26	NUM
ejpam-6202	13	11	can	can	AUX
ejpam-6202	13	12	be	be	AUX
ejpam-6202	13	13	represented	represent	VERB
ejpam-6202	13	14	as	as	ADP
ejpam-6202	13	15	the	the	DET
ejpam-6202	13	16	number	number	NOUN
ejpam-6202	13	17	of	of	ADP
ejpam-6202	13	18	permutations	permutation	NOUN
ejpam-6202	13	19	of	of	ADP
ejpam-6202	13	20	the	the	DET
ejpam-6202	13	21	set	set	NOUN
ejpam-6202	13	22	{	{	PUNCT
ejpam-6202	13	23	1	1	NUM
ejpam-6202	13	24	,	,	PUNCT
ejpam-6202	13	25	...	...	PUNCT
ejpam-6202	13	26	,	,	PUNCT
ejpam-6202	13	27	n	n	CCONJ
ejpam-6202	13	28	}	}	PUNCT
ejpam-6202	13	29	having	have	VERB
ejpam-6202	13	30	m	m	NOUN
ejpam-6202	13	31	cycles	cycle	NOUN
ejpam-6202	13	32	,	,	PUNCT
ejpam-6202	13	33	such	such	ADJ
ejpam-6202	13	34	that	that	SCONJ
ejpam-6202	13	35	the	the	DET
ejpam-6202	13	36	numbers	number	NOUN
ejpam-6202	13	37	1	1	NUM
ejpam-6202	13	38	,	,	PUNCT
ejpam-6202	13	39	2	2	NUM
ejpam-6202	13	40	,	,	PUNCT
ejpam-6202	13	41	...	...	PUNCT
ejpam-6202	13	42	,	,	PUNCT
ejpam-6202	13	43	r	r	NOUN
ejpam-6202	13	44	are	be	AUX
ejpam-6202	13	45	in	in	ADP
ejpam-6202	13	46	distinct	distinct	ADJ
ejpam-6202	13	47	.	.	PUNCT
ejpam-6202	13	48	{	{	PUNCT
ejpam-6202	14	1	n	n	PROPN
ejpam-6202	14	2	k	k	NOUN
ejpam-6202	14	3	}	}	PUNCT
ejpam-6202	14	4	r	r	NOUN
ejpam-6202	14	5	can	can	AUX
ejpam-6202	14	6	be	be	AUX
ejpam-6202	14	7	represented	represent	VERB
ejpam-6202	14	8	as	as	ADP
ejpam-6202	14	9	the	the	DET
ejpam-6202	14	10	number	number	NOUN
ejpam-6202	14	11	of	of	ADP
ejpam-6202	14	12	partitions	partition	NOUN
ejpam-6202	14	13	of	of	ADP
ejpam-6202	14	14	the	the	DET
ejpam-6202	14	15	set	set	NOUN
ejpam-6202	14	16	{	{	PUNCT
ejpam-6202	14	17	1	1	NUM
ejpam-6202	14	18	,	,	PUNCT
ejpam-6202	14	19	...	...	PUNCT
ejpam-6202	14	20	,	,	PUNCT
ejpam-6202	14	21	n	n	CCONJ
ejpam-6202	14	22	}	}	PUNCT
ejpam-6202	14	23	into	into	ADP
ejpam-6202	14	24	m	m	PROPN
ejpam-6202	14	25	non	non	ADJ
ejpam-6202	14	26	-	-	ADJ
ejpam-6202	14	27	empty	empty	ADJ
ejpam-6202	14	28	disjoint	disjoint	NOUN
ejpam-6202	14	29	subsets	subset	NOUN
ejpam-6202	14	30	such	such	ADJ
ejpam-6202	14	31	that	that	SCONJ
ejpam-6202	14	32	the	the	DET
ejpam-6202	14	33	numbers	number	NOUN
ejpam-6202	14	34	1	1	NUM
ejpam-6202	14	35	,	,	PUNCT
ejpam-6202	14	36	2	2	NUM
ejpam-6202	14	37	,	,	PUNCT
ejpam-6202	14	38	...	...	PUNCT
ejpam-6202	14	39	,	,	PUNCT
ejpam-6202	14	40	r	r	NOUN
ejpam-6202	14	41	are	be	AUX
ejpam-6202	14	42	in	in	ADP
ejpam-6202	14	43	distinct	distinct	ADJ
ejpam-6202	14	44	subsets	subset	NOUN
ejpam-6202	14	45	.	.	PUNCT
ejpam-6202	15	1	since	since	SCONJ
ejpam-6202	15	2	broder	broder	PROPN
ejpam-6202	15	3	’s	’s	PART
ejpam-6202	15	4	formulation	formulation	NOUN
ejpam-6202	15	5	was	be	AUX
ejpam-6202	15	6	primarily	primarily	ADV
ejpam-6202	15	7	combinatorial	combinatorial	ADJ
ejpam-6202	15	8	,	,	PUNCT
ejpam-6202	15	9	corcino	corcino	NOUN
ejpam-6202	15	10	et.al	et.al	NOUN
ejpam-6202	16	1	[	[	X
ejpam-6202	16	2	3	3	NUM
ejpam-6202	16	3	]	]	PUNCT
ejpam-6202	16	4	later	later	ADV
ejpam-6202	16	5	introduced	introduce	VERB
ejpam-6202	16	6	an	an	DET
ejpam-6202	16	7	algebraic	algebraic	ADJ
ejpam-6202	16	8	approach	approach	NOUN
ejpam-6202	16	9	by	by	ADP
ejpam-6202	16	10	defining	define	VERB
ejpam-6202	16	11	r	r	NOUN
ejpam-6202	16	12	-	-	PUNCT
ejpam-6202	16	13	stirling	stirling	NOUN
ejpam-6202	16	14	numbers	number	NOUN
ejpam-6202	16	15	using	use	VERB
ejpam-6202	16	16	exponential	exponential	ADJ
ejpam-6202	16	17	generating	generating	NOUN
ejpam-6202	16	18	functions	function	NOUN
ejpam-6202	16	19	:	:	PUNCT
ejpam-6202	16	20	∞∑	∞∑	NUM
ejpam-6202	16	21	n=0	n=0	NUM
ejpam-6202	17	1	̂[n+	̂[n+	ADP
ejpam-6202	17	2	r	r	NOUN
ejpam-6202	17	3	k	k	NOUN
ejpam-6202	18	1	+	+	CCONJ
ejpam-6202	18	2	r	r	NOUN
ejpam-6202	18	3	]	]	PUNCT
ejpam-6202	18	4	r	r	NOUN
ejpam-6202	18	5	tn	tn	NOUN
ejpam-6202	18	6	n	n	CCONJ
ejpam-6202	18	7	!	!	PUNCT
ejpam-6202	19	1	=	=	PUNCT
ejpam-6202	19	2	(	(	PUNCT
ejpam-6202	19	3	1	1	NUM
ejpam-6202	19	4	1	1	NUM
ejpam-6202	19	5	+	+	NUM
ejpam-6202	19	6	t	t	NOUN
ejpam-6202	19	7	)	)	PUNCT
ejpam-6202	19	8	r	r	NOUN
ejpam-6202	19	9	lnk(1	lnk(1	NOUN
ejpam-6202	19	10	+	+	CCONJ
ejpam-6202	19	11	t	t	X
ejpam-6202	19	12	)	)	PUNCT
ejpam-6202	19	13	k	k	NOUN
ejpam-6202	19	14	!	!	PUNCT
ejpam-6202	20	1	∞∑	∞∑	ADJ
ejpam-6202	20	2	n=0	n=0	NUM
ejpam-6202	20	3	{	{	PUNCT
ejpam-6202	20	4	n+	n+	ADP
ejpam-6202	20	5	r	r	NOUN
ejpam-6202	20	6	k	k	NOUN
ejpam-6202	20	7	+	+	CCONJ
ejpam-6202	20	8	r	r	NOUN
ejpam-6202	20	9	}	}	PUNCT
ejpam-6202	20	10	r	r	NOUN
ejpam-6202	20	11	tn	tn	NOUN
ejpam-6202	20	12	n	n	ADV
ejpam-6202	20	13	!	!	PUNCT
ejpam-6202	21	1	=	=	NOUN
ejpam-6202	21	2	ert(et	ert(et	X
ejpam-6202	21	3	−	−	PROPN
ejpam-6202	21	4	1)k	1)k	NUM
ejpam-6202	21	5	k	k	NOUN
ejpam-6202	21	6	!	!	PUNCT
ejpam-6202	22	1	a	a	DET
ejpam-6202	22	2	natural	natural	ADJ
ejpam-6202	22	3	extension	extension	NOUN
ejpam-6202	22	4	of	of	ADP
ejpam-6202	22	5	these	these	DET
ejpam-6202	22	6	ideas	idea	NOUN
ejpam-6202	22	7	leads	lead	VERB
ejpam-6202	22	8	to	to	ADP
ejpam-6202	22	9	genocchi	genocchi	PROPN
ejpam-6202	22	10	numbers	number	NOUN
ejpam-6202	22	11	,	,	PUNCT
ejpam-6202	22	12	first	first	ADV
ejpam-6202	22	13	studied	study	VERB
ejpam-6202	22	14	by	by	ADP
ejpam-6202	22	15	angelo	angelo	PROPN
ejpam-6202	22	16	genocchi	genocchi	PROPN
ejpam-6202	22	17	.	.	PUNCT
ejpam-6202	23	1	the	the	DET
ejpam-6202	23	2	genocchi	genocchi	PROPN
ejpam-6202	23	3	numbers	number	NOUN
ejpam-6202	23	4	gn	gn	INTJ
ejpam-6202	23	5	satisfy	satisfy	VERB
ejpam-6202	23	6	the	the	DET
ejpam-6202	23	7	generating	generate	VERB
ejpam-6202	23	8	function	function	NOUN
ejpam-6202	23	9	given	give	VERB
ejpam-6202	23	10	as	as	SCONJ
ejpam-6202	23	11	follows	follow	VERB
ejpam-6202	23	12	∞∑	∞∑	PROPN
ejpam-6202	23	13	n=0	n=0	NUM
ejpam-6202	23	14	gn	gn	PROPN
ejpam-6202	23	15	tn	tn	PROPN
ejpam-6202	23	16	n	n	PROPN
ejpam-6202	23	17	!	!	PUNCT
ejpam-6202	24	1	=	=	PUNCT
ejpam-6202	25	1	2	2	NUM
ejpam-6202	25	2	t	t	NOUN
ejpam-6202	25	3	et	et	NOUN
ejpam-6202	25	4	+	+	CCONJ
ejpam-6202	25	5	1	1	NUM
ejpam-6202	25	6	moreover	moreover	ADV
ejpam-6202	25	7	,	,	PUNCT
ejpam-6202	25	8	the	the	DET
ejpam-6202	25	9	genocchi	genocchi	PROPN
ejpam-6202	25	10	polynomials	polynomial	VERB
ejpam-6202	25	11	and	and	CCONJ
ejpam-6202	25	12	genocchi	genocchi	PROPN
ejpam-6202	25	13	polynomials	polynomial	NOUN
ejpam-6202	25	14	of	of	ADP
ejpam-6202	25	15	higher	high	ADJ
ejpam-6202	25	16	order	order	NOUN
ejpam-6202	25	17	,	,	PUNCT
ejpam-6202	25	18	which	which	PRON
ejpam-6202	25	19	are	be	AUX
ejpam-6202	25	20	respectively	respectively	ADV
ejpam-6202	25	21	defined	define	VERB
ejpam-6202	25	22	by	by	ADP
ejpam-6202	25	23	∞∑	∞∑	NUM
ejpam-6202	25	24	n=0	n=0	NUM
ejpam-6202	25	25	gn(x	gn(x	NOUN
ejpam-6202	25	26	)	)	PUNCT
ejpam-6202	25	27	tn	tn	NOUN
ejpam-6202	25	28	n	n	NOUN
ejpam-6202	25	29	!	!	PUNCT
ejpam-6202	26	1	=	=	PUNCT
ejpam-6202	27	1	2	2	NUM
ejpam-6202	27	2	t	t	NOUN
ejpam-6202	27	3	et	et	NOUN
ejpam-6202	27	4	+	+	CCONJ
ejpam-6202	27	5	1	1	NUM
ejpam-6202	27	6	ext	ext	NOUN
ejpam-6202	27	7	,	,	PUNCT
ejpam-6202	27	8	|t|	|t|	VERB
ejpam-6202	27	9	<	<	X
ejpam-6202	27	10	π	π	PROPN
ejpam-6202	27	11	,	,	PUNCT
ejpam-6202	27	12	(	(	PUNCT
ejpam-6202	27	13	1.1	1.1	NUM
ejpam-6202	27	14	)	)	PUNCT
ejpam-6202	27	15	∞∑	∞∑	PRON
ejpam-6202	27	16	n=0	n=0	PUNCT
ejpam-6202	27	17	g(k	g(k	NOUN
ejpam-6202	27	18	)	)	PUNCT
ejpam-6202	27	19	n	n	CCONJ
ejpam-6202	27	20	(	(	PUNCT
ejpam-6202	27	21	x	x	X
ejpam-6202	27	22	)	)	PUNCT
ejpam-6202	27	23	tn	tn	PROPN
ejpam-6202	27	24	n	n	NOUN
ejpam-6202	27	25	!	!	PUNCT
ejpam-6202	28	1	=	=	PUNCT
ejpam-6202	28	2	(	(	PUNCT
ejpam-6202	28	3	2	2	NUM
ejpam-6202	28	4	t	t	NOUN
ejpam-6202	28	5	et	et	NOUN
ejpam-6202	28	6	+	+	CCONJ
ejpam-6202	28	7	1	1	X
ejpam-6202	28	8	)	)	PUNCT
ejpam-6202	28	9	k	k	PROPN
ejpam-6202	28	10	ext	ext	PROPN
ejpam-6202	28	11	,	,	PUNCT
ejpam-6202	28	12	(	(	PUNCT
ejpam-6202	28	13	1.2	1.2	NUM
ejpam-6202	28	14	)	)	PUNCT
ejpam-6202	28	15	(	(	PUNCT
ejpam-6202	28	16	see	see	VERB
ejpam-6202	28	17	[	[	X
ejpam-6202	28	18	4–6	4–6	X
ejpam-6202	28	19	]	]	X
ejpam-6202	28	20	)	)	PUNCT
ejpam-6202	28	21	.	.	PUNCT
ejpam-6202	29	1	it	it	PRON
ejpam-6202	29	2	is	be	AUX
ejpam-6202	29	3	important	important	ADJ
ejpam-6202	29	4	to	to	PART
ejpam-6202	29	5	note	note	VERB
ejpam-6202	29	6	that	that	SCONJ
ejpam-6202	29	7	the	the	DET
ejpam-6202	29	8	genocchi	genocchi	PROPN
ejpam-6202	29	9	polynomials	polynomial	VERB
ejpam-6202	29	10	satisfy	satisfy	VERB
ejpam-6202	29	11	the	the	DET
ejpam-6202	29	12	following	follow	VERB
ejpam-6202	29	13	relation	relation	NOUN
ejpam-6202	29	14	gn(x	gn(x	PUNCT
ejpam-6202	29	15	)	)	PUNCT
ejpam-6202	30	1	=	=	SYM
ejpam-6202	30	2	n∑	n∑	PROPN
ejpam-6202	30	3	m=0	m=0	PROPN
ejpam-6202	30	4	(	(	PUNCT
ejpam-6202	30	5	n	n	NOUN
ejpam-6202	30	6	m	m	PROPN
ejpam-6202	30	7	)	)	PUNCT
ejpam-6202	30	8	gn−mxm	gn−mxm	NOUN
ejpam-6202	30	9	(	(	PUNCT
ejpam-6202	30	10	1.3	1.3	NUM
ejpam-6202	30	11	)	)	PUNCT
ejpam-6202	30	12	expressing	express	VERB
ejpam-6202	30	13	gn(x	gn(x	PUNCT
ejpam-6202	30	14	)	)	PUNCT
ejpam-6202	30	15	as	as	ADV
ejpam-6202	30	16	polynomial	polynomial	ADJ
ejpam-6202	30	17	in	in	ADP
ejpam-6202	30	18	x.	x.	PROPN
ejpam-6202	30	19	in	in	ADP
ejpam-6202	30	20	relation	relation	NOUN
ejpam-6202	30	21	to	to	ADP
ejpam-6202	30	22	this	this	PRON
ejpam-6202	30	23	,	,	PUNCT
ejpam-6202	30	24	we	we	PRON
ejpam-6202	30	25	define	define	VERB
ejpam-6202	30	26	genocchi	genocchi	PROPN
ejpam-6202	30	27	factorial	factorial	NOUN
ejpam-6202	30	28	polynomials	polynomial	NOUN
ejpam-6202	30	29	,	,	PUNCT
ejpam-6202	30	30	denoted	denote	VERB
ejpam-6202	30	31	by	by	ADP
ejpam-6202	30	32	gn(x	gn(x	NOUN
ejpam-6202	30	33	)	)	PUNCT
ejpam-6202	30	34	,	,	PUNCT
ejpam-6202	30	35	as	as	SCONJ
ejpam-6202	30	36	follows	follow	VERB
ejpam-6202	30	37	gn(x	gn(x	PUNCT
ejpam-6202	30	38	)	)	PUNCT
ejpam-6202	31	1	=	=	SYM
ejpam-6202	31	2	n∑	n∑	PROPN
ejpam-6202	31	3	m=0	m=0	PROPN
ejpam-6202	31	4	(	(	PUNCT
ejpam-6202	31	5	n	n	NOUN
ejpam-6202	31	6	m	m	PROPN
ejpam-6202	31	7	)	)	PUNCT
ejpam-6202	31	8	gn−m(x)m	gn−m(x)m	PROPN
ejpam-6202	31	9	.	.	PUNCT
ejpam-6202	32	1	(	(	PUNCT
ejpam-6202	32	2	1.4	1.4	NUM
ejpam-6202	32	3	)	)	PUNCT
ejpam-6202	32	4	3	3	NUM
ejpam-6202	32	5	of	of	ADP
ejpam-6202	32	6	26	26	NUM
ejpam-6202	32	7	different	different	ADJ
ejpam-6202	32	8	variations	variation	NOUN
ejpam-6202	32	9	of	of	ADP
ejpam-6202	32	10	genocchi	genocchi	PROPN
ejpam-6202	32	11	numbers	number	NOUN
ejpam-6202	32	12	and	and	CCONJ
ejpam-6202	32	13	polynomials	polynomial	NOUN
ejpam-6202	32	14	and	and	CCONJ
ejpam-6202	32	15	their	their	PRON
ejpam-6202	32	16	properties	property	NOUN
ejpam-6202	32	17	are	be	AUX
ejpam-6202	32	18	discussed	discuss	VERB
ejpam-6202	32	19	in	in	ADP
ejpam-6202	32	20	[	[	X
ejpam-6202	32	21	7–9	7–9	X
ejpam-6202	32	22	]	]	X
ejpam-6202	32	23	in	in	ADP
ejpam-6202	32	24	this	this	DET
ejpam-6202	32	25	paper	paper	NOUN
ejpam-6202	32	26	,	,	PUNCT
ejpam-6202	32	27	it	it	PRON
ejpam-6202	32	28	presents	present	VERB
ejpam-6202	32	29	a	a	DET
ejpam-6202	32	30	new	new	ADJ
ejpam-6202	32	31	class	class	NOUN
ejpam-6202	32	32	of	of	ADP
ejpam-6202	32	33	numbers	number	NOUN
ejpam-6202	32	34	called	call	VERB
ejpam-6202	32	35	r	r	NOUN
ejpam-6202	32	36	-	-	PUNCT
ejpam-6202	32	37	stirling	stirling	NOUN
ejpam-6202	32	38	genocchi	genocchi	PROPN
ejpam-6202	32	39	numbers	number	NOUN
ejpam-6202	32	40	,	,	PUNCT
ejpam-6202	32	41	created	create	VERB
ejpam-6202	32	42	by	by	ADP
ejpam-6202	32	43	merging	merge	VERB
ejpam-6202	32	44	the	the	DET
ejpam-6202	32	45	r	r	NOUN
ejpam-6202	32	46	-	-	PUNCT
ejpam-6202	32	47	stirling	stirling	NOUN
ejpam-6202	32	48	numbers	number	NOUN
ejpam-6202	32	49	with	with	ADP
ejpam-6202	32	50	genocchi	genocchi	PROPN
ejpam-6202	32	51	numbers	number	NOUN
ejpam-6202	32	52	and	and	CCONJ
ejpam-6202	32	53	explore	explore	VERB
ejpam-6202	32	54	its	its	PRON
ejpam-6202	32	55	behavior	behavior	NOUN
ejpam-6202	32	56	by	by	ADP
ejpam-6202	32	57	generating	generate	VERB
ejpam-6202	32	58	results.the	results.the	DET
ejpam-6202	32	59	r	r	NOUN
ejpam-6202	32	60	-	-	PUNCT
ejpam-6202	32	61	stirling	stirling	NOUN
ejpam-6202	32	62	genocchi	genocchi	PROPN
ejpam-6202	32	63	numbers	number	NOUN
ejpam-6202	32	64	defined	define	VERB
ejpam-6202	32	65	by	by	ADP
ejpam-6202	32	66	means	mean	NOUN
ejpam-6202	32	67	of	of	ADP
ejpam-6202	32	68	exponential	exponential	ADJ
ejpam-6202	32	69	generating	generating	NOUN
ejpam-6202	32	70	function	function	NOUN
ejpam-6202	32	71	are	be	AUX
ejpam-6202	32	72	as	as	SCONJ
ejpam-6202	32	73	follows	follow	VERB
ejpam-6202	32	74	:	:	PUNCT
ejpam-6202	32	75	∞∑	∞∑	NUM
ejpam-6202	32	76	n=0	n=0	NUM
ejpam-6202	32	77	sg1	sg1	NOUN
ejpam-6202	32	78	n(k	n(k	PROPN
ejpam-6202	32	79	;	;	PUNCT
ejpam-6202	32	80	r	r	X
ejpam-6202	32	81	)	)	PUNCT
ejpam-6202	32	82	tn	tn	NOUN
ejpam-6202	32	83	n	n	NOUN
ejpam-6202	32	84	!	!	PUNCT
ejpam-6202	33	1	=	=	PUNCT
ejpam-6202	33	2	(	(	PUNCT
ejpam-6202	33	3	1	1	NUM
ejpam-6202	33	4	1	1	NUM
ejpam-6202	33	5	+	+	NUM
ejpam-6202	33	6	t	t	NOUN
ejpam-6202	33	7	)	)	PUNCT
ejpam-6202	33	8	r	r	NOUN
ejpam-6202	33	9	2	2	NUM
ejpam-6202	33	10	t	t	NOUN
ejpam-6202	33	11	lnk(1	lnk(1	NOUN
ejpam-6202	33	12	+	+	CCONJ
ejpam-6202	33	13	t	t	NOUN
ejpam-6202	33	14	)	)	PUNCT
ejpam-6202	33	15	k!(et	k!(et	NOUN
ejpam-6202	33	16	+	+	NOUN
ejpam-6202	33	17	1	1	NUM
ejpam-6202	33	18	)	)	PUNCT
ejpam-6202	33	19	(	(	PUNCT
ejpam-6202	33	20	1	1	X
ejpam-6202	33	21	)	)	PUNCT
ejpam-6202	33	22	∞∑	∞∑	PROPN
ejpam-6202	33	23	n=0	n=0	PUNCT
ejpam-6202	33	24	sg2	sg2	PROPN
ejpam-6202	33	25	n(k	n(k	PROPN
ejpam-6202	33	26	;	;	PUNCT
ejpam-6202	33	27	r	r	X
ejpam-6202	33	28	)	)	PUNCT
ejpam-6202	33	29	tn	tn	NOUN
ejpam-6202	33	30	n	n	NOUN
ejpam-6202	33	31	!	!	PUNCT
ejpam-6202	34	1	=	=	NOUN
ejpam-6202	35	1	2tert(et	2tert(et	NUM
ejpam-6202	35	2	−	−	PRON
ejpam-6202	35	3	1)k	1)k	NUM
ejpam-6202	35	4	k!(et	k!(et	NOUN
ejpam-6202	35	5	+	+	CCONJ
ejpam-6202	35	6	1	1	NUM
ejpam-6202	35	7	)	)	PUNCT
ejpam-6202	35	8	(	(	PUNCT
ejpam-6202	35	9	2	2	X
ejpam-6202	35	10	)	)	PUNCT
ejpam-6202	35	11	where	where	SCONJ
ejpam-6202	35	12	sg1	sg1	NOUN
ejpam-6202	35	13	n(k	n(k	PROPN
ejpam-6202	35	14	;	;	PUNCT
ejpam-6202	35	15	r	r	X
ejpam-6202	35	16	)	)	PUNCT
ejpam-6202	35	17	referred	refer	VERB
ejpam-6202	35	18	to	to	ADP
ejpam-6202	35	19	as	as	ADP
ejpam-6202	35	20	the	the	DET
ejpam-6202	35	21	r	r	NOUN
ejpam-6202	35	22	-	-	PUNCT
ejpam-6202	35	23	stirling	stirling	NOUN
ejpam-6202	35	24	genocchi	genocchi	PROPN
ejpam-6202	35	25	number	number	NOUN
ejpam-6202	35	26	of	of	ADP
ejpam-6202	35	27	the	the	DET
ejpam-6202	35	28	first	first	ADJ
ejpam-6202	35	29	kind	kind	NOUN
ejpam-6202	35	30	and	and	CCONJ
ejpam-6202	35	31	sg2	sg2	PROPN
ejpam-6202	35	32	n(k	n(k	PROPN
ejpam-6202	35	33	;	;	PUNCT
ejpam-6202	35	34	r	r	X
ejpam-6202	35	35	)	)	PUNCT
ejpam-6202	35	36	is	be	AUX
ejpam-6202	35	37	the	the	DET
ejpam-6202	35	38	r	r	NOUN
ejpam-6202	35	39	-	-	PUNCT
ejpam-6202	35	40	stirling	stirling	NOUN
ejpam-6202	35	41	genocchi	genocchi	PROPN
ejpam-6202	35	42	number	number	NOUN
ejpam-6202	35	43	of	of	ADP
ejpam-6202	35	44	the	the	DET
ejpam-6202	35	45	second	second	ADJ
ejpam-6202	35	46	kind	kind	NOUN
ejpam-6202	35	47	.	.	PUNCT
ejpam-6202	36	1	theorem	theorem	VERB
ejpam-6202	36	2	1.1	1.1	NUM
ejpam-6202	36	3	.	.	PUNCT
ejpam-6202	37	1	convolution	convolution	NOUN
ejpam-6202	37	2	formula	formula	NOUN
ejpam-6202	37	3	of	of	ADP
ejpam-6202	37	4	the	the	DET
ejpam-6202	37	5	r	r	NOUN
ejpam-6202	37	6	-	-	PUNCT
ejpam-6202	37	7	stirling	stirling	NOUN
ejpam-6202	37	8	numbers	number	NOUN
ejpam-6202	37	9	and	and	CCONJ
ejpam-6202	37	10	genocchi	genocchi	PROPN
ejpam-6202	37	11	numbers	number	NOUN
ejpam-6202	37	12	are	be	AUX
ejpam-6202	37	13	given	give	VERB
ejpam-6202	37	14	as	as	SCONJ
ejpam-6202	37	15	follows	follow	VERB
ejpam-6202	37	16	:	:	PUNCT
ejpam-6202	38	1	sg1	sg1	PROPN
ejpam-6202	38	2	n(k	n(k	PROPN
ejpam-6202	38	3	;	;	PUNCT
ejpam-6202	38	4	r	r	X
ejpam-6202	38	5	)	)	PUNCT
ejpam-6202	38	6	=	=	SYM
ejpam-6202	38	7	n∑	n∑	PROPN
ejpam-6202	38	8	j	j	PROPN
ejpam-6202	39	1	=	=	PROPN
ejpam-6202	39	2	k	k	PROPN
ejpam-6202	39	3	̂[j	̂[j	PROPN
ejpam-6202	40	1	+	+	CCONJ
ejpam-6202	41	1	r	r	X
ejpam-6202	41	2	k	k	NOUN
ejpam-6202	42	1	+	+	CCONJ
ejpam-6202	42	2	r	r	NOUN
ejpam-6202	42	3	]	]	X
ejpam-6202	42	4	r	r	NOUN
ejpam-6202	42	5	(	(	PUNCT
ejpam-6202	42	6	n	n	CCONJ
ejpam-6202	42	7	j	j	PROPN
ejpam-6202	42	8	)	)	PUNCT
ejpam-6202	42	9	gn−j	gn−j	PROPN
ejpam-6202	42	10	(	(	PUNCT
ejpam-6202	42	11	3	3	X
ejpam-6202	42	12	)	)	PUNCT
ejpam-6202	42	13	sg2	sg2	PROPN
ejpam-6202	42	14	n(k	n(k	PROPN
ejpam-6202	42	15	;	;	PUNCT
ejpam-6202	42	16	r	r	X
ejpam-6202	42	17	)	)	PUNCT
ejpam-6202	42	18	=	=	SYM
ejpam-6202	42	19	n∑	n∑	PROPN
ejpam-6202	42	20	j	j	PROPN
ejpam-6202	43	1	=	=	PROPN
ejpam-6202	43	2	k	k	PROPN
ejpam-6202	43	3	{	{	PUNCT
ejpam-6202	43	4	j	j	PROPN
ejpam-6202	43	5	+	+	CCONJ
ejpam-6202	43	6	r	r	NOUN
ejpam-6202	43	7	k	k	NOUN
ejpam-6202	43	8	+	+	CCONJ
ejpam-6202	43	9	r	r	NOUN
ejpam-6202	43	10	}	}	PUNCT
ejpam-6202	43	11	r	r	NOUN
ejpam-6202	43	12	(	(	PUNCT
ejpam-6202	43	13	n	n	CCONJ
ejpam-6202	43	14	j	j	PROPN
ejpam-6202	43	15	)	)	PUNCT
ejpam-6202	43	16	gn−j	gn−j	PROPN
ejpam-6202	43	17	(	(	PUNCT
ejpam-6202	43	18	4	4	NUM
ejpam-6202	43	19	)	)	PUNCT
ejpam-6202	43	20	where	where	SCONJ
ejpam-6202	43	21	n	n	PRON
ejpam-6202	43	22	≥	≥	NOUN
ejpam-6202	44	1	k	k	NOUN
ejpam-6202	44	2	otherwise	otherwise	ADV
ejpam-6202	44	3	sg1	sg1	VERB
ejpam-6202	44	4	n(k	n(k	PROPN
ejpam-6202	44	5	;	;	PUNCT
ejpam-6202	44	6	r	r	X
ejpam-6202	44	7	)	)	PUNCT
ejpam-6202	44	8	=	=	PUNCT
ejpam-6202	45	1	sg2	sg2	PROPN
ejpam-6202	45	2	n(k	n(k	PROPN
ejpam-6202	45	3	;	;	PUNCT
ejpam-6202	45	4	r	r	X
ejpam-6202	45	5	)	)	PUNCT
ejpam-6202	45	6	=	=	SYM
ejpam-6202	45	7	0	0	NUM
ejpam-6202	45	8	proof	proof	NOUN
ejpam-6202	45	9	.	.	PUNCT
ejpam-6202	46	1	the	the	DET
ejpam-6202	46	2	exponential	exponential	ADJ
ejpam-6202	46	3	generating	generating	NOUN
ejpam-6202	46	4	function	function	NOUN
ejpam-6202	46	5	in	in	ADP
ejpam-6202	46	6	(	(	PUNCT
ejpam-6202	46	7	1	1	X
ejpam-6202	46	8	)	)	PUNCT
ejpam-6202	46	9	can	can	AUX
ejpam-6202	46	10	be	be	AUX
ejpam-6202	46	11	written	write	VERB
ejpam-6202	46	12	as	as	ADP
ejpam-6202	46	13	∞∑	∞∑	NUM
ejpam-6202	46	14	n=0	n=0	NUM
ejpam-6202	46	15	sg1	sg1	NOUN
ejpam-6202	46	16	n(k	n(k	PROPN
ejpam-6202	46	17	;	;	PUNCT
ejpam-6202	46	18	r	r	X
ejpam-6202	46	19	)	)	PUNCT
ejpam-6202	46	20	tn	tn	NOUN
ejpam-6202	46	21	n	n	NOUN
ejpam-6202	46	22	!	!	PUNCT
ejpam-6202	47	1	=	=	PUNCT
ejpam-6202	47	2	(	(	PUNCT
ejpam-6202	47	3	1	1	NUM
ejpam-6202	47	4	1	1	NUM
ejpam-6202	47	5	+	+	NUM
ejpam-6202	47	6	t	t	NOUN
ejpam-6202	47	7	)	)	PUNCT
ejpam-6202	47	8	r	r	NOUN
ejpam-6202	47	9	2	2	NUM
ejpam-6202	47	10	t	t	NOUN
ejpam-6202	47	11	lnk(1	lnk(1	NOUN
ejpam-6202	47	12	+	+	CCONJ
ejpam-6202	47	13	t	t	NOUN
ejpam-6202	47	14	)	)	PUNCT
ejpam-6202	47	15	k!(et	k!(et	NOUN
ejpam-6202	47	16	+	+	NOUN
ejpam-6202	47	17	1	1	X
ejpam-6202	47	18	)	)	PUNCT
ejpam-6202	47	19	=	=	NOUN
ejpam-6202	47	20	(	(	PUNCT
ejpam-6202	47	21	1	1	NUM
ejpam-6202	47	22	1	1	NUM
ejpam-6202	47	23	+	+	NUM
ejpam-6202	47	24	t	t	NOUN
ejpam-6202	47	25	)	)	PUNCT
ejpam-6202	47	26	r	r	NOUN
ejpam-6202	47	27	lnk(1	lnk(1	NOUN
ejpam-6202	47	28	+	+	CCONJ
ejpam-6202	47	29	t	t	X
ejpam-6202	47	30	)	)	PUNCT
ejpam-6202	47	31	k	k	NOUN
ejpam-6202	47	32	!	!	PROPN
ejpam-6202	47	33	2	2	NUM
ejpam-6202	47	34	t	t	NOUN
ejpam-6202	47	35	(	(	PUNCT
ejpam-6202	47	36	et	et	NOUN
ejpam-6202	47	37	+	+	NOUN
ejpam-6202	47	38	1	1	X
ejpam-6202	47	39	)	)	PUNCT
ejpam-6202	47	40	=	=	NOUN
ejpam-6202	47	41	(	(	PUNCT
ejpam-6202	47	42	∞∑	∞∑	NUM
ejpam-6202	47	43	n=0	n=0	NUM
ejpam-6202	47	44	̂[n+	̂[n+	ADP
ejpam-6202	47	45	r	r	NOUN
ejpam-6202	47	46	k	k	NOUN
ejpam-6202	48	1	+	+	CCONJ
ejpam-6202	48	2	r	r	NOUN
ejpam-6202	48	3	]	]	PUNCT
ejpam-6202	48	4	r	r	NOUN
ejpam-6202	48	5	tn	tn	PROPN
ejpam-6202	48	6	n	n	CCONJ
ejpam-6202	48	7	!	!	PUNCT
ejpam-6202	48	8	)	)	PUNCT
ejpam-6202	49	1	(	(	PUNCT
ejpam-6202	49	2	∞∑	∞∑	PROPN
ejpam-6202	49	3	n=0	n=0	NUM
ejpam-6202	49	4	gn	gn	PROPN
ejpam-6202	49	5	tn	tn	PROPN
ejpam-6202	49	6	n	n	PROPN
ejpam-6202	49	7	!	!	PUNCT
ejpam-6202	49	8	)	)	PUNCT
ejpam-6202	50	1	=	=	PUNCT
ejpam-6202	51	1	∞∑	∞∑	NUM
ejpam-6202	51	2	n=0	n=0	NUM
ejpam-6202	51	3	n∑	n∑	ADV
ejpam-6202	51	4	j=0	j=0	PROPN
ejpam-6202	51	5	̂[j	̂[j	NOUN
ejpam-6202	51	6	+	+	CCONJ
ejpam-6202	51	7	r	r	X
ejpam-6202	51	8	k	k	NOUN
ejpam-6202	52	1	+	+	CCONJ
ejpam-6202	52	2	r	r	NOUN
ejpam-6202	52	3	]	]	PUNCT
ejpam-6202	52	4	r	r	NOUN
ejpam-6202	52	5	tj	tj	PROPN
ejpam-6202	52	6	j	j	PROPN
ejpam-6202	52	7	!	!	PUNCT
ejpam-6202	52	8	gn−j	gn−j	PROPN
ejpam-6202	52	9	tn−j	tn−j	NOUN
ejpam-6202	52	10	(	(	PUNCT
ejpam-6202	52	11	n−	n−	NOUN
ejpam-6202	52	12	j	j	NOUN
ejpam-6202	52	13	)	)	PUNCT
ejpam-6202	52	14	!	!	PUNCT
ejpam-6202	53	1	=	=	PUNCT
ejpam-6202	54	1	∞∑	∞∑	PRON
ejpam-6202	54	2	n=0	n=0	NUM
ejpam-6202	54	3			PUNCT
ejpam-6202	54	4	n∑	n∑	NOUN
ejpam-6202	54	5	j=0	j=0	PROPN
ejpam-6202	54	6	̂[j	̂[j	NOUN
ejpam-6202	54	7	+	+	CCONJ
ejpam-6202	54	8	r	r	X
ejpam-6202	54	9	k	k	NOUN
ejpam-6202	55	1	+	+	CCONJ
ejpam-6202	55	2	r	r	NOUN
ejpam-6202	55	3	]	]	PUNCT
ejpam-6202	55	4	r	r	NOUN
ejpam-6202	55	5	n	n	NOUN
ejpam-6202	55	6	!	!	PUNCT
ejpam-6202	56	1	(	(	PUNCT
ejpam-6202	56	2	n−	n−	NOUN
ejpam-6202	56	3	j)!j	j)!j	PROPN
ejpam-6202	56	4	!	!	PUNCT
ejpam-6202	57	1	gn−j	gn−j	PROPN
ejpam-6202	57	2			PROPN
ejpam-6202	57	3	tn	tn	PROPN
ejpam-6202	57	4	n	n	CCONJ
ejpam-6202	57	5	!	!	PROPN
ejpam-6202	57	6	4	4	NUM
ejpam-6202	57	7	of	of	ADP
ejpam-6202	57	8	26	26	NUM
ejpam-6202	57	9	=	=	NOUN
ejpam-6202	57	10	∞∑	∞∑	NUM
ejpam-6202	57	11	n=0	n=0	NUM
ejpam-6202	57	12			PUNCT
ejpam-6202	57	13	n∑	n∑	NOUN
ejpam-6202	57	14	j=0	j=0	PROPN
ejpam-6202	57	15	̂[j	̂[j	NOUN
ejpam-6202	58	1	+	+	CCONJ
ejpam-6202	59	1	r	r	X
ejpam-6202	59	2	k	k	NOUN
ejpam-6202	60	1	+	+	CCONJ
ejpam-6202	60	2	r	r	NOUN
ejpam-6202	60	3	]	]	X
ejpam-6202	60	4	r	r	NOUN
ejpam-6202	60	5	(	(	PUNCT
ejpam-6202	60	6	n	n	CCONJ
ejpam-6202	60	7	j	j	PROPN
ejpam-6202	60	8	)	)	PUNCT
ejpam-6202	60	9	gn−j	gn−j	NOUN
ejpam-6202	60	10			PROPN
ejpam-6202	60	11	tn	tn	PROPN
ejpam-6202	60	12	n	n	CCONJ
ejpam-6202	60	13	!	!	PUNCT
ejpam-6202	60	14	comparing	compare	VERB
ejpam-6202	60	15	the	the	DET
ejpam-6202	60	16	coefficients	coefficient	NOUN
ejpam-6202	60	17	of	of	ADP
ejpam-6202	60	18	tn	tn	NOUN
ejpam-6202	60	19	n	n	X
ejpam-6202	60	20	!	!	PUNCT
ejpam-6202	60	21	yields	yield	VERB
ejpam-6202	60	22	the	the	DET
ejpam-6202	60	23	desired	desire	VERB
ejpam-6202	60	24	convolution	convolution	NOUN
ejpam-6202	60	25	formula	formula	NOUN
ejpam-6202	60	26	in	in	ADP
ejpam-6202	60	27	(	(	PUNCT
ejpam-6202	60	28	3	3	NUM
ejpam-6202	60	29	)	)	PUNCT
ejpam-6202	60	30	.	.	PUNCT
ejpam-6202	61	1	on	on	ADP
ejpam-6202	61	2	the	the	DET
ejpam-6202	61	3	other	other	ADJ
ejpam-6202	61	4	hand	hand	NOUN
ejpam-6202	61	5	,	,	PUNCT
ejpam-6202	61	6	the	the	DET
ejpam-6202	61	7	exponential	exponential	ADJ
ejpam-6202	61	8	generating	generating	NOUN
ejpam-6202	61	9	function	function	NOUN
ejpam-6202	61	10	in	in	ADP
ejpam-6202	61	11	(	(	PUNCT
ejpam-6202	61	12	2	2	X
ejpam-6202	61	13	)	)	PUNCT
ejpam-6202	61	14	can	can	AUX
ejpam-6202	61	15	be	be	AUX
ejpam-6202	61	16	written	write	VERB
ejpam-6202	61	17	as	as	ADP
ejpam-6202	61	18	∞∑	∞∑	NUM
ejpam-6202	61	19	n=0	n=0	NUM
ejpam-6202	61	20	sg2	sg2	PROPN
ejpam-6202	61	21	n(k	n(k	PROPN
ejpam-6202	61	22	;	;	PUNCT
ejpam-6202	61	23	r	r	X
ejpam-6202	61	24	)	)	PUNCT
ejpam-6202	61	25	tn	tn	NOUN
ejpam-6202	61	26	n	n	NOUN
ejpam-6202	61	27	!	!	PUNCT
ejpam-6202	62	1	=	=	NOUN
ejpam-6202	63	1	2tert(et	2tert(et	NUM
ejpam-6202	63	2	−	−	PRON
ejpam-6202	63	3	1)k	1)k	NUM
ejpam-6202	63	4	k!(et	k!(et	NOUN
ejpam-6202	63	5	+	+	CCONJ
ejpam-6202	63	6	1	1	X
ejpam-6202	63	7	)	)	PUNCT
ejpam-6202	63	8	=	=	NOUN
ejpam-6202	63	9	ert(et	ert(et	X
ejpam-6202	63	10	−	−	PROPN
ejpam-6202	63	11	1)k	1)k	NUM
ejpam-6202	63	12	k	k	NOUN
ejpam-6202	63	13	!	!	PROPN
ejpam-6202	64	1	2	2	NUM
ejpam-6202	64	2	t	t	NOUN
ejpam-6202	64	3	(	(	PUNCT
ejpam-6202	64	4	et	et	NOUN
ejpam-6202	64	5	+	+	NOUN
ejpam-6202	64	6	1	1	X
ejpam-6202	64	7	)	)	PUNCT
ejpam-6202	64	8	=	=	NOUN
ejpam-6202	64	9	(	(	PUNCT
ejpam-6202	64	10	∞∑	∞∑	NUM
ejpam-6202	64	11	n=0	n=0	NUM
ejpam-6202	64	12	{	{	PUNCT
ejpam-6202	64	13	n+	n+	ADP
ejpam-6202	64	14	r	r	NOUN
ejpam-6202	64	15	k	k	NOUN
ejpam-6202	64	16	+	+	CCONJ
ejpam-6202	64	17	r	r	NOUN
ejpam-6202	64	18	}	}	PUNCT
ejpam-6202	64	19	r	r	NOUN
ejpam-6202	64	20	tn	tn	NOUN
ejpam-6202	64	21	n	n	CCONJ
ejpam-6202	64	22	!	!	PUNCT
ejpam-6202	64	23	)	)	PUNCT
ejpam-6202	65	1	(	(	PUNCT
ejpam-6202	65	2	∞∑	∞∑	PROPN
ejpam-6202	65	3	n=0	n=0	NUM
ejpam-6202	65	4	gn	gn	PROPN
ejpam-6202	65	5	tn	tn	PROPN
ejpam-6202	65	6	n	n	PROPN
ejpam-6202	65	7	!	!	PUNCT
ejpam-6202	65	8	)	)	PUNCT
ejpam-6202	66	1	=	=	PUNCT
ejpam-6202	67	1	∞∑	∞∑	NUM
ejpam-6202	67	2	n=0	n=0	PROPN
ejpam-6202	67	3	n∑	n∑	PRON
ejpam-6202	67	4	j=0	j=0	PROPN
ejpam-6202	67	5	{	{	PUNCT
ejpam-6202	67	6	j	j	PROPN
ejpam-6202	68	1	+	+	CCONJ
ejpam-6202	68	2	r	r	NOUN
ejpam-6202	68	3	k	k	NOUN
ejpam-6202	69	1	+	+	CCONJ
ejpam-6202	69	2	r	r	NOUN
ejpam-6202	69	3	}	}	PUNCT
ejpam-6202	69	4	r	r	PROPN
ejpam-6202	69	5	tj	tj	PROPN
ejpam-6202	69	6	j	j	PROPN
ejpam-6202	69	7	!	!	PUNCT
ejpam-6202	69	8	gn−j	gn−j	PROPN
ejpam-6202	69	9	tn−j	tn−j	NOUN
ejpam-6202	69	10	(	(	PUNCT
ejpam-6202	69	11	n−	n−	NOUN
ejpam-6202	69	12	j	j	NOUN
ejpam-6202	69	13	)	)	PUNCT
ejpam-6202	69	14	!	!	PUNCT
ejpam-6202	70	1	=	=	PUNCT
ejpam-6202	71	1	∞∑	∞∑	PRON
ejpam-6202	71	2	n=0	n=0	NUM
ejpam-6202	71	3			PUNCT
ejpam-6202	71	4	n∑	n∑	NOUN
ejpam-6202	71	5	j=0	j=0	PROPN
ejpam-6202	71	6	{	{	PUNCT
ejpam-6202	71	7	j	j	PROPN
ejpam-6202	71	8	+	+	CCONJ
ejpam-6202	71	9	r	r	NOUN
ejpam-6202	71	10	k	k	NOUN
ejpam-6202	72	1	+	+	CCONJ
ejpam-6202	72	2	r	r	NOUN
ejpam-6202	72	3	}	}	PUNCT
ejpam-6202	72	4	r	r	NOUN
ejpam-6202	72	5	n	n	NOUN
ejpam-6202	72	6	!	!	PUNCT
ejpam-6202	73	1	(	(	PUNCT
ejpam-6202	73	2	n−	n−	NOUN
ejpam-6202	73	3	j)!j	j)!j	PROPN
ejpam-6202	73	4	!	!	PUNCT
ejpam-6202	74	1	gn−j	gn−j	PROPN
ejpam-6202	74	2			PROPN
ejpam-6202	74	3	tn	tn	NOUN
ejpam-6202	74	4	n	n	CCONJ
ejpam-6202	74	5	!	!	PUNCT
ejpam-6202	75	1	=	=	PUNCT
ejpam-6202	76	1	∞∑	∞∑	PRON
ejpam-6202	76	2	n=0	n=0	NUM
ejpam-6202	76	3			PUNCT
ejpam-6202	76	4	n∑	n∑	NOUN
ejpam-6202	76	5	j=0	j=0	PROPN
ejpam-6202	76	6	{	{	PUNCT
ejpam-6202	76	7	j	j	PROPN
ejpam-6202	77	1	+	+	CCONJ
ejpam-6202	77	2	r	r	NOUN
ejpam-6202	77	3	k	k	NOUN
ejpam-6202	78	1	+	+	CCONJ
ejpam-6202	78	2	r	r	NOUN
ejpam-6202	78	3	}	}	PUNCT
ejpam-6202	78	4	r	r	NOUN
ejpam-6202	78	5	(	(	PUNCT
ejpam-6202	78	6	n	n	CCONJ
ejpam-6202	78	7	j	j	PROPN
ejpam-6202	78	8	)	)	PUNCT
ejpam-6202	78	9	gn−j	gn−j	NOUN
ejpam-6202	78	10			PROPN
ejpam-6202	78	11	tn	tn	PROPN
ejpam-6202	78	12	n	n	CCONJ
ejpam-6202	78	13	!	!	PUNCT
ejpam-6202	79	1	comparing	compare	VERB
ejpam-6202	79	2	the	the	DET
ejpam-6202	79	3	coefficients	coefficient	NOUN
ejpam-6202	79	4	of	of	ADP
ejpam-6202	79	5	tn	tn	NOUN
ejpam-6202	79	6	n	n	X
ejpam-6202	79	7	!	!	PUNCT
ejpam-6202	80	1	yields	yield	VERB
ejpam-6202	80	2	the	the	DET
ejpam-6202	80	3	desired	desire	VERB
ejpam-6202	80	4	convolution	convolution	NOUN
ejpam-6202	80	5	formula	formula	NOUN
ejpam-6202	80	6	in	in	ADP
ejpam-6202	80	7	(	(	PUNCT
ejpam-6202	80	8	4	4	NUM
ejpam-6202	80	9	)	)	PUNCT
ejpam-6202	80	10	.	.	PUNCT
ejpam-6202	81	1	theorem	theorem	VERB
ejpam-6202	81	2	1.2	1.2	NUM
ejpam-6202	81	3	.	.	PUNCT
ejpam-6202	82	1	the	the	DET
ejpam-6202	82	2	horizontal	horizontal	ADJ
ejpam-6202	82	3	generating	generate	VERB
ejpam-6202	82	4	function	function	NOUN
ejpam-6202	82	5	for	for	ADP
ejpam-6202	82	6	both	both	DET
ejpam-6202	82	7	kinds	kind	NOUN
ejpam-6202	82	8	of	of	ADP
ejpam-6202	82	9	r	r	NOUN
ejpam-6202	82	10	-	-	PUNCT
ejpam-6202	82	11	stirling	stirling	NOUN
ejpam-6202	82	12	genocchi	genocchi	PROPN
ejpam-6202	82	13	numbers	number	NOUN
ejpam-6202	82	14	are	be	AUX
ejpam-6202	82	15	given	give	VERB
ejpam-6202	82	16	as	as	SCONJ
ejpam-6202	82	17	follows	follow	VERB
ejpam-6202	82	18	:	:	PUNCT
ejpam-6202	82	19	gn(z	gn(z	PUNCT
ejpam-6202	82	20	−	−	NOUN
ejpam-6202	82	21	r	r	NOUN
ejpam-6202	82	22	)	)	PUNCT
ejpam-6202	82	23	=	=	SYM
ejpam-6202	83	1	n∑	n∑	PROPN
ejpam-6202	83	2	k=0	k=0	PROPN
ejpam-6202	83	3	sg1	sg1	PROPN
ejpam-6202	83	4	n(k	n(k	PROPN
ejpam-6202	83	5	;	;	PUNCT
ejpam-6202	83	6	r)z	r)z	X
ejpam-6202	83	7	k	k	X
ejpam-6202	83	8	(	(	PUNCT
ejpam-6202	83	9	5	5	NUM
ejpam-6202	83	10	)	)	PUNCT
ejpam-6202	83	11	gn(z	gn(z	NOUN
ejpam-6202	83	12	+	+	CCONJ
ejpam-6202	83	13	r	r	X
ejpam-6202	83	14	)	)	PUNCT
ejpam-6202	83	15	=	=	SYM
ejpam-6202	83	16	n∑	n∑	PROPN
ejpam-6202	83	17	k=0	k=0	PROPN
ejpam-6202	83	18	sg2	sg2	PROPN
ejpam-6202	83	19	n(k	n(k	PROPN
ejpam-6202	83	20	;	;	PUNCT
ejpam-6202	83	21	r)z	r)z	X
ejpam-6202	83	22	k	k	X
ejpam-6202	83	23	(	(	PUNCT
ejpam-6202	83	24	6	6	NUM
ejpam-6202	83	25	)	)	PUNCT
ejpam-6202	83	26	proof	proof	NOUN
ejpam-6202	83	27	.	.	PUNCT
ejpam-6202	84	1	the	the	DET
ejpam-6202	84	2	exponential	exponential	ADJ
ejpam-6202	84	3	generating	generating	NOUN
ejpam-6202	84	4	function	function	NOUN
ejpam-6202	84	5	of	of	ADP
ejpam-6202	84	6	(	(	PUNCT
ejpam-6202	84	7	1	1	X
ejpam-6202	84	8	)	)	PUNCT
ejpam-6202	84	9	can	can	AUX
ejpam-6202	84	10	be	be	AUX
ejpam-6202	84	11	written	write	VERB
ejpam-6202	84	12	as	as	ADP
ejpam-6202	84	13	∞∑	∞∑	NUM
ejpam-6202	84	14	k=0	k=0	PROPN
ejpam-6202	84	15	{	{	PUNCT
ejpam-6202	84	16	∞∑	∞∑	PROPN
ejpam-6202	84	17	n	n	CCONJ
ejpam-6202	84	18	=	=	SYM
ejpam-6202	84	19	k	k	PROPN
ejpam-6202	84	20	sg1	sg1	PROPN
ejpam-6202	84	21	n(k	n(k	PROPN
ejpam-6202	84	22	;	;	PUNCT
ejpam-6202	84	23	r	r	X
ejpam-6202	84	24	)	)	PUNCT
ejpam-6202	84	25	tn	tn	NOUN
ejpam-6202	84	26	n	n	NOUN
ejpam-6202	84	27	!	!	PUNCT
ejpam-6202	84	28	}	}	PUNCT
ejpam-6202	85	1	zk	zk	PROPN
ejpam-6202	86	1	=	=	PUNCT
ejpam-6202	87	1	(	(	PUNCT
ejpam-6202	87	2	1	1	NUM
ejpam-6202	87	3	1	1	NUM
ejpam-6202	87	4	+	+	NUM
ejpam-6202	87	5	t	t	NOUN
ejpam-6202	87	6	)	)	PUNCT
ejpam-6202	87	7	r	r	NOUN
ejpam-6202	87	8	2	2	NUM
ejpam-6202	87	9	t	t	NOUN
ejpam-6202	87	10	(	(	PUNCT
ejpam-6202	87	11	et	et	NOUN
ejpam-6202	87	12	+	+	NOUN
ejpam-6202	87	13	1	1	NUM
ejpam-6202	87	14	)	)	PUNCT
ejpam-6202	87	15	∑	∑	PUNCT
ejpam-6202	87	16	k≥0	k≥0	VERB
ejpam-6202	87	17	lnk(1	lnk(1	NOUN
ejpam-6202	87	18	+	+	CCONJ
ejpam-6202	87	19	t	t	X
ejpam-6202	87	20	)	)	PUNCT
ejpam-6202	88	1	k	k	NOUN
ejpam-6202	88	2	!	!	PUNCT
ejpam-6202	88	3	zk	zk	X
ejpam-6202	89	1	=	=	PUNCT
ejpam-6202	89	2	(	(	PUNCT
ejpam-6202	89	3	1	1	NUM
ejpam-6202	89	4	1	1	NUM
ejpam-6202	89	5	+	+	NUM
ejpam-6202	89	6	t	t	NOUN
ejpam-6202	89	7	)	)	PUNCT
ejpam-6202	89	8	r	r	NOUN
ejpam-6202	89	9	2	2	NUM
ejpam-6202	89	10	t	t	NOUN
ejpam-6202	89	11	(	(	PUNCT
ejpam-6202	89	12	et	et	NOUN
ejpam-6202	89	13	+	+	NOUN
ejpam-6202	89	14	1	1	NUM
ejpam-6202	89	15	)	)	PUNCT
ejpam-6202	89	16	∑	∑	PUNCT
ejpam-6202	89	17	k≥0	k≥0	PROPN
ejpam-6202	89	18	[	[	X
ejpam-6202	89	19	z	z	X
ejpam-6202	89	20	ln(1	ln(1	NOUN
ejpam-6202	89	21	+	+	NOUN
ejpam-6202	89	22	t)]k	t)]k	NOUN
ejpam-6202	89	23	k	k	X
ejpam-6202	89	24	!	!	PROPN
ejpam-6202	89	25	5	5	NUM
ejpam-6202	89	26	of	of	ADP
ejpam-6202	89	27	26	26	NUM
ejpam-6202	89	28	=	=	SYM
ejpam-6202	89	29	(	(	PUNCT
ejpam-6202	89	30	1	1	NUM
ejpam-6202	89	31	1	1	NUM
ejpam-6202	89	32	+	+	NUM
ejpam-6202	89	33	t	t	NOUN
ejpam-6202	89	34	)	)	PUNCT
ejpam-6202	89	35	r	r	NOUN
ejpam-6202	89	36	eln(1+t)z	eln(1+t)z	NOUN
ejpam-6202	89	37	2	2	NUM
ejpam-6202	89	38	t	t	NOUN
ejpam-6202	89	39	(	(	PUNCT
ejpam-6202	89	40	et	et	NOUN
ejpam-6202	89	41	+	+	NOUN
ejpam-6202	89	42	1	1	X
ejpam-6202	89	43	)	)	PUNCT
ejpam-6202	89	44	=	=	PUNCT
ejpam-6202	89	45	∑	∑	PUNCT
ejpam-6202	89	46	n≥0	n≥0	PROPN
ejpam-6202	89	47	(	(	PUNCT
ejpam-6202	89	48	z	z	NOUN
ejpam-6202	89	49	−	−	PROPN
ejpam-6202	89	50	r	r	NOUN
ejpam-6202	89	51	n	n	NOUN
ejpam-6202	89	52	)	)	PUNCT
ejpam-6202	89	53	tn	tn	NOUN
ejpam-6202	90	1	∞∑	∞∑	PROPN
ejpam-6202	90	2	n=0	n=0	NUM
ejpam-6202	90	3	gn	gn	PROPN
ejpam-6202	90	4	tn	tn	PROPN
ejpam-6202	90	5	n	n	PROPN
ejpam-6202	90	6	!	!	PUNCT
ejpam-6202	91	1	=	=	PUNCT
ejpam-6202	92	1	∑	∑	NOUN
ejpam-6202	92	2	n≥0	n≥0	PROPN
ejpam-6202	92	3	(	(	PUNCT
ejpam-6202	92	4	z	z	NOUN
ejpam-6202	92	5	−	−	NOUN
ejpam-6202	92	6	r)n	r)n	NOUN
ejpam-6202	92	7	tn	tn	NOUN
ejpam-6202	92	8	n	n	X
ejpam-6202	92	9	!	!	PUNCT
ejpam-6202	93	1			PROPN
ejpam-6202	93	2	(	(	PUNCT
ejpam-6202	93	3	∞∑	∞∑	PROPN
ejpam-6202	93	4	n=0	n=0	NUM
ejpam-6202	93	5	gn	gn	PROPN
ejpam-6202	93	6	tn	tn	PROPN
ejpam-6202	93	7	n	n	PROPN
ejpam-6202	93	8	!	!	PUNCT
ejpam-6202	93	9	)	)	PUNCT
ejpam-6202	94	1	=	=	PUNCT
ejpam-6202	95	1	∞∑	∞∑	NUM
ejpam-6202	95	2	n=0	n=0	NUM
ejpam-6202	95	3	n∑	n∑	NOUN
ejpam-6202	95	4	m=0	m=0	PROPN
ejpam-6202	95	5	(	(	PUNCT
ejpam-6202	95	6	z	z	NOUN
ejpam-6202	95	7	−	−	NOUN
ejpam-6202	95	8	r)m	r)m	NOUN
ejpam-6202	95	9	tm	tm	PROPN
ejpam-6202	95	10	m	m	PROPN
ejpam-6202	95	11	!	!	PUNCT
ejpam-6202	95	12	gn−m	gn−m	PROPN
ejpam-6202	95	13	tn−m	tn−m	PROPN
ejpam-6202	95	14	(	(	PUNCT
ejpam-6202	95	15	n−m	n−m	PROPN
ejpam-6202	95	16	)	)	PUNCT
ejpam-6202	95	17	!	!	PUNCT
ejpam-6202	96	1	=	=	PUNCT
ejpam-6202	97	1	∞∑	∞∑	PRON
ejpam-6202	97	2	n=0	n=0	NUM
ejpam-6202	97	3	{	{	PUNCT
ejpam-6202	97	4	n∑	n∑	PROPN
ejpam-6202	97	5	m=0	m=0	PROPN
ejpam-6202	97	6	(	(	PUNCT
ejpam-6202	97	7	z	z	NOUN
ejpam-6202	97	8	−	−	NOUN
ejpam-6202	97	9	r)m	r)m	NOUN
ejpam-6202	97	10	1	1	NUM
ejpam-6202	97	11	(	(	PUNCT
ejpam-6202	97	12	n−m)!m	n−m)!m	PROPN
ejpam-6202	97	13	!	!	PROPN
ejpam-6202	97	14	gn−m	gn−m	NOUN
ejpam-6202	97	15	}	}	PUNCT
ejpam-6202	97	16	tn	tn	NOUN
ejpam-6202	98	1	=	=	SYM
ejpam-6202	98	2	∞∑	∞∑	NUM
ejpam-6202	98	3	n=0	n=0	PRON
ejpam-6202	98	4	{	{	PUNCT
ejpam-6202	98	5	n∑	n∑	PROPN
ejpam-6202	98	6	m=0	m=0	PROPN
ejpam-6202	98	7	(	(	PUNCT
ejpam-6202	98	8	z	z	NOUN
ejpam-6202	98	9	−	−	NOUN
ejpam-6202	98	10	r)m	r)m	NOUN
ejpam-6202	98	11	(	(	PUNCT
ejpam-6202	98	12	n	n	X
ejpam-6202	98	13	m	m	NOUN
ejpam-6202	98	14	)	)	PUNCT
ejpam-6202	98	15	gn−m	gn−m	NOUN
ejpam-6202	98	16	}	}	PUNCT
ejpam-6202	98	17	tn	tn	PROPN
ejpam-6202	98	18	n	n	NOUN
ejpam-6202	98	19	!	!	PUNCT
ejpam-6202	98	20	=	=	NOUN
ejpam-6202	99	1	∞∑	∞∑	PRON
ejpam-6202	99	2	n=0	n=0	NUM
ejpam-6202	99	3	{	{	PUNCT
ejpam-6202	99	4	n∑	n∑	NOUN
ejpam-6202	99	5	m=0	m=0	PROPN
ejpam-6202	99	6	(	(	PUNCT
ejpam-6202	99	7	n	n	NOUN
ejpam-6202	99	8	m	m	PROPN
ejpam-6202	99	9	)	)	PUNCT
ejpam-6202	100	1	gn−m(z	gn−m(z	X
ejpam-6202	100	2	−	−	NOUN
ejpam-6202	100	3	r)m	r)m	NOUN
ejpam-6202	100	4	}	}	PUNCT
ejpam-6202	100	5	tn	tn	PROPN
ejpam-6202	100	6	n	n	CCONJ
ejpam-6202	100	7	!	!	PUNCT
ejpam-6202	101	1	rewriting	rewrite	VERB
ejpam-6202	101	2	∞∑	∞∑	PRON
ejpam-6202	101	3	n=0	n=0	PROPN
ejpam-6202	101	4	{	{	PUNCT
ejpam-6202	101	5	n∑	n∑	NOUN
ejpam-6202	101	6	k=0	k=0	PROPN
ejpam-6202	101	7	sg1	sg1	PROPN
ejpam-6202	101	8	n(k	n(k	PROPN
ejpam-6202	101	9	;	;	PUNCT
ejpam-6202	101	10	r)z	r)z	X
ejpam-6202	101	11	k	k	X
ejpam-6202	101	12	}	}	PUNCT
ejpam-6202	101	13	tn	tn	PROPN
ejpam-6202	101	14	n	n	CCONJ
ejpam-6202	101	15	!	!	PUNCT
ejpam-6202	102	1	=	=	NOUN
ejpam-6202	103	1	∞∑	∞∑	PRON
ejpam-6202	103	2	n=0	n=0	NUM
ejpam-6202	103	3	{	{	PUNCT
ejpam-6202	103	4	n∑	n∑	NOUN
ejpam-6202	103	5	m=0	m=0	PROPN
ejpam-6202	103	6	(	(	PUNCT
ejpam-6202	103	7	n	n	NOUN
ejpam-6202	103	8	m	m	PROPN
ejpam-6202	103	9	)	)	PUNCT
ejpam-6202	104	1	gn−m(z	gn−m(z	X
ejpam-6202	104	2	−	−	NOUN
ejpam-6202	104	3	r)m	r)m	NOUN
ejpam-6202	104	4	}	}	PUNCT
ejpam-6202	104	5	tn	tn	PROPN
ejpam-6202	104	6	n	n	X
ejpam-6202	104	7	!	!	PUNCT
ejpam-6202	105	1	comparing	compare	VERB
ejpam-6202	105	2	the	the	DET
ejpam-6202	105	3	coefficients	coefficient	NOUN
ejpam-6202	105	4	of	of	ADP
ejpam-6202	105	5	tn	tn	NOUN
ejpam-6202	105	6	n	n	CCONJ
ejpam-6202	105	7	!	!	PROPN
ejpam-6202	106	1	,	,	PUNCT
ejpam-6202	106	2	we	we	PRON
ejpam-6202	106	3	have	have	VERB
ejpam-6202	106	4	n∑	n∑	ADJ
ejpam-6202	106	5	k=0	k=0	PROPN
ejpam-6202	106	6	sg1	sg1	PROPN
ejpam-6202	106	7	n(k	n(k	PROPN
ejpam-6202	106	8	;	;	PUNCT
ejpam-6202	106	9	r)z	r)z	X
ejpam-6202	106	10	k	k	X
ejpam-6202	107	1	=	=	PUNCT
ejpam-6202	107	2	n∑	n∑	PROPN
ejpam-6202	107	3	m=0	m=0	PROPN
ejpam-6202	107	4	(	(	PUNCT
ejpam-6202	107	5	n	n	NOUN
ejpam-6202	107	6	m	m	PROPN
ejpam-6202	107	7	)	)	PUNCT
ejpam-6202	108	1	gn−m(z	gn−m(z	X
ejpam-6202	108	2	−	−	NOUN
ejpam-6202	108	3	r)m	r)m	NOUN
ejpam-6202	108	4	=	=	SYM
ejpam-6202	108	5	gn(z	gn(z	NOUN
ejpam-6202	108	6	−	−	NOUN
ejpam-6202	108	7	r	r	NOUN
ejpam-6202	108	8	)	)	PUNCT
ejpam-6202	108	9	similarly	similarly	ADV
ejpam-6202	108	10	(	(	PUNCT
ejpam-6202	108	11	2	2	X
ejpam-6202	108	12	)	)	PUNCT
ejpam-6202	108	13	can	can	AUX
ejpam-6202	108	14	be	be	AUX
ejpam-6202	108	15	written	write	VERB
ejpam-6202	108	16	as	as	ADP
ejpam-6202	108	17	∞∑	∞∑	NUM
ejpam-6202	108	18	k=0	k=0	PROPN
ejpam-6202	108	19	{	{	PUNCT
ejpam-6202	108	20	∞∑	∞∑	PROPN
ejpam-6202	108	21	n	n	X
ejpam-6202	108	22	=	=	SYM
ejpam-6202	108	23	k	k	PROPN
ejpam-6202	108	24	sg2	sg2	PROPN
ejpam-6202	108	25	n(k	n(k	PROPN
ejpam-6202	108	26	;	;	PUNCT
ejpam-6202	108	27	r	r	X
ejpam-6202	108	28	)	)	PUNCT
ejpam-6202	108	29	tn	tn	NOUN
ejpam-6202	108	30	n	n	NOUN
ejpam-6202	108	31	!	!	PUNCT
ejpam-6202	108	32	}	}	PUNCT
ejpam-6202	108	33	zk	zk	PROPN
ejpam-6202	109	1	=	=	PUNCT
ejpam-6202	110	1	∞∑	∞∑	NUM
ejpam-6202	110	2	k=0	k=0	PROPN
ejpam-6202	110	3	{	{	PUNCT
ejpam-6202	110	4	2tert(et	2tert(et	NUM
ejpam-6202	110	5	−	−	PROPN
ejpam-6202	110	6	1)k	1)k	NUM
ejpam-6202	110	7	k!(et	k!(et	NOUN
ejpam-6202	110	8	+	+	CCONJ
ejpam-6202	110	9	1	1	NUM
ejpam-6202	110	10	)	)	PUNCT
ejpam-6202	110	11	}	}	PUNCT
ejpam-6202	110	12	zk	zk	X
ejpam-6202	111	1	=	=	PUNCT
ejpam-6202	111	2	2tert	2tert	NUM
ejpam-6202	111	3	(	(	PUNCT
ejpam-6202	111	4	et	et	NOUN
ejpam-6202	111	5	+	+	NOUN
ejpam-6202	111	6	1	1	X
ejpam-6202	111	7	)	)	PUNCT
ejpam-6202	111	8	∞∑	∞∑	PRON
ejpam-6202	111	9	k=0	k=0	PROPN
ejpam-6202	111	10	(	(	PUNCT
ejpam-6202	111	11	z	z	NOUN
ejpam-6202	111	12	k	k	NOUN
ejpam-6202	111	13	)	)	PUNCT
ejpam-6202	111	14	(	(	PUNCT
ejpam-6202	111	15	et	et	NOUN
ejpam-6202	111	16	−	−	PROPN
ejpam-6202	111	17	1)k	1)k	NUM
ejpam-6202	112	1	=	=	SYM
ejpam-6202	112	2	2tert	2tert	NUM
ejpam-6202	112	3	(	(	PUNCT
ejpam-6202	112	4	et	et	NOUN
ejpam-6202	112	5	+	+	NOUN
ejpam-6202	112	6	1	1	X
ejpam-6202	112	7	)	)	PUNCT
ejpam-6202	112	8	(	(	PUNCT
ejpam-6202	112	9	1	1	NUM
ejpam-6202	112	10	+	+	CCONJ
ejpam-6202	112	11	(	(	PUNCT
ejpam-6202	112	12	et	et	NOUN
ejpam-6202	112	13	−	−	PROPN
ejpam-6202	112	14	1))z	1))z	NUM
ejpam-6202	112	15	=	=	SYM
ejpam-6202	112	16	2	2	NUM
ejpam-6202	112	17	t	t	NOUN
ejpam-6202	112	18	(	(	PUNCT
ejpam-6202	112	19	et	et	NOUN
ejpam-6202	112	20	+	+	NOUN
ejpam-6202	112	21	1	1	NUM
ejpam-6202	112	22	)	)	PUNCT
ejpam-6202	112	23	ert(1	ert(1	NOUN
ejpam-6202	112	24	+	+	CCONJ
ejpam-6202	112	25	(	(	PUNCT
ejpam-6202	112	26	et	et	NOUN
ejpam-6202	112	27	−	−	PROPN
ejpam-6202	112	28	1))z	1))z	NUM
ejpam-6202	112	29	6	6	NUM
ejpam-6202	112	30	of	of	ADP
ejpam-6202	112	31	26	26	NUM
ejpam-6202	112	32	=	=	SYM
ejpam-6202	112	33	e(z+r)t	e(z+r)t	PROPN
ejpam-6202	112	34	2	2	NUM
ejpam-6202	112	35	t	t	PROPN
ejpam-6202	112	36	(	(	PUNCT
ejpam-6202	112	37	et	et	NOUN
ejpam-6202	112	38	+	+	NOUN
ejpam-6202	112	39	1	1	X
ejpam-6202	112	40	)	)	PUNCT
ejpam-6202	112	41	=	=	NOUN
ejpam-6202	112	42	(	(	PUNCT
ejpam-6202	112	43	∞∑	∞∑	NUM
ejpam-6202	112	44	n=0	n=0	NUM
ejpam-6202	112	45	(	(	PUNCT
ejpam-6202	112	46	z	z	NOUN
ejpam-6202	112	47	+	+	NOUN
ejpam-6202	112	48	r)n	r)n	X
ejpam-6202	112	49	tn	tn	NOUN
ejpam-6202	112	50	n	n	CCONJ
ejpam-6202	112	51	!	!	PUNCT
ejpam-6202	112	52	)	)	PUNCT
ejpam-6202	113	1	(	(	PUNCT
ejpam-6202	113	2	∞∑	∞∑	PROPN
ejpam-6202	113	3	n=0	n=0	NUM
ejpam-6202	113	4	gn	gn	PROPN
ejpam-6202	113	5	tn	tn	PROPN
ejpam-6202	113	6	n	n	PROPN
ejpam-6202	113	7	!	!	PUNCT
ejpam-6202	113	8	)	)	PUNCT
ejpam-6202	114	1	=	=	PUNCT
ejpam-6202	115	1	∞∑	∞∑	NUM
ejpam-6202	115	2	n=0	n=0	NUM
ejpam-6202	115	3	n∑	n∑	NOUN
ejpam-6202	115	4	m=0	m=0	PROPN
ejpam-6202	115	5	(	(	PUNCT
ejpam-6202	115	6	z	z	NOUN
ejpam-6202	115	7	+	+	NOUN
ejpam-6202	115	8	r)m	r)m	NOUN
ejpam-6202	115	9	tm	tm	PROPN
ejpam-6202	115	10	m	m	PROPN
ejpam-6202	115	11	!	!	PUNCT
ejpam-6202	115	12	gn−m	gn−m	PROPN
ejpam-6202	115	13	tn−m	tn−m	PROPN
ejpam-6202	115	14	(	(	PUNCT
ejpam-6202	115	15	n−m	n−m	PROPN
ejpam-6202	115	16	)	)	PUNCT
ejpam-6202	115	17	!	!	PUNCT
ejpam-6202	116	1	=	=	PUNCT
ejpam-6202	117	1	∞∑	∞∑	PRON
ejpam-6202	117	2	n=0	n=0	NUM
ejpam-6202	117	3	{	{	PUNCT
ejpam-6202	117	4	n∑	n∑	PROPN
ejpam-6202	117	5	m=0	m=0	PROPN
ejpam-6202	117	6	(	(	PUNCT
ejpam-6202	117	7	z	z	NOUN
ejpam-6202	117	8	+	+	NOUN
ejpam-6202	117	9	r)m	r)m	NOUN
ejpam-6202	117	10	1	1	NUM
ejpam-6202	117	11	(	(	PUNCT
ejpam-6202	117	12	n−m)!m	n−m)!m	PROPN
ejpam-6202	117	13	!	!	PROPN
ejpam-6202	117	14	gn−m	gn−m	NOUN
ejpam-6202	117	15	}	}	PUNCT
ejpam-6202	117	16	tn	tn	NOUN
ejpam-6202	118	1	=	=	SYM
ejpam-6202	118	2	∞∑	∞∑	NUM
ejpam-6202	118	3	n=0	n=0	PRON
ejpam-6202	118	4	{	{	PUNCT
ejpam-6202	118	5	n∑	n∑	PROPN
ejpam-6202	118	6	m=0	m=0	PROPN
ejpam-6202	118	7	(	(	PUNCT
ejpam-6202	118	8	z	z	NOUN
ejpam-6202	118	9	+	+	NOUN
ejpam-6202	118	10	r)m	r)m	NOUN
ejpam-6202	118	11	(	(	PUNCT
ejpam-6202	118	12	n	n	X
ejpam-6202	118	13	m	m	NOUN
ejpam-6202	118	14	)	)	PUNCT
ejpam-6202	118	15	gn−m	gn−m	NOUN
ejpam-6202	118	16	}	}	PUNCT
ejpam-6202	118	17	tn	tn	PROPN
ejpam-6202	118	18	n	n	NOUN
ejpam-6202	118	19	!	!	PUNCT
ejpam-6202	118	20	=	=	NOUN
ejpam-6202	119	1	∞∑	∞∑	PRON
ejpam-6202	119	2	n=0	n=0	NUM
ejpam-6202	119	3	{	{	PUNCT
ejpam-6202	119	4	n∑	n∑	NOUN
ejpam-6202	119	5	m=0	m=0	PROPN
ejpam-6202	119	6	(	(	PUNCT
ejpam-6202	119	7	n	n	NOUN
ejpam-6202	119	8	m	m	PROPN
ejpam-6202	119	9	)	)	PUNCT
ejpam-6202	119	10	gn−m(z	gn−m(z	X
ejpam-6202	119	11	+	+	CCONJ
ejpam-6202	119	12	r)m	r)m	NOUN
ejpam-6202	119	13	}	}	PUNCT
ejpam-6202	119	14	tn	tn	PROPN
ejpam-6202	119	15	n	n	CCONJ
ejpam-6202	119	16	!	!	PUNCT
ejpam-6202	120	1	rewriting	rewrite	VERB
ejpam-6202	120	2	∞∑	∞∑	PRON
ejpam-6202	120	3	n=0	n=0	PROPN
ejpam-6202	120	4	{	{	PUNCT
ejpam-6202	120	5	n∑	n∑	PROPN
ejpam-6202	120	6	k=0	k=0	PROPN
ejpam-6202	120	7	sg2	sg2	PROPN
ejpam-6202	120	8	n(k	n(k	PROPN
ejpam-6202	120	9	;	;	PUNCT
ejpam-6202	120	10	r)z	r)z	X
ejpam-6202	120	11	k	k	X
ejpam-6202	120	12	}	}	PUNCT
ejpam-6202	120	13	tn	tn	PROPN
ejpam-6202	120	14	n	n	CCONJ
ejpam-6202	120	15	!	!	PUNCT
ejpam-6202	121	1	=	=	NOUN
ejpam-6202	122	1	∞∑	∞∑	PRON
ejpam-6202	122	2	n=0	n=0	NUM
ejpam-6202	122	3	{	{	PUNCT
ejpam-6202	122	4	n∑	n∑	NOUN
ejpam-6202	122	5	m=0	m=0	PROPN
ejpam-6202	122	6	(	(	PUNCT
ejpam-6202	122	7	n	n	NOUN
ejpam-6202	122	8	m	m	PROPN
ejpam-6202	122	9	)	)	PUNCT
ejpam-6202	122	10	gn−m(z	gn−m(z	X
ejpam-6202	122	11	+	+	CCONJ
ejpam-6202	122	12	r)m	r)m	NOUN
ejpam-6202	122	13	}	}	PUNCT
ejpam-6202	122	14	tn	tn	PROPN
ejpam-6202	122	15	n	n	NOUN
ejpam-6202	122	16	!	!	PUNCT
ejpam-6202	122	17	comparing	compare	VERB
ejpam-6202	122	18	the	the	DET
ejpam-6202	122	19	coefficients	coefficient	NOUN
ejpam-6202	122	20	of	of	ADP
ejpam-6202	122	21	tn	tn	NOUN
ejpam-6202	122	22	n	n	CCONJ
ejpam-6202	122	23	!	!	PROPN
ejpam-6202	122	24	,	,	PUNCT
ejpam-6202	122	25	we	we	PRON
ejpam-6202	122	26	have	have	VERB
ejpam-6202	122	27	n∑	n∑	PROPN
ejpam-6202	122	28	k=0	k=0	PROPN
ejpam-6202	122	29	sg2	sg2	PROPN
ejpam-6202	122	30	n(k	n(k	PROPN
ejpam-6202	122	31	;	;	PUNCT
ejpam-6202	122	32	r)z	r)z	X
ejpam-6202	122	33	k	k	X
ejpam-6202	123	1	=	=	PUNCT
ejpam-6202	123	2	n∑	n∑	PROPN
ejpam-6202	123	3	m=0	m=0	PROPN
ejpam-6202	123	4	(	(	PUNCT
ejpam-6202	123	5	n	n	NOUN
ejpam-6202	123	6	m	m	PROPN
ejpam-6202	123	7	)	)	PUNCT
ejpam-6202	123	8	gn−m(z	gn−m(z	X
ejpam-6202	123	9	+	+	CCONJ
ejpam-6202	123	10	r)m	r)m	NOUN
ejpam-6202	123	11	=	=	SYM
ejpam-6202	123	12	gn(z	gn(z	NOUN
ejpam-6202	123	13	+	+	CCONJ
ejpam-6202	123	14	r	r	NOUN
ejpam-6202	123	15	)	)	PUNCT
ejpam-6202	123	16	hence	hence	ADV
ejpam-6202	123	17	,	,	PUNCT
ejpam-6202	123	18	we	we	PRON
ejpam-6202	123	19	proved	prove	VERB
ejpam-6202	123	20	the	the	DET
ejpam-6202	123	21	horizontal	horizontal	ADJ
ejpam-6202	123	22	generating	generating	NOUN
ejpam-6202	123	23	function	function	NOUN
ejpam-6202	123	24	in	in	ADP
ejpam-6202	123	25	(	(	PUNCT
ejpam-6202	123	26	5	5	NUM
ejpam-6202	123	27	)	)	PUNCT
ejpam-6202	123	28	and	and	CCONJ
ejpam-6202	123	29	(	(	PUNCT
ejpam-6202	123	30	6	6	NUM
ejpam-6202	123	31	)	)	PUNCT
ejpam-6202	123	32	.	.	PUNCT
ejpam-6202	124	1	an	an	DET
ejpam-6202	124	2	essential	essential	ADJ
ejpam-6202	124	3	characteristic	characteristic	NOUN
ejpam-6202	124	4	of	of	ADP
ejpam-6202	124	5	a	a	DET
ejpam-6202	124	6	special	special	ADJ
ejpam-6202	124	7	number	number	NOUN
ejpam-6202	124	8	is	be	AUX
ejpam-6202	124	9	its	its	PRON
ejpam-6202	124	10	explicit	explicit	ADJ
ejpam-6202	124	11	formula	formula	NOUN
ejpam-6202	124	12	,	,	PUNCT
ejpam-6202	124	13	which	which	PRON
ejpam-6202	124	14	is	be	AUX
ejpam-6202	124	15	valuable	valuable	ADJ
ejpam-6202	124	16	for	for	ADP
ejpam-6202	124	17	directly	directly	ADV
ejpam-6202	124	18	calculating	calculate	VERB
ejpam-6202	124	19	the	the	DET
ejpam-6202	124	20	number	number	NOUN
ejpam-6202	124	21	’s	’s	PART
ejpam-6202	124	22	value	value	NOUN
ejpam-6202	124	23	for	for	ADP
ejpam-6202	124	24	particular	particular	ADJ
ejpam-6202	124	25	parameter	parameter	NOUN
ejpam-6202	124	26	inputs	input	NOUN
ejpam-6202	124	27	.	.	PUNCT
ejpam-6202	125	1	the	the	DET
ejpam-6202	125	2	following	follow	VERB
ejpam-6202	125	3	theorem	theorem	NOUN
ejpam-6202	125	4	presents	present	VERB
ejpam-6202	125	5	the	the	DET
ejpam-6202	125	6	explicit	explicit	ADJ
ejpam-6202	125	7	formula	formula	NOUN
ejpam-6202	125	8	for	for	ADP
ejpam-6202	125	9	the	the	DET
ejpam-6202	125	10	r	r	NOUN
ejpam-6202	125	11	-	-	PUNCT
ejpam-6202	125	12	stirling	stirling	NOUN
ejpam-6202	125	13	genocchi	genocchi	PROPN
ejpam-6202	125	14	numbers	number	NOUN
ejpam-6202	125	15	.	.	PUNCT
ejpam-6202	126	1	theorem	theorem	VERB
ejpam-6202	126	2	1.3	1.3	NUM
ejpam-6202	126	3	.	.	PUNCT
ejpam-6202	127	1	the	the	DET
ejpam-6202	127	2	formula	formula	NOUN
ejpam-6202	127	3	for	for	ADP
ejpam-6202	127	4	the	the	DET
ejpam-6202	127	5	first	first	ADJ
ejpam-6202	127	6	kind	kind	NOUN
ejpam-6202	127	7	of	of	ADP
ejpam-6202	127	8	r	r	NOUN
ejpam-6202	127	9	-	-	PUNCT
ejpam-6202	127	10	stirling	stirling	NOUN
ejpam-6202	127	11	genocchi	genocchi	PROPN
ejpam-6202	127	12	numbers	number	NOUN
ejpam-6202	127	13	is	be	AUX
ejpam-6202	127	14	explicitly	explicitly	ADV
ejpam-6202	127	15	stated	state	VERB
ejpam-6202	127	16	as	as	SCONJ
ejpam-6202	127	17	follows	follow	VERB
ejpam-6202	127	18	:	:	PUNCT
ejpam-6202	128	1	sg1	sg1	PROPN
ejpam-6202	128	2	n(k	n(k	PROPN
ejpam-6202	128	3	;	;	PUNCT
ejpam-6202	128	4	r	r	X
ejpam-6202	128	5	)	)	PUNCT
ejpam-6202	128	6	=	=	SYM
ejpam-6202	128	7	n∑	n∑	PROPN
ejpam-6202	128	8	m=0	m=0	PROPN
ejpam-6202	128	9	n∑	n∑	PROPN
ejpam-6202	128	10	j	j	PROPN
ejpam-6202	129	1	=	=	NOUN
ejpam-6202	129	2	m	m	VERB
ejpam-6202	129	3	m−k∑	m−k∑	X
ejpam-6202	130	1	f=0	f=0	X
ejpam-6202	130	2	f∑	f∑	PROPN
ejpam-6202	131	1	d	d	X
ejpam-6202	132	1	=	=	X
ejpam-6202	132	2	i	i	PRON
ejpam-6202	132	3	(	(	PUNCT
ejpam-6202	132	4	−1)n−j+d+fgj−m	−1)n−j+d+fgj−m	PROPN
ejpam-6202	132	5	(	(	PUNCT
ejpam-6202	132	6	j	j	PROPN
ejpam-6202	132	7	m	m	VERB
ejpam-6202	132	8	)	)	PUNCT
ejpam-6202	132	9	(	(	PUNCT
ejpam-6202	132	10	n	n	X
ejpam-6202	132	11	j	j	NOUN
ejpam-6202	132	12	)	)	PUNCT
ejpam-6202	132	13	(	(	PUNCT
ejpam-6202	132	14	f	f	PROPN
ejpam-6202	132	15	d	d	PROPN
ejpam-6202	132	16	)	)	PUNCT
ejpam-6202	132	17	(	(	PUNCT
ejpam-6202	132	18	m−	m−	PROPN
ejpam-6202	132	19	1	1	NUM
ejpam-6202	132	20	+	+	CCONJ
ejpam-6202	132	21	f	f	PROPN
ejpam-6202	132	22	m−	m−	PROPN
ejpam-6202	132	23	k	k	PROPN
ejpam-6202	133	1	+	+	CCONJ
ejpam-6202	133	2	f	f	NOUN
ejpam-6202	133	3	)	)	PUNCT
ejpam-6202	134	1	(	(	PUNCT
ejpam-6202	134	2	2m−	2m−	NUM
ejpam-6202	134	3	k	k	NOUN
ejpam-6202	134	4	m−	m−	PROPN
ejpam-6202	134	5	k	k	PROPN
ejpam-6202	135	1	+	+	CCONJ
ejpam-6202	135	2	f	f	PROPN
ejpam-6202	135	3	)	)	PUNCT
ejpam-6202	136	1	(	(	PUNCT
ejpam-6202	136	2	f	f	X
ejpam-6202	136	3	−	−	PROPN
ejpam-6202	136	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	136	5	f	f	X
ejpam-6202	136	6	!	!	PUNCT
ejpam-6202	137	1	rn−j	rn−j	PROPN
ejpam-6202	137	2	7	7	NUM
ejpam-6202	137	3	of	of	ADP
ejpam-6202	137	4	26	26	NUM
ejpam-6202	137	5	proof	proof	NOUN
ejpam-6202	137	6	.	.	PUNCT
ejpam-6202	138	1	the	the	DET
ejpam-6202	138	2	exponential	exponential	ADJ
ejpam-6202	138	3	generating	generating	NOUN
ejpam-6202	138	4	function	function	NOUN
ejpam-6202	138	5	in	in	ADP
ejpam-6202	138	6	(	(	PUNCT
ejpam-6202	138	7	1	1	NUM
ejpam-6202	138	8	)	)	PUNCT
ejpam-6202	138	9	composed	compose	VERB
ejpam-6202	138	10	of	of	ADP
ejpam-6202	138	11	three	three	NUM
ejpam-6202	138	12	functions	function	NOUN
ejpam-6202	138	13	.	.	PUNCT
ejpam-6202	139	1	the	the	DET
ejpam-6202	139	2	first	first	ADJ
ejpam-6202	139	3	function	function	NOUN
ejpam-6202	139	4	can	can	AUX
ejpam-6202	139	5	be	be	AUX
ejpam-6202	139	6	expressed	express	VERB
ejpam-6202	139	7	as	as	ADP
ejpam-6202	139	8	(	(	PUNCT
ejpam-6202	139	9	1	1	NUM
ejpam-6202	139	10	1−	1−	NUM
ejpam-6202	139	11	t	t	NOUN
ejpam-6202	139	12	)	)	PUNCT
ejpam-6202	139	13	r	r	NOUN
ejpam-6202	139	14	=	=	SYM
ejpam-6202	139	15	(	(	PUNCT
ejpam-6202	139	16	1−	1−	NUM
ejpam-6202	139	17	t)−r	t)−r	NUM
ejpam-6202	139	18	=	=	PUNCT
ejpam-6202	140	1	∑	∑	PUNCT
ejpam-6202	140	2	n≥0	n≥0	PROPN
ejpam-6202	140	3	(	(	PUNCT
ejpam-6202	140	4	−r	−r	ADJ
ejpam-6202	140	5	n	n	CCONJ
ejpam-6202	140	6	)	)	PUNCT
ejpam-6202	140	7	tn	tn	PROPN
ejpam-6202	141	1	=	=	SYM
ejpam-6202	141	2	(	(	PUNCT
ejpam-6202	141	3	−r	−r	PROPN
ejpam-6202	141	4	0	0	NUM
ejpam-6202	141	5	)	)	PUNCT
ejpam-6202	141	6	(	(	PUNCT
ejpam-6202	141	7	−t)0	−t)0	NOUN
ejpam-6202	141	8	+	+	CCONJ
ejpam-6202	141	9	∑	∑	PROPN
ejpam-6202	141	10	n>0	n>0	PROPN
ejpam-6202	141	11	n	n	PROPN
ejpam-6202	141	12	(	(	PUNCT
ejpam-6202	141	13	−r	−r	PROPN
ejpam-6202	141	14	n	n	X
ejpam-6202	141	15	)	)	PUNCT
ejpam-6202	141	16	tn	tn	PROPN
ejpam-6202	141	17	by	by	ADP
ejpam-6202	141	18	newtons	newton	NOUN
ejpam-6202	141	19	binomial	binomial	PROPN
ejpam-6202	141	20	theorem	theorem	PROPN
ejpam-6202	141	21	,	,	PUNCT
ejpam-6202	141	22	(	(	PUNCT
ejpam-6202	141	23	1	1	NUM
ejpam-6202	141	24	1−	1−	NUM
ejpam-6202	141	25	t	t	NOUN
ejpam-6202	141	26	)	)	PUNCT
ejpam-6202	142	1	r	r	NOUN
ejpam-6202	142	2	=	=	PUNCT
ejpam-6202	142	3	∑	∑	PROPN
ejpam-6202	142	4	n≥0	n≥0	PROPN
ejpam-6202	142	5	(	(	PUNCT
ejpam-6202	142	6	−r)(−r	−r)(−r	NOUN
ejpam-6202	142	7	−	−	PROPN
ejpam-6202	142	8	1	1	NUM
ejpam-6202	142	9	)	)	PUNCT
ejpam-6202	142	10	.	.	PUNCT
ejpam-6202	142	11	.	.	PUNCT
ejpam-6202	142	12	.	.	PUNCT
ejpam-6202	143	1	(	(	PUNCT
ejpam-6202	143	2	−r	−r	ADJ
ejpam-6202	143	3	−	−	PROPN
ejpam-6202	143	4	n+	n+	NOUN
ejpam-6202	143	5	1	1	NUM
ejpam-6202	143	6	)	)	PUNCT
ejpam-6202	143	7	n	n	CCONJ
ejpam-6202	143	8	!	!	PUNCT
ejpam-6202	144	1	(	(	PUNCT
ejpam-6202	144	2	−t)n	−t)n	NOUN
ejpam-6202	144	3	=	=	PUNCT
ejpam-6202	144	4	∑	∑	PUNCT
ejpam-6202	144	5	n≥0	n≥0	PROPN
ejpam-6202	144	6	(	(	PUNCT
ejpam-6202	144	7	−1)n	−1)n	X
ejpam-6202	144	8	(	(	PUNCT
ejpam-6202	144	9	r)(r	r)(r	NOUN
ejpam-6202	144	10	+	+	NOUN
ejpam-6202	144	11	1	1	NUM
ejpam-6202	144	12	)	)	PUNCT
ejpam-6202	144	13	.	.	PUNCT
ejpam-6202	144	14	.	.	PUNCT
ejpam-6202	144	15	.	.	PUNCT
ejpam-6202	145	1	(	(	PUNCT
ejpam-6202	145	2	r	r	NOUN
ejpam-6202	145	3	+	+	NUM
ejpam-6202	145	4	n−	n−	NOUN
ejpam-6202	145	5	1	1	NUM
ejpam-6202	145	6	)	)	PUNCT
ejpam-6202	145	7	n	n	CCONJ
ejpam-6202	145	8	!	!	PUNCT
ejpam-6202	145	9	(	(	PUNCT
ejpam-6202	145	10	−1)n(t)n	−1)n(t)n	NOUN
ejpam-6202	145	11	and	and	CCONJ
ejpam-6202	145	12	by	by	ADP
ejpam-6202	145	13	the	the	DET
ejpam-6202	145	14	definition	definition	NOUN
ejpam-6202	145	15	of	of	ADP
ejpam-6202	145	16	a	a	DET
ejpam-6202	145	17	rising	rise	VERB
ejpam-6202	145	18	factorial	factorial	NOUN
ejpam-6202	145	19	,	,	PUNCT
ejpam-6202	145	20	(	(	PUNCT
ejpam-6202	145	21	1	1	NUM
ejpam-6202	145	22	1−	1−	NUM
ejpam-6202	145	23	t	t	NOUN
ejpam-6202	145	24	)	)	PUNCT
ejpam-6202	145	25	r	r	NOUN
ejpam-6202	145	26	=	=	PUNCT
ejpam-6202	145	27	∑	∑	PUNCT
ejpam-6202	145	28	n≥0	n≥0	PROPN
ejpam-6202	145	29	(	(	PUNCT
ejpam-6202	145	30	−1)nrn	−1)nrn	PROPN
ejpam-6202	145	31	tn	tn	PROPN
ejpam-6202	145	32	n	n	NOUN
ejpam-6202	145	33	!	!	PUNCT
ejpam-6202	145	34	where	where	SCONJ
ejpam-6202	145	35	rn	rn	PROPN
ejpam-6202	145	36	=	=	SYM
ejpam-6202	145	37	r(r	r(r	PROPN
ejpam-6202	145	38	+	+	CCONJ
ejpam-6202	145	39	1	1	NUM
ejpam-6202	145	40	)	)	PUNCT
ejpam-6202	145	41	.	.	PUNCT
ejpam-6202	145	42	.	.	PUNCT
ejpam-6202	145	43	.	.	PUNCT
ejpam-6202	146	1	(	(	PUNCT
ejpam-6202	146	2	r	r	NOUN
ejpam-6202	146	3	+	+	NUM
ejpam-6202	146	4	n−	n−	NOUN
ejpam-6202	146	5	1	1	NUM
ejpam-6202	146	6	)	)	PUNCT
ejpam-6202	146	7	the	the	DET
ejpam-6202	146	8	second	second	ADJ
ejpam-6202	146	9	function	function	NOUN
ejpam-6202	146	10	can	can	AUX
ejpam-6202	146	11	be	be	AUX
ejpam-6202	146	12	expresses	express	NOUN
ejpam-6202	146	13	as	as	ADP
ejpam-6202	146	14	the	the	DET
ejpam-6202	146	15	genocchi	genocchi	PROPN
ejpam-6202	146	16	number	number	NOUN
ejpam-6202	146	17	,	,	PUNCT
ejpam-6202	146	18	2	2	NUM
ejpam-6202	146	19	t	t	NOUN
ejpam-6202	146	20	(	(	PUNCT
ejpam-6202	146	21	et	et	NOUN
ejpam-6202	146	22	+	+	NOUN
ejpam-6202	146	23	1	1	X
ejpam-6202	146	24	)	)	PUNCT
ejpam-6202	146	25	=	=	NOUN
ejpam-6202	147	1	∞∑	∞∑	PROPN
ejpam-6202	147	2	n=0	n=0	NUM
ejpam-6202	147	3	gn	gn	PROPN
ejpam-6202	147	4	tn	tn	PROPN
ejpam-6202	147	5	n	n	PROPN
ejpam-6202	147	6	!	!	PUNCT
ejpam-6202	148	1	lastly	lastly	ADV
ejpam-6202	148	2	the	the	DET
ejpam-6202	148	3	third	third	ADJ
ejpam-6202	148	4	function	function	NOUN
ejpam-6202	148	5	can	can	AUX
ejpam-6202	148	6	be	be	AUX
ejpam-6202	148	7	expressed	express	VERB
ejpam-6202	148	8	1	1	NUM
ejpam-6202	148	9	k	k	NOUN
ejpam-6202	148	10	!	!	PUNCT
ejpam-6202	149	1	[	[	X
ejpam-6202	149	2	ln	ln	ADJ
ejpam-6202	149	3	1	1	NUM
ejpam-6202	149	4	+	+	NUM
ejpam-6202	149	5	t]k	t]k	NOUN
ejpam-6202	149	6	=	=	SYM
ejpam-6202	149	7	∑	∑	PUNCT
ejpam-6202	149	8	n≥k	n≥k	PROPN
ejpam-6202	149	9	s(n	s(n	PROPN
ejpam-6202	149	10	,	,	PUNCT
ejpam-6202	149	11	k	k	NOUN
ejpam-6202	149	12	)	)	PUNCT
ejpam-6202	149	13	tn	tn	PROPN
ejpam-6202	149	14	n	n	PROPN
ejpam-6202	149	15	!	!	PUNCT
ejpam-6202	150	1	hence	hence	ADV
ejpam-6202	150	2	,	,	PUNCT
ejpam-6202	150	3	using	use	VERB
ejpam-6202	150	4	cauchy	cauchy	PROPN
ejpam-6202	150	5	’s	’s	PART
ejpam-6202	150	6	rule	rule	NOUN
ejpam-6202	150	7	for	for	ADP
ejpam-6202	150	8	the	the	DET
ejpam-6202	150	9	product	product	NOUN
ejpam-6202	150	10	of	of	ADP
ejpam-6202	150	11	power	power	NOUN
ejpam-6202	150	12	series	series	NOUN
ejpam-6202	150	13	,	,	PUNCT
ejpam-6202	150	14	we	we	PRON
ejpam-6202	150	15	have	have	VERB
ejpam-6202	150	16	n∑	n∑	ADJ
ejpam-6202	150	17	k≥0	k≥0	PROPN
ejpam-6202	150	18	sg1	sg1	PROPN
ejpam-6202	150	19	n(k	n(k	PROPN
ejpam-6202	150	20	;	;	PUNCT
ejpam-6202	150	21	r	r	X
ejpam-6202	150	22	)	)	PUNCT
ejpam-6202	150	23	tn	tn	NOUN
ejpam-6202	150	24	n	n	NOUN
ejpam-6202	150	25	!	!	PUNCT
ejpam-6202	151	1	=	=	PUNCT
ejpam-6202	152	1	∑	∑	NOUN
ejpam-6202	152	2	n≥0	n≥0	PROPN
ejpam-6202	152	3	(	(	PUNCT
ejpam-6202	152	4	−1)nrn	−1)nrn	PROPN
ejpam-6202	152	5	tn	tn	PROPN
ejpam-6202	152	6	n	n	ADV
ejpam-6202	152	7	!	!	PUNCT
ejpam-6202	153	1			PROPN
ejpam-6202	153	2	(	(	PUNCT
ejpam-6202	153	3	∞∑	∞∑	PROPN
ejpam-6202	153	4	n=0	n=0	NUM
ejpam-6202	153	5	gn	gn	PROPN
ejpam-6202	153	6	tn	tn	PROPN
ejpam-6202	153	7	n	n	PROPN
ejpam-6202	153	8	!	!	PUNCT
ejpam-6202	153	9	)	)	PUNCT
ejpam-6202	153	10	∑	∑	NOUN
ejpam-6202	153	11	n≥k	n≥k	PROPN
ejpam-6202	153	12	s(n	s(n	PROPN
ejpam-6202	153	13	,	,	PUNCT
ejpam-6202	153	14	k	k	NOUN
ejpam-6202	153	15	)	)	PUNCT
ejpam-6202	153	16	tn	tn	PROPN
ejpam-6202	153	17	n	n	NOUN
ejpam-6202	153	18	!	!	PUNCT
ejpam-6202	154	1			PROPN
ejpam-6202	154	2	8	8	NUM
ejpam-6202	154	3	of	of	ADP
ejpam-6202	154	4	26	26	NUM
ejpam-6202	154	5	=	=	PUNCT
ejpam-6202	154	6	∑	∑	NOUN
ejpam-6202	154	7	n≥0	n≥0	PROPN
ejpam-6202	154	8	(	(	PUNCT
ejpam-6202	154	9	−1)nrn	−1)nrn	PROPN
ejpam-6202	154	10	tn	tn	PROPN
ejpam-6202	154	11	n	n	ADV
ejpam-6202	154	12	!	!	PUNCT
ejpam-6202	155	1			PROPN
ejpam-6202	155	2	(	(	PUNCT
ejpam-6202	155	3	∞∑	∞∑	PROPN
ejpam-6202	155	4	n=0	n=0	PROPN
ejpam-6202	155	5	{	{	PUNCT
ejpam-6202	155	6	n∑	n∑	NOUN
ejpam-6202	155	7	m	m	PROPN
ejpam-6202	155	8	=	=	PROPN
ejpam-6202	155	9	k	k	PROPN
ejpam-6202	155	10	s(m	s(m	PROPN
ejpam-6202	155	11	,	,	PUNCT
ejpam-6202	155	12	k	k	NOUN
ejpam-6202	155	13	)	)	PUNCT
ejpam-6202	155	14	(	(	PUNCT
ejpam-6202	155	15	n	n	X
ejpam-6202	155	16	m	m	NOUN
ejpam-6202	155	17	)	)	PUNCT
ejpam-6202	155	18	gn−m	gn−m	NOUN
ejpam-6202	155	19	}	}	PUNCT
ejpam-6202	155	20	tn	tn	PROPN
ejpam-6202	155	21	n	n	NOUN
ejpam-6202	155	22	!	!	PUNCT
ejpam-6202	155	23	)	)	PUNCT
ejpam-6202	156	1	=	=	PUNCT
ejpam-6202	157	1	∞∑	∞∑	NUM
ejpam-6202	157	2	n=0	n=0	NUM
ejpam-6202	157	3	n∑	n∑	DET
ejpam-6202	157	4	j=0	j=0	PROPN
ejpam-6202	157	5	j∑	j∑	PROPN
ejpam-6202	157	6	m	m	PROPN
ejpam-6202	157	7	=	=	PROPN
ejpam-6202	157	8	k	k	PROPN
ejpam-6202	157	9	s(m	s(m	PROPN
ejpam-6202	157	10	,	,	PUNCT
ejpam-6202	157	11	k	k	NOUN
ejpam-6202	157	12	)	)	PUNCT
ejpam-6202	157	13	(	(	PUNCT
ejpam-6202	157	14	j	j	PROPN
ejpam-6202	157	15	m	m	NOUN
ejpam-6202	157	16	)	)	PUNCT
ejpam-6202	157	17	gj−m	gj−m	PROPN
ejpam-6202	157	18	tj	tj	PROPN
ejpam-6202	157	19	j	j	PROPN
ejpam-6202	157	20	!	!	PUNCT
ejpam-6202	157	21	(	(	PUNCT
ejpam-6202	157	22	−1)n−jrn−j	−1)n−jrn−j	ADV
ejpam-6202	157	23	tn−j	tn−j	NOUN
ejpam-6202	157	24	(	(	PUNCT
ejpam-6202	157	25	n−	n−	NOUN
ejpam-6202	157	26	j	j	NOUN
ejpam-6202	157	27	)	)	PUNCT
ejpam-6202	157	28	!	!	PUNCT
ejpam-6202	158	1	=	=	PUNCT
ejpam-6202	159	1	∞∑	∞∑	DET
ejpam-6202	159	2	n=0	n=0	NUM
ejpam-6202	159	3	n∑	n∑	DET
ejpam-6202	159	4	j=0	j=0	PROPN
ejpam-6202	159	5	j∑	j∑	PROPN
ejpam-6202	159	6	m	m	PROPN
ejpam-6202	159	7	=	=	PROPN
ejpam-6202	159	8	k	k	PROPN
ejpam-6202	159	9	s(m	s(m	PROPN
ejpam-6202	159	10	,	,	PUNCT
ejpam-6202	159	11	k	k	NOUN
ejpam-6202	159	12	)	)	PUNCT
ejpam-6202	159	13	(	(	PUNCT
ejpam-6202	159	14	j	j	PROPN
ejpam-6202	159	15	m	m	NOUN
ejpam-6202	159	16	)	)	PUNCT
ejpam-6202	159	17	gj−m	gj−m	NOUN
ejpam-6202	159	18	tj−j+n	tj−j+n	NOUN
ejpam-6202	159	19	(	(	PUNCT
ejpam-6202	159	20	n−	n−	NOUN
ejpam-6202	159	21	j)!j	j)!j	PROPN
ejpam-6202	159	22	!	!	PUNCT
ejpam-6202	160	1	(	(	PUNCT
ejpam-6202	160	2	−1)n−jrn−j	−1)n−jrn−j	ADV
ejpam-6202	160	3	=	=	VERB
ejpam-6202	161	1	∞∑	∞∑	NUM
ejpam-6202	161	2	n=0	n=0	NUM
ejpam-6202	161	3			PUNCT
ejpam-6202	161	4	n∑	n∑	PROPN
ejpam-6202	161	5	m=0	m=0	PROPN
ejpam-6202	161	6	n∑	n∑	PROPN
ejpam-6202	161	7	j	j	PROPN
ejpam-6202	162	1	=	=	PROPN
ejpam-6202	162	2	m	m	PROPN
ejpam-6202	162	3	s(m	s(m	PROPN
ejpam-6202	162	4	,	,	PUNCT
ejpam-6202	162	5	k	k	NOUN
ejpam-6202	162	6	)	)	PUNCT
ejpam-6202	162	7	(	(	PUNCT
ejpam-6202	162	8	j	j	PROPN
ejpam-6202	162	9	m	m	NOUN
ejpam-6202	162	10	)	)	PUNCT
ejpam-6202	162	11	gj−m	gj−m	NOUN
ejpam-6202	162	12	1	1	NUM
ejpam-6202	162	13	(	(	PUNCT
ejpam-6202	162	14	n−	n−	NOUN
ejpam-6202	162	15	j)!j	j)!j	PROPN
ejpam-6202	162	16	!	!	PUNCT
ejpam-6202	163	1	(	(	PUNCT
ejpam-6202	163	2	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	163	3			ADV
ejpam-6202	163	4	tn	tn	NOUN
ejpam-6202	164	1	=	=	PUNCT
ejpam-6202	164	2	∞∑	∞∑	NUM
ejpam-6202	164	3	n=0	n=0	NUM
ejpam-6202	164	4			PUNCT
ejpam-6202	164	5	n∑	n∑	PROPN
ejpam-6202	164	6	m=0	m=0	PROPN
ejpam-6202	164	7	n∑	n∑	PROPN
ejpam-6202	164	8	j	j	PROPN
ejpam-6202	165	1	=	=	PROPN
ejpam-6202	165	2	m	m	PROPN
ejpam-6202	165	3	s(m	s(m	PROPN
ejpam-6202	165	4	,	,	PUNCT
ejpam-6202	165	5	k	k	NOUN
ejpam-6202	165	6	)	)	PUNCT
ejpam-6202	165	7	(	(	PUNCT
ejpam-6202	165	8	j	j	PROPN
ejpam-6202	165	9	m	m	NOUN
ejpam-6202	165	10	)	)	PUNCT
ejpam-6202	165	11	gj−m	gj−m	NOUN
ejpam-6202	165	12	(	(	PUNCT
ejpam-6202	165	13	n	n	NOUN
ejpam-6202	165	14	j	j	PROPN
ejpam-6202	165	15	)	)	PUNCT
ejpam-6202	165	16	(	(	PUNCT
ejpam-6202	165	17	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	165	18			PROPN
ejpam-6202	165	19	tn	tn	PROPN
ejpam-6202	165	20	n	n	CCONJ
ejpam-6202	165	21	!	!	PUNCT
ejpam-6202	166	1	comparing	compare	VERB
ejpam-6202	166	2	the	the	DET
ejpam-6202	166	3	coefficients	coefficient	NOUN
ejpam-6202	166	4	of	of	ADP
ejpam-6202	166	5	tn	tn	NOUN
ejpam-6202	166	6	n	n	CCONJ
ejpam-6202	166	7	!	!	PUNCT
ejpam-6202	166	8	,	,	PUNCT
ejpam-6202	166	9	sg1	sg1	PROPN
ejpam-6202	166	10	n(k	n(k	PROPN
ejpam-6202	166	11	;	;	PUNCT
ejpam-6202	167	1	r	r	X
ejpam-6202	167	2	)	)	PUNCT
ejpam-6202	167	3	=	=	SYM
ejpam-6202	167	4	n∑	n∑	PROPN
ejpam-6202	167	5	m=0	m=0	PROPN
ejpam-6202	167	6	n∑	n∑	PROPN
ejpam-6202	167	7	j	j	PROPN
ejpam-6202	167	8	=	=	PROPN
ejpam-6202	167	9	m	m	PROPN
ejpam-6202	167	10	s(m	s(m	PROPN
ejpam-6202	167	11	,	,	PUNCT
ejpam-6202	167	12	k	k	NOUN
ejpam-6202	167	13	)	)	PUNCT
ejpam-6202	167	14	(	(	PUNCT
ejpam-6202	167	15	j	j	PROPN
ejpam-6202	167	16	m	m	NOUN
ejpam-6202	167	17	)	)	PUNCT
ejpam-6202	167	18	gj−m	gj−m	NOUN
ejpam-6202	167	19	(	(	PUNCT
ejpam-6202	167	20	n	n	NOUN
ejpam-6202	167	21	j	j	PROPN
ejpam-6202	167	22	)	)	PUNCT
ejpam-6202	167	23	(	(	PUNCT
ejpam-6202	167	24	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	167	25	using	use	VERB
ejpam-6202	167	26	the	the	DET
ejpam-6202	167	27	schlömilch	schlömilch	NOUN
ejpam-6202	167	28	formula	formula	NOUN
ejpam-6202	167	29	for	for	ADP
ejpam-6202	167	30	the	the	DET
ejpam-6202	167	31	stirling	stirling	NOUN
ejpam-6202	167	32	numbers	number	NOUN
ejpam-6202	167	33	of	of	ADP
ejpam-6202	167	34	the	the	DET
ejpam-6202	167	35	first	first	ADJ
ejpam-6202	167	36	kind	kind	NOUN
ejpam-6202	167	37	,	,	PUNCT
ejpam-6202	167	38	s(n	s(n	PROPN
ejpam-6202	167	39	,	,	PUNCT
ejpam-6202	167	40	k	k	NOUN
ejpam-6202	167	41	)	)	PUNCT
ejpam-6202	167	42	=	=	PUNCT
ejpam-6202	168	1	n−k∑	n−k∑	NOUN
ejpam-6202	168	2	r=0	r=0	VERB
ejpam-6202	168	3	r∑	r∑	PRON
ejpam-6202	168	4	j	j	X
ejpam-6202	169	1	=	=	NOUN
ejpam-6202	169	2	i	i	PROPN
ejpam-6202	169	3	(	(	PUNCT
ejpam-6202	169	4	−1)j+r	−1)j+r	NOUN
ejpam-6202	169	5	(	(	PUNCT
ejpam-6202	169	6	r	r	NOUN
ejpam-6202	169	7	j	j	PROPN
ejpam-6202	169	8	)	)	PUNCT
ejpam-6202	169	9	(	(	PUNCT
ejpam-6202	169	10	n−	n−	NOUN
ejpam-6202	169	11	1	1	NUM
ejpam-6202	169	12	+	+	CCONJ
ejpam-6202	169	13	r	r	NOUN
ejpam-6202	169	14	n−	n−	NOUN
ejpam-6202	169	15	k	k	NOUN
ejpam-6202	169	16	+	+	CCONJ
ejpam-6202	169	17	r	r	NOUN
ejpam-6202	169	18	)	)	PUNCT
ejpam-6202	169	19	(	(	PUNCT
ejpam-6202	169	20	2n−	2n−	NUM
ejpam-6202	169	21	k	k	NOUN
ejpam-6202	169	22	n−	n−	NOUN
ejpam-6202	169	23	k	k	NOUN
ejpam-6202	170	1	+	+	CCONJ
ejpam-6202	170	2	r	r	NOUN
ejpam-6202	170	3	)	)	PUNCT
ejpam-6202	170	4	(	(	PUNCT
ejpam-6202	170	5	r	r	NOUN
ejpam-6202	170	6	−	−	PROPN
ejpam-6202	170	7	j)n−k+r	j)n−k+r	PROPN
ejpam-6202	170	8	r	r	NOUN
ejpam-6202	170	9	!	!	PUNCT
ejpam-6202	171	1	then	then	ADV
ejpam-6202	171	2	the	the	DET
ejpam-6202	171	3	schlömilch	schlömilch	ADJ
ejpam-6202	171	4	formula	formula	NOUN
ejpam-6202	171	5	for	for	ADP
ejpam-6202	171	6	the	the	DET
ejpam-6202	171	7	r	r	NOUN
ejpam-6202	171	8	-	-	PUNCT
ejpam-6202	171	9	stirling	stirling	NOUN
ejpam-6202	171	10	genocchi	genocchi	PROPN
ejpam-6202	171	11	number	number	NOUN
ejpam-6202	171	12	of	of	ADP
ejpam-6202	171	13	the	the	DET
ejpam-6202	171	14	first	first	ADJ
ejpam-6202	171	15	kind	kind	NOUN
ejpam-6202	171	16	is	be	AUX
ejpam-6202	171	17	given	give	VERB
ejpam-6202	171	18	by	by	ADP
ejpam-6202	171	19	sg1	sg1	NOUN
ejpam-6202	171	20	n(k	n(k	PROPN
ejpam-6202	171	21	;	;	PUNCT
ejpam-6202	171	22	r	r	X
ejpam-6202	171	23	)	)	PUNCT
ejpam-6202	171	24	=	=	SYM
ejpam-6202	171	25	n∑	n∑	PROPN
ejpam-6202	171	26	m=0	m=0	PROPN
ejpam-6202	171	27	n∑	n∑	PROPN
ejpam-6202	171	28	j	j	PROPN
ejpam-6202	171	29	=	=	NOUN
ejpam-6202	171	30	m	m	PROPN
ejpam-6202	171	31	(	(	PUNCT
ejpam-6202	171	32	j	j	PROPN
ejpam-6202	171	33	m	m	NOUN
ejpam-6202	171	34	)	)	PUNCT
ejpam-6202	171	35	gj−m	gj−m	NOUN
ejpam-6202	171	36	(	(	PUNCT
ejpam-6202	171	37	n	n	NOUN
ejpam-6202	171	38	j	j	PROPN
ejpam-6202	171	39	)	)	PUNCT
ejpam-6202	171	40	(	(	PUNCT
ejpam-6202	171	41	−1)n−jrn−j	−1)n−jrn−j	ADV
ejpam-6202	171	42	m−k∑	m−k∑	X
ejpam-6202	172	1	f=0	f=0	X
ejpam-6202	172	2	f∑	f∑	PROPN
ejpam-6202	173	1	d	d	X
ejpam-6202	174	1	=	=	X
ejpam-6202	174	2	i	i	PROPN
ejpam-6202	174	3	(	(	PUNCT
ejpam-6202	174	4	−1)d+f	−1)d+f	X
ejpam-6202	174	5	(	(	PUNCT
ejpam-6202	174	6	f	f	NOUN
ejpam-6202	174	7	d	d	PROPN
ejpam-6202	174	8	)	)	PUNCT
ejpam-6202	174	9	(	(	PUNCT
ejpam-6202	174	10	m−	m−	PROPN
ejpam-6202	174	11	1	1	NUM
ejpam-6202	174	12	+	+	CCONJ
ejpam-6202	174	13	f	f	PROPN
ejpam-6202	174	14	m−	m−	PROPN
ejpam-6202	174	15	k	k	PROPN
ejpam-6202	175	1	+	+	CCONJ
ejpam-6202	175	2	f	f	NOUN
ejpam-6202	175	3	)	)	PUNCT
ejpam-6202	176	1	(	(	PUNCT
ejpam-6202	176	2	2m−	2m−	NUM
ejpam-6202	176	3	k	k	NOUN
ejpam-6202	176	4	m−	m−	PROPN
ejpam-6202	176	5	k	k	PROPN
ejpam-6202	177	1	+	+	CCONJ
ejpam-6202	177	2	f	f	PROPN
ejpam-6202	177	3	)	)	PUNCT
ejpam-6202	178	1	(	(	PUNCT
ejpam-6202	178	2	f	f	X
ejpam-6202	178	3	−	−	PROPN
ejpam-6202	178	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	178	5	f	f	X
ejpam-6202	178	6	!	!	PUNCT
ejpam-6202	179	1	=	=	PUNCT
ejpam-6202	180	1	n∑	n∑	PROPN
ejpam-6202	180	2	m=0	m=0	PROPN
ejpam-6202	180	3	n∑	n∑	PROPN
ejpam-6202	180	4	j	j	PROPN
ejpam-6202	181	1	=	=	NOUN
ejpam-6202	181	2	m	m	VERB
ejpam-6202	181	3	m−k∑	m−k∑	X
ejpam-6202	182	1	f=0	f=0	X
ejpam-6202	182	2	f∑	f∑	PROPN
ejpam-6202	183	1	d	d	X
ejpam-6202	184	1	=	=	X
ejpam-6202	184	2	i	i	PROPN
ejpam-6202	184	3	(	(	PUNCT
ejpam-6202	184	4	j	j	PROPN
ejpam-6202	184	5	m	m	NOUN
ejpam-6202	184	6	)	)	PUNCT
ejpam-6202	184	7	gj−m	gj−m	NOUN
ejpam-6202	184	8	(	(	PUNCT
ejpam-6202	184	9	n	n	NOUN
ejpam-6202	184	10	j	j	PROPN
ejpam-6202	184	11	)	)	PUNCT
ejpam-6202	184	12	(	(	PUNCT
ejpam-6202	184	13	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	184	14	(	(	PUNCT
ejpam-6202	184	15	−1)d+f	−1)d+f	NUM
ejpam-6202	184	16	(	(	PUNCT
ejpam-6202	184	17	f	f	NOUN
ejpam-6202	184	18	d	d	PROPN
ejpam-6202	184	19	)	)	PUNCT
ejpam-6202	184	20	(	(	PUNCT
ejpam-6202	184	21	m−	m−	PROPN
ejpam-6202	184	22	1	1	NUM
ejpam-6202	184	23	+	+	CCONJ
ejpam-6202	184	24	f	f	PROPN
ejpam-6202	184	25	m−	m−	PROPN
ejpam-6202	184	26	k	k	PROPN
ejpam-6202	185	1	+	+	CCONJ
ejpam-6202	185	2	f	f	NOUN
ejpam-6202	185	3	)	)	PUNCT
ejpam-6202	186	1	(	(	PUNCT
ejpam-6202	186	2	2m−	2m−	NUM
ejpam-6202	186	3	k	k	NOUN
ejpam-6202	186	4	m−	m−	PROPN
ejpam-6202	186	5	k	k	PROPN
ejpam-6202	187	1	+	+	CCONJ
ejpam-6202	187	2	f	f	PROPN
ejpam-6202	187	3	)	)	PUNCT
ejpam-6202	188	1	(	(	PUNCT
ejpam-6202	188	2	f	f	X
ejpam-6202	188	3	−	−	PROPN
ejpam-6202	188	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	188	5	f	f	X
ejpam-6202	188	6	!	!	PUNCT
ejpam-6202	189	1	9	9	NUM
ejpam-6202	189	2	of	of	ADP
ejpam-6202	189	3	26	26	NUM
ejpam-6202	189	4	=	=	SYM
ejpam-6202	189	5	n∑	n∑	PROPN
ejpam-6202	189	6	m=0	m=0	PROPN
ejpam-6202	189	7	n∑	n∑	PROPN
ejpam-6202	189	8	j	j	PROPN
ejpam-6202	190	1	=	=	NOUN
ejpam-6202	190	2	m	m	VERB
ejpam-6202	190	3	m−k∑	m−k∑	X
ejpam-6202	191	1	f=0	f=0	X
ejpam-6202	191	2	f∑	f∑	PROPN
ejpam-6202	192	1	d	d	X
ejpam-6202	192	2	=	=	X
ejpam-6202	192	3	i	i	PROPN
ejpam-6202	192	4	(	(	PUNCT
ejpam-6202	192	5	−1)n−j+d+fgj−m	−1)n−j+d+fgj−m	PROPN
ejpam-6202	192	6	(	(	PUNCT
ejpam-6202	192	7	j	j	PROPN
ejpam-6202	192	8	m	m	PROPN
ejpam-6202	192	9	)	)	PUNCT
ejpam-6202	192	10	(	(	PUNCT
ejpam-6202	192	11	n	n	X
ejpam-6202	192	12	j	j	NOUN
ejpam-6202	192	13	)	)	PUNCT
ejpam-6202	192	14	(	(	PUNCT
ejpam-6202	192	15	f	f	PROPN
ejpam-6202	192	16	d	d	PROPN
ejpam-6202	192	17	)	)	PUNCT
ejpam-6202	192	18	(	(	PUNCT
ejpam-6202	192	19	m−	m−	PROPN
ejpam-6202	192	20	1	1	NUM
ejpam-6202	192	21	+	+	CCONJ
ejpam-6202	192	22	f	f	PROPN
ejpam-6202	192	23	m−	m−	PROPN
ejpam-6202	192	24	k	k	PROPN
ejpam-6202	193	1	+	+	CCONJ
ejpam-6202	193	2	f	f	NOUN
ejpam-6202	193	3	)	)	PUNCT
ejpam-6202	194	1	(	(	PUNCT
ejpam-6202	194	2	2m−	2m−	NUM
ejpam-6202	194	3	k	k	NOUN
ejpam-6202	194	4	m−	m−	PROPN
ejpam-6202	194	5	k	k	PROPN
ejpam-6202	195	1	+	+	CCONJ
ejpam-6202	195	2	f	f	PROPN
ejpam-6202	195	3	)	)	PUNCT
ejpam-6202	196	1	(	(	PUNCT
ejpam-6202	196	2	f	f	X
ejpam-6202	196	3	−	−	PROPN
ejpam-6202	196	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	196	5	f	f	X
ejpam-6202	196	6	!	!	PUNCT
ejpam-6202	197	1	rn−j	rn−j	PROPN
ejpam-6202	197	2	theorem	theorem	VERB
ejpam-6202	197	3	1.4	1.4	NUM
ejpam-6202	197	4	.	.	PUNCT
ejpam-6202	198	1	the	the	DET
ejpam-6202	198	2	formula	formula	NOUN
ejpam-6202	198	3	for	for	ADP
ejpam-6202	198	4	the	the	DET
ejpam-6202	198	5	second	second	ADJ
ejpam-6202	198	6	kind	kind	NOUN
ejpam-6202	198	7	of	of	ADP
ejpam-6202	198	8	r	r	NOUN
ejpam-6202	198	9	-	-	PUNCT
ejpam-6202	198	10	stirling	stirling	NOUN
ejpam-6202	198	11	genocchi	genocchi	PROPN
ejpam-6202	198	12	numbers	number	NOUN
ejpam-6202	198	13	is	be	AUX
ejpam-6202	198	14	explicitly	explicitly	ADV
ejpam-6202	198	15	defined	define	VERB
ejpam-6202	198	16	by	by	ADP
ejpam-6202	198	17	the	the	DET
ejpam-6202	198	18	following	follow	VERB
ejpam-6202	198	19	formula	formula	NOUN
ejpam-6202	198	20	:	:	PUNCT
ejpam-6202	198	21	sg2	sg2	PROPN
ejpam-6202	198	22	n(k	n(k	PROPN
ejpam-6202	198	23	;	;	PUNCT
ejpam-6202	198	24	r	r	X
ejpam-6202	198	25	)	)	PUNCT
ejpam-6202	198	26	=	=	SYM
ejpam-6202	198	27	n∑	n∑	PROPN
ejpam-6202	198	28	m=0	m=0	PROPN
ejpam-6202	198	29	{	{	PUNCT
ejpam-6202	199	1	m+	m+	NOUN
ejpam-6202	199	2	r	r	NOUN
ejpam-6202	199	3	k	k	PROPN
ejpam-6202	200	1	+	+	CCONJ
ejpam-6202	200	2	r	r	NOUN
ejpam-6202	200	3	}	}	PUNCT
ejpam-6202	200	4	r	r	NOUN
ejpam-6202	200	5	(	(	PUNCT
ejpam-6202	200	6	n	n	NOUN
ejpam-6202	200	7	m	m	NOUN
ejpam-6202	200	8	)	)	PUNCT
ejpam-6202	200	9	gn−m	gn−m	NOUN
ejpam-6202	200	10	proof	proof	NOUN
ejpam-6202	200	11	.	.	PUNCT
ejpam-6202	201	1	the	the	DET
ejpam-6202	201	2	exponential	exponential	ADJ
ejpam-6202	201	3	generating	generating	NOUN
ejpam-6202	201	4	function	function	NOUN
ejpam-6202	201	5	in	in	ADP
ejpam-6202	201	6	(	(	PUNCT
ejpam-6202	201	7	2	2	X
ejpam-6202	201	8	)	)	PUNCT
ejpam-6202	201	9	can	can	AUX
ejpam-6202	201	10	be	be	AUX
ejpam-6202	201	11	written	write	VERB
ejpam-6202	201	12	as	as	ADP
ejpam-6202	201	13	n∑	n∑	PROPN
ejpam-6202	201	14	n≥k	n≥k	PROPN
ejpam-6202	201	15	k!sg2	k!sg2	PROPN
ejpam-6202	201	16	n(k	n(k	PROPN
ejpam-6202	201	17	;	;	PUNCT
ejpam-6202	201	18	r	r	X
ejpam-6202	201	19	)	)	PUNCT
ejpam-6202	201	20	tn	tn	NOUN
ejpam-6202	201	21	n	n	NOUN
ejpam-6202	201	22	!	!	PUNCT
ejpam-6202	202	1	=	=	PUNCT
ejpam-6202	203	1	2tert	2tert	NUM
ejpam-6202	203	2	(	(	PUNCT
ejpam-6202	203	3	et	et	NOUN
ejpam-6202	203	4	+	+	NOUN
ejpam-6202	203	5	1	1	NUM
ejpam-6202	203	6	k∑	k∑	NOUN
ejpam-6202	203	7	i=0	i=0	PROPN
ejpam-6202	204	1	(	(	PUNCT
ejpam-6202	204	2	k	k	NOUN
ejpam-6202	204	3	i	i	PROPN
ejpam-6202	204	4	)	)	PUNCT
ejpam-6202	204	5	(	(	PUNCT
ejpam-6202	204	6	et)k−i(−1)i	et)k−i(−1)i	X
ejpam-6202	204	7	=	=	SYM
ejpam-6202	204	8	2	2	NUM
ejpam-6202	204	9	t	t	NOUN
ejpam-6202	204	10	(	(	PUNCT
ejpam-6202	204	11	et	et	NOUN
ejpam-6202	204	12	+	+	NOUN
ejpam-6202	204	13	1	1	X
ejpam-6202	204	14	)	)	PUNCT
ejpam-6202	204	15	k∑	k∑	NOUN
ejpam-6202	205	1	i=0	i=0	PROPN
ejpam-6202	205	2	(	(	PUNCT
ejpam-6202	205	3	k	k	NOUN
ejpam-6202	205	4	i	i	PROPN
ejpam-6202	205	5	)	)	PUNCT
ejpam-6202	205	6	ert(et)k−i(−1)i	ert(et)k−i(−1)i	PROPN
ejpam-6202	205	7	=	=	SYM
ejpam-6202	205	8	2	2	NUM
ejpam-6202	205	9	t	t	NOUN
ejpam-6202	205	10	(	(	PUNCT
ejpam-6202	205	11	et	et	NOUN
ejpam-6202	205	12	+	+	NOUN
ejpam-6202	205	13	1	1	X
ejpam-6202	205	14	)	)	PUNCT
ejpam-6202	205	15	k∑	k∑	NOUN
ejpam-6202	205	16	i=0	i=0	PROPN
ejpam-6202	205	17	(	(	PUNCT
ejpam-6202	205	18	k	k	NOUN
ejpam-6202	205	19	i	i	PROPN
ejpam-6202	205	20	)	)	PUNCT
ejpam-6202	205	21	ert+(k−i)t(−1)i	ert+(k−i)t(−1)i	X
ejpam-6202	206	1	=	=	SYM
ejpam-6202	206	2	k∑	k∑	PROPN
ejpam-6202	206	3	i=0	i=0	PROPN
ejpam-6202	206	4	(	(	PUNCT
ejpam-6202	206	5	k	k	NOUN
ejpam-6202	206	6	i	i	PROPN
ejpam-6202	206	7	)	)	PUNCT
ejpam-6202	206	8	ert(et)k−i(−1)i	ert(et)k−i(−1)i	VERB
ejpam-6202	206	9	∞∑	∞∑	DET
ejpam-6202	206	10	n=0	n=0	NUM
ejpam-6202	206	11	gn	gn	PROPN
ejpam-6202	206	12	tn	tn	PROPN
ejpam-6202	206	13	n	n	PROPN
ejpam-6202	206	14	!	!	PUNCT
ejpam-6202	207	1	=	=	PUNCT
ejpam-6202	208	1			PROPN
ejpam-6202	208	2	k∑	k∑	PROPN
ejpam-6202	208	3	i=0	i=0	PROPN
ejpam-6202	208	4	(	(	PUNCT
ejpam-6202	208	5	k	k	NOUN
ejpam-6202	208	6	i	i	PROPN
ejpam-6202	208	7	)	)	PUNCT
ejpam-6202	208	8	∑	∑	PROPN
ejpam-6202	208	9	n≥0	n≥0	ADP
ejpam-6202	208	10	[	[	X
ejpam-6202	208	11	(	(	PUNCT
ejpam-6202	208	12	(	(	PUNCT
ejpam-6202	208	13	k	k	NOUN
ejpam-6202	208	14	−	−	PROPN
ejpam-6202	208	15	i	i	PROPN
ejpam-6202	208	16	)	)	PUNCT
ejpam-6202	208	17	+	+	NUM
ejpam-6202	208	18	r)t]n	r)t]n	NOUN
ejpam-6202	208	19	n	n	CCONJ
ejpam-6202	208	20	!	!	PUNCT
ejpam-6202	209	1	(	(	PUNCT
ejpam-6202	209	2	−1)i	−1)i	X
ejpam-6202	209	3			PROPN
ejpam-6202	209	4	(	(	PUNCT
ejpam-6202	209	5	∞∑	∞∑	PROPN
ejpam-6202	209	6	n=0	n=0	NUM
ejpam-6202	209	7	gn	gn	PROPN
ejpam-6202	209	8	tn	tn	PROPN
ejpam-6202	209	9	n	n	PROPN
ejpam-6202	209	10	!	!	PUNCT
ejpam-6202	209	11	)	)	PUNCT
ejpam-6202	210	1	=	=	PUNCT
ejpam-6202	211	1			PROPN
ejpam-6202	211	2	∞∑	∞∑	NUM
ejpam-6202	211	3	n≥0	n≥0	PROPN
ejpam-6202	211	4	{	{	PUNCT
ejpam-6202	211	5	k∑	k∑	NOUN
ejpam-6202	211	6	i=0	i=0	PROPN
ejpam-6202	211	7	(	(	PUNCT
ejpam-6202	211	8	−1)i	−1)i	X
ejpam-6202	211	9	(	(	PUNCT
ejpam-6202	211	10	k	k	X
ejpam-6202	211	11	i	i	PROPN
ejpam-6202	211	12	)	)	PUNCT
ejpam-6202	211	13	(	(	PUNCT
ejpam-6202	211	14	(	(	PUNCT
ejpam-6202	211	15	k	k	X
ejpam-6202	211	16	−	−	PROPN
ejpam-6202	211	17	i	i	PROPN
ejpam-6202	211	18	)	)	PUNCT
ejpam-6202	211	19	+	+	PUNCT
ejpam-6202	211	20	r)n	r)n	X
ejpam-6202	211	21	}	}	PUNCT
ejpam-6202	211	22	tn	tn	PROPN
ejpam-6202	211	23	n	n	NOUN
ejpam-6202	211	24	!	!	PUNCT
ejpam-6202	212	1			PROPN
ejpam-6202	212	2	(	(	PUNCT
ejpam-6202	212	3	∞∑	∞∑	PROPN
ejpam-6202	212	4	n=0	n=0	NUM
ejpam-6202	212	5	gn	gn	PROPN
ejpam-6202	212	6	tn	tn	PROPN
ejpam-6202	212	7	n	n	PROPN
ejpam-6202	212	8	!	!	PUNCT
ejpam-6202	212	9	)	)	PUNCT
ejpam-6202	213	1	=	=	PUNCT
ejpam-6202	214	1			PROPN
ejpam-6202	214	2	∞∑	∞∑	NUM
ejpam-6202	214	3	n≥0	n≥0	PROPN
ejpam-6202	214	4	k	k	NOUN
ejpam-6202	214	5	!	!	PUNCT
ejpam-6202	214	6	{	{	PUNCT
ejpam-6202	215	1	n+	n+	ADP
ejpam-6202	215	2	r	r	NOUN
ejpam-6202	215	3	k	k	NOUN
ejpam-6202	216	1	+	+	CCONJ
ejpam-6202	216	2	r	r	NOUN
ejpam-6202	216	3	}	}	PUNCT
ejpam-6202	216	4	r	r	NOUN
ejpam-6202	216	5	tn	tn	NOUN
ejpam-6202	216	6	n	n	ADV
ejpam-6202	216	7	!	!	PUNCT
ejpam-6202	217	1			PROPN
ejpam-6202	217	2	(	(	PUNCT
ejpam-6202	217	3	∞∑	∞∑	PROPN
ejpam-6202	217	4	n=0	n=0	NUM
ejpam-6202	217	5	gn	gn	PROPN
ejpam-6202	217	6	tn	tn	PROPN
ejpam-6202	217	7	n	n	PROPN
ejpam-6202	217	8	!	!	PUNCT
ejpam-6202	217	9	)	)	PUNCT
ejpam-6202	218	1	=	=	PUNCT
ejpam-6202	219	1	∞∑	∞∑	NUM
ejpam-6202	219	2	n=0	n=0	NUM
ejpam-6202	219	3	n∑	n∑	NOUN
ejpam-6202	219	4	m=0	m=0	PROPN
ejpam-6202	219	5	k	k	PROPN
ejpam-6202	219	6	!	!	PUNCT
ejpam-6202	219	7	{	{	PUNCT
ejpam-6202	220	1	m+	m+	NOUN
ejpam-6202	221	1	r	r	NOUN
ejpam-6202	221	2	k	k	PROPN
ejpam-6202	222	1	+	+	CCONJ
ejpam-6202	222	2	r	r	NOUN
ejpam-6202	222	3	}	}	PUNCT
ejpam-6202	222	4	r	r	NOUN
ejpam-6202	222	5	tm	tm	PROPN
ejpam-6202	222	6	m	m	PROPN
ejpam-6202	222	7	!	!	PUNCT
ejpam-6202	222	8	gn−m	gn−m	PROPN
ejpam-6202	222	9	tn−m	tn−m	PROPN
ejpam-6202	222	10	(	(	PUNCT
ejpam-6202	222	11	n−m	n−m	PROPN
ejpam-6202	222	12	)	)	PUNCT
ejpam-6202	222	13	!	!	PUNCT
ejpam-6202	223	1	=	=	PUNCT
ejpam-6202	224	1	∞∑	∞∑	PRON
ejpam-6202	224	2	n=0	n=0	PRON
ejpam-6202	224	3	{	{	PUNCT
ejpam-6202	224	4	n∑	n∑	NOUN
ejpam-6202	224	5	m=0	m=0	PROPN
ejpam-6202	224	6	k	k	PROPN
ejpam-6202	224	7	!	!	PUNCT
ejpam-6202	224	8	{	{	PUNCT
ejpam-6202	225	1	m+	m+	NOUN
ejpam-6202	226	1	r	r	NOUN
ejpam-6202	226	2	k	k	PROPN
ejpam-6202	227	1	+	+	CCONJ
ejpam-6202	227	2	r	r	NOUN
ejpam-6202	227	3	}	}	PUNCT
ejpam-6202	227	4	r	r	NOUN
ejpam-6202	227	5	1	1	NUM
ejpam-6202	227	6	(	(	PUNCT
ejpam-6202	227	7	n−m)!m	n−m)!m	PROPN
ejpam-6202	227	8	!	!	PROPN
ejpam-6202	227	9	gn−m	gn−m	NOUN
ejpam-6202	227	10	}	}	PUNCT
ejpam-6202	227	11	tn	tn	PROPN
ejpam-6202	227	12	10	10	NUM
ejpam-6202	227	13	of	of	ADP
ejpam-6202	227	14	26	26	NUM
ejpam-6202	227	15	=	=	NOUN
ejpam-6202	227	16	∞∑	∞∑	NUM
ejpam-6202	227	17	n=0	n=0	PRON
ejpam-6202	227	18	{	{	PUNCT
ejpam-6202	227	19	n∑	n∑	NOUN
ejpam-6202	227	20	m=0	m=0	PROPN
ejpam-6202	227	21	k	k	PROPN
ejpam-6202	227	22	!	!	PUNCT
ejpam-6202	227	23	{	{	PUNCT
ejpam-6202	228	1	m+	m+	NOUN
ejpam-6202	229	1	r	r	NOUN
ejpam-6202	229	2	k	k	PROPN
ejpam-6202	230	1	+	+	CCONJ
ejpam-6202	230	2	r	r	NOUN
ejpam-6202	230	3	}	}	PUNCT
ejpam-6202	230	4	r	r	NOUN
ejpam-6202	230	5	(	(	PUNCT
ejpam-6202	230	6	n	n	NOUN
ejpam-6202	230	7	m	m	NOUN
ejpam-6202	230	8	)	)	PUNCT
ejpam-6202	230	9	gn−m	gn−m	NOUN
ejpam-6202	230	10	}	}	PUNCT
ejpam-6202	230	11	tn	tn	PROPN
ejpam-6202	230	12	n	n	CCONJ
ejpam-6202	230	13	!	!	PUNCT
ejpam-6202	230	14	comparing	compare	VERB
ejpam-6202	230	15	the	the	DET
ejpam-6202	230	16	coefficients	coefficient	NOUN
ejpam-6202	230	17	of	of	ADP
ejpam-6202	230	18	tn	tn	NOUN
ejpam-6202	230	19	n	n	CCONJ
ejpam-6202	230	20	!	!	PROPN
ejpam-6202	230	21	,	,	PUNCT
ejpam-6202	230	22	we	we	PRON
ejpam-6202	230	23	have	have	VERB
ejpam-6202	230	24	k!sg2	k!sg2	PROPN
ejpam-6202	230	25	n(k	n(k	PROPN
ejpam-6202	230	26	;	;	PUNCT
ejpam-6202	231	1	r	r	X
ejpam-6202	231	2	)	)	PUNCT
ejpam-6202	231	3	=	=	SYM
ejpam-6202	231	4	n∑	n∑	PROPN
ejpam-6202	231	5	m=0	m=0	PROPN
ejpam-6202	231	6	k	k	PROPN
ejpam-6202	231	7	!	!	PUNCT
ejpam-6202	231	8	{	{	PUNCT
ejpam-6202	232	1	m+	m+	NOUN
ejpam-6202	233	1	r	r	NOUN
ejpam-6202	233	2	k	k	PROPN
ejpam-6202	234	1	+	+	CCONJ
ejpam-6202	234	2	r	r	NOUN
ejpam-6202	234	3	}	}	PUNCT
ejpam-6202	234	4	r	r	NOUN
ejpam-6202	234	5	(	(	PUNCT
ejpam-6202	234	6	n	n	NOUN
ejpam-6202	234	7	m	m	NOUN
ejpam-6202	234	8	)	)	PUNCT
ejpam-6202	234	9	gn−m	gn−m	NOUN
ejpam-6202	234	10	sg2	sg2	PROPN
ejpam-6202	234	11	n(k	n(k	PROPN
ejpam-6202	234	12	;	;	PUNCT
ejpam-6202	234	13	r	r	X
ejpam-6202	234	14	)	)	PUNCT
ejpam-6202	235	1	=	=	SYM
ejpam-6202	235	2	n∑	n∑	PROPN
ejpam-6202	235	3	m=0	m=0	PROPN
ejpam-6202	235	4	{	{	PUNCT
ejpam-6202	236	1	m+	m+	NOUN
ejpam-6202	237	1	r	r	NOUN
ejpam-6202	237	2	k	k	PROPN
ejpam-6202	238	1	+	+	CCONJ
ejpam-6202	238	2	r	r	NOUN
ejpam-6202	238	3	}	}	PUNCT
ejpam-6202	238	4	r	r	NOUN
ejpam-6202	238	5	(	(	PUNCT
ejpam-6202	238	6	n	n	NOUN
ejpam-6202	238	7	m	m	NOUN
ejpam-6202	238	8	)	)	PUNCT
ejpam-6202	238	9	gn−m	gn−m	VERB
ejpam-6202	238	10	the	the	DET
ejpam-6202	238	11	following	follow	VERB
ejpam-6202	238	12	sections	section	NOUN
ejpam-6202	238	13	investigates	investigate	VERB
ejpam-6202	238	14	the	the	DET
ejpam-6202	238	15	convolutions	convolution	NOUN
ejpam-6202	238	16	of	of	ADP
ejpam-6202	238	17	r	r	NOUN
ejpam-6202	238	18	-	-	PUNCT
ejpam-6202	238	19	stirling	stirling	NOUN
ejpam-6202	238	20	numbers	number	NOUN
ejpam-6202	238	21	with	with	ADP
ejpam-6202	238	22	the	the	DET
ejpam-6202	238	23	genocchi	genocchi	PROPN
ejpam-6202	238	24	polynomials	polynomial	NOUN
ejpam-6202	238	25	and	and	CCONJ
ejpam-6202	238	26	higher	high	ADJ
ejpam-6202	238	27	order	order	NOUN
ejpam-6202	238	28	genocchi	genocchi	NOUN
ejpam-6202	238	29	polynomials	polynomial	NOUN
ejpam-6202	238	30	.	.	PUNCT
ejpam-6202	239	1	2	2	X
ejpam-6202	239	2	.	.	X
ejpam-6202	239	3	r	r	X
ejpam-6202	239	4	-	-	PUNCT
ejpam-6202	239	5	stirling	stirling	NOUN
ejpam-6202	239	6	genocchi	genocchi	PROPN
ejpam-6202	239	7	polynomials	polynomial	VERB
ejpam-6202	239	8	the	the	DET
ejpam-6202	239	9	genocchi	genocchi	PROPN
ejpam-6202	239	10	polynomials	polynomial	NOUN
ejpam-6202	239	11	satisfy	satisfy	VERB
ejpam-6202	239	12	the	the	DET
ejpam-6202	239	13	relation	relation	NOUN
ejpam-6202	239	14	∞∑	∞∑	ADJ
ejpam-6202	239	15	n=0	n=0	NUM
ejpam-6202	239	16	gn(x	gn(x	NUM
ejpam-6202	239	17	)	)	PUNCT
ejpam-6202	239	18	tn	tn	NOUN
ejpam-6202	239	19	n	n	NOUN
ejpam-6202	239	20	!	!	PUNCT
ejpam-6202	240	1	=	=	PUNCT
ejpam-6202	241	1	2	2	NUM
ejpam-6202	241	2	t	t	NOUN
ejpam-6202	241	3	et	et	NOUN
ejpam-6202	241	4	+	+	NOUN
ejpam-6202	241	5	1	1	NUM
ejpam-6202	241	6	ext	ext	NOUN
ejpam-6202	241	7	the	the	DET
ejpam-6202	241	8	r	r	NOUN
ejpam-6202	241	9	-	-	PUNCT
ejpam-6202	241	10	stirling	stirling	NOUN
ejpam-6202	241	11	genocchi	genocchi	PROPN
ejpam-6202	241	12	polynomials	polynomial	NOUN
ejpam-6202	241	13	defined	define	VERB
ejpam-6202	241	14	by	by	ADP
ejpam-6202	241	15	means	mean	NOUN
ejpam-6202	241	16	of	of	ADP
ejpam-6202	241	17	exponential	exponential	ADJ
ejpam-6202	241	18	generating	generating	NOUN
ejpam-6202	241	19	function	function	NOUN
ejpam-6202	241	20	are	be	AUX
ejpam-6202	241	21	as	as	SCONJ
ejpam-6202	241	22	follows	follow	VERB
ejpam-6202	241	23	:	:	PUNCT
ejpam-6202	241	24	∞∑	∞∑	NUM
ejpam-6202	241	25	n=0	n=0	NUM
ejpam-6202	241	26	sg1	sg1	NOUN
ejpam-6202	241	27	n(x	n(x	PROPN
ejpam-6202	241	28	;	;	PUNCT
ejpam-6202	241	29	k	k	X
ejpam-6202	241	30	;	;	PUNCT
ejpam-6202	241	31	r	r	X
ejpam-6202	241	32	)	)	PUNCT
ejpam-6202	241	33	tn	tn	NOUN
ejpam-6202	241	34	n	n	NOUN
ejpam-6202	241	35	!	!	PUNCT
ejpam-6202	242	1	=	=	PUNCT
ejpam-6202	242	2	(	(	PUNCT
ejpam-6202	242	3	1	1	NUM
ejpam-6202	242	4	1	1	NUM
ejpam-6202	242	5	+	+	NUM
ejpam-6202	242	6	t	t	NOUN
ejpam-6202	242	7	)	)	PUNCT
ejpam-6202	242	8	r	r	NOUN
ejpam-6202	242	9	2text	2text	NUM
ejpam-6202	242	10	lnk(1	lnk(1	NOUN
ejpam-6202	242	11	+	+	CCONJ
ejpam-6202	242	12	t	t	NOUN
ejpam-6202	242	13	)	)	PUNCT
ejpam-6202	242	14	k!(et	k!(et	NOUN
ejpam-6202	242	15	+	+	NOUN
ejpam-6202	242	16	1	1	NUM
ejpam-6202	242	17	)	)	PUNCT
ejpam-6202	242	18	(	(	PUNCT
ejpam-6202	242	19	7	7	X
ejpam-6202	242	20	)	)	PUNCT
ejpam-6202	242	21	∞∑	∞∑	PROPN
ejpam-6202	242	22	n=0	n=0	PUNCT
ejpam-6202	242	23	sg2	sg2	PROPN
ejpam-6202	242	24	n(x	n(x	PROPN
ejpam-6202	242	25	;	;	PUNCT
ejpam-6202	242	26	k	k	X
ejpam-6202	242	27	;	;	PUNCT
ejpam-6202	242	28	r	r	X
ejpam-6202	242	29	)	)	PUNCT
ejpam-6202	242	30	tn	tn	NOUN
ejpam-6202	242	31	n	n	NOUN
ejpam-6202	242	32	!	!	PUNCT
ejpam-6202	243	1	=	=	SYM
ejpam-6202	243	2	2textert(et	2textert(et	NUM
ejpam-6202	243	3	−	−	PRON
ejpam-6202	243	4	1)k	1)k	NUM
ejpam-6202	243	5	k!(et	k!(et	NOUN
ejpam-6202	243	6	+	+	CCONJ
ejpam-6202	243	7	1	1	NUM
ejpam-6202	243	8	)	)	PUNCT
ejpam-6202	243	9	(	(	PUNCT
ejpam-6202	243	10	8)	8)	NUM
ejpam-6202	243	11	theorem	theorem	VERB
ejpam-6202	243	12	2.1	2.1	NUM
ejpam-6202	243	13	.	.	PUNCT
ejpam-6202	244	1	convolution	convolution	NOUN
ejpam-6202	244	2	formula	formula	NOUN
ejpam-6202	244	3	of	of	ADP
ejpam-6202	244	4	the	the	DET
ejpam-6202	244	5	r	r	NOUN
ejpam-6202	244	6	-	-	PUNCT
ejpam-6202	244	7	stirling	stirling	NOUN
ejpam-6202	244	8	numbers	number	NOUN
ejpam-6202	244	9	and	and	CCONJ
ejpam-6202	244	10	genocchi	genocchi	PROPN
ejpam-6202	244	11	polynomials	polynomial	NOUN
ejpam-6202	244	12	are	be	AUX
ejpam-6202	244	13	given	give	VERB
ejpam-6202	244	14	as	as	SCONJ
ejpam-6202	244	15	follows	follow	VERB
ejpam-6202	244	16	:	:	PUNCT
ejpam-6202	244	17	sg1	sg1	PROPN
ejpam-6202	244	18	n(x	n(x	PROPN
ejpam-6202	244	19	;	;	PUNCT
ejpam-6202	245	1	k	k	X
ejpam-6202	245	2	,	,	PUNCT
ejpam-6202	245	3	r	r	NOUN
ejpam-6202	245	4	)	)	PUNCT
ejpam-6202	245	5	=	=	SYM
ejpam-6202	245	6	n∑	n∑	PROPN
ejpam-6202	245	7	i=0	i=0	PROPN
ejpam-6202	245	8	n∑	n∑	PROPN
ejpam-6202	245	9	j	j	PROPN
ejpam-6202	246	1	=	=	NOUN
ejpam-6202	246	2	i	i	PROPN
ejpam-6202	246	3	̂	̂	PROPN
ejpam-6202	246	4	[	[	PUNCT
ejpam-6202	246	5	n−	n−	NOUN
ejpam-6202	246	6	j	j	NOUN
ejpam-6202	247	1	+	+	CCONJ
ejpam-6202	247	2	r	r	NOUN
ejpam-6202	247	3	k	k	NOUN
ejpam-6202	248	1	+	+	CCONJ
ejpam-6202	248	2	r	r	NOUN
ejpam-6202	248	3	]	]	X
ejpam-6202	248	4	r	r	NOUN
ejpam-6202	248	5	(	(	PUNCT
ejpam-6202	248	6	n	n	NOUN
ejpam-6202	248	7	j	j	PROPN
ejpam-6202	248	8	)	)	PUNCT
ejpam-6202	248	9	(	(	PUNCT
ejpam-6202	248	10	j	j	PROPN
ejpam-6202	248	11	i	i	PROPN
ejpam-6202	248	12	)	)	PUNCT
ejpam-6202	248	13	gj−ix	gj−ix	NOUN
ejpam-6202	248	14	i	i	PRON
ejpam-6202	248	15	(	(	PUNCT
ejpam-6202	248	16	9	9	X
ejpam-6202	248	17	)	)	PUNCT
ejpam-6202	248	18	sg2	sg2	PROPN
ejpam-6202	248	19	n(x	n(x	PROPN
ejpam-6202	248	20	;	;	PUNCT
ejpam-6202	248	21	k	k	X
ejpam-6202	248	22	,	,	PUNCT
ejpam-6202	248	23	r	r	NOUN
ejpam-6202	248	24	)	)	PUNCT
ejpam-6202	249	1	=	=	SYM
ejpam-6202	249	2	n∑	n∑	PROPN
ejpam-6202	249	3	i=0	i=0	PROPN
ejpam-6202	249	4	n∑	n∑	PROPN
ejpam-6202	249	5	j	j	PROPN
ejpam-6202	250	1	=	=	PRON
ejpam-6202	250	2	i	i	PROPN
ejpam-6202	250	3	{	{	PUNCT
ejpam-6202	250	4	n−	n−	NOUN
ejpam-6202	250	5	j	j	PROPN
ejpam-6202	250	6	+	+	CCONJ
ejpam-6202	250	7	r	r	NOUN
ejpam-6202	250	8	k	k	NOUN
ejpam-6202	250	9	+	+	CCONJ
ejpam-6202	250	10	r	r	NOUN
ejpam-6202	250	11	}	}	PUNCT
ejpam-6202	250	12	r	r	NOUN
ejpam-6202	250	13	(	(	PUNCT
ejpam-6202	250	14	n	n	NOUN
ejpam-6202	250	15	j	j	PROPN
ejpam-6202	250	16	)	)	PUNCT
ejpam-6202	250	17	(	(	PUNCT
ejpam-6202	250	18	j	j	PROPN
ejpam-6202	250	19	i	i	PROPN
ejpam-6202	250	20	)	)	PUNCT
ejpam-6202	250	21	gj−ix	gj−ix	NOUN
ejpam-6202	250	22	i	i	PRON
ejpam-6202	250	23	(	(	PUNCT
ejpam-6202	250	24	10	10	NUM
ejpam-6202	250	25	)	)	PUNCT
ejpam-6202	251	1	where	where	SCONJ
ejpam-6202	251	2	n	n	PRON
ejpam-6202	251	3	≥	≥	NOUN
ejpam-6202	251	4	k	k	NOUN
ejpam-6202	251	5	otherwise	otherwise	ADV
ejpam-6202	251	6	sg1	sg1	VERB
ejpam-6202	251	7	n(k	n(k	PROPN
ejpam-6202	251	8	;	;	PUNCT
ejpam-6202	251	9	r	r	X
ejpam-6202	251	10	)	)	PUNCT
ejpam-6202	252	1	=	=	PUNCT
ejpam-6202	253	1	sg2	sg2	PROPN
ejpam-6202	253	2	n(k	n(k	PROPN
ejpam-6202	253	3	;	;	PUNCT
ejpam-6202	253	4	r	r	X
ejpam-6202	253	5	)	)	PUNCT
ejpam-6202	253	6	=	=	SYM
ejpam-6202	253	7	0	0	NUM
ejpam-6202	253	8	11	11	NUM
ejpam-6202	253	9	of	of	ADP
ejpam-6202	253	10	26	26	NUM
ejpam-6202	253	11	proof	proof	NOUN
ejpam-6202	253	12	.	.	PUNCT
ejpam-6202	254	1	the	the	DET
ejpam-6202	254	2	exponential	exponential	ADJ
ejpam-6202	254	3	generating	generating	NOUN
ejpam-6202	254	4	function	function	NOUN
ejpam-6202	254	5	in	in	ADP
ejpam-6202	254	6	(	(	PUNCT
ejpam-6202	254	7	7	7	X
ejpam-6202	254	8	)	)	PUNCT
ejpam-6202	254	9	can	can	AUX
ejpam-6202	254	10	be	be	AUX
ejpam-6202	254	11	written	write	VERB
ejpam-6202	254	12	as	as	ADP
ejpam-6202	254	13	∞∑	∞∑	NUM
ejpam-6202	254	14	n=0	n=0	NUM
ejpam-6202	254	15	sg1	sg1	NOUN
ejpam-6202	254	16	n(x	n(x	PROPN
ejpam-6202	254	17	;	;	PUNCT
ejpam-6202	254	18	k	k	X
ejpam-6202	254	19	,	,	PUNCT
ejpam-6202	254	20	r	r	NOUN
ejpam-6202	254	21	)	)	PUNCT
ejpam-6202	254	22	tn	tn	NOUN
ejpam-6202	254	23	n	n	NOUN
ejpam-6202	254	24	!	!	PUNCT
ejpam-6202	255	1	=	=	PUNCT
ejpam-6202	255	2	(	(	PUNCT
ejpam-6202	255	3	1	1	NUM
ejpam-6202	255	4	1	1	NUM
ejpam-6202	255	5	+	+	NUM
ejpam-6202	255	6	t	t	NOUN
ejpam-6202	255	7	)	)	PUNCT
ejpam-6202	255	8	r	r	NOUN
ejpam-6202	255	9	2text	2text	NUM
ejpam-6202	255	10	lnk(1	lnk(1	NOUN
ejpam-6202	255	11	+	+	CCONJ
ejpam-6202	255	12	t	t	NOUN
ejpam-6202	255	13	)	)	PUNCT
ejpam-6202	255	14	k!(et	k!(et	NOUN
ejpam-6202	255	15	+	+	NOUN
ejpam-6202	255	16	1	1	X
ejpam-6202	255	17	)	)	PUNCT
ejpam-6202	255	18	=	=	NOUN
ejpam-6202	255	19	(	(	PUNCT
ejpam-6202	255	20	1	1	NUM
ejpam-6202	255	21	1	1	NUM
ejpam-6202	255	22	+	+	NUM
ejpam-6202	255	23	t	t	NOUN
ejpam-6202	255	24	)	)	PUNCT
ejpam-6202	255	25	r	r	NOUN
ejpam-6202	255	26	lnk(1	lnk(1	NOUN
ejpam-6202	255	27	+	+	CCONJ
ejpam-6202	255	28	t	t	X
ejpam-6202	255	29	)	)	PUNCT
ejpam-6202	255	30	k	k	NOUN
ejpam-6202	255	31	!	!	PUNCT
ejpam-6202	256	1	2text	2text	NUM
ejpam-6202	256	2	(	(	PUNCT
ejpam-6202	256	3	et	et	NOUN
ejpam-6202	256	4	+	+	NOUN
ejpam-6202	256	5	1	1	X
ejpam-6202	256	6	)	)	PUNCT
ejpam-6202	256	7	=	=	NOUN
ejpam-6202	256	8	(	(	PUNCT
ejpam-6202	256	9	∞∑	∞∑	NUM
ejpam-6202	256	10	n=0	n=0	NUM
ejpam-6202	257	1	̂[n+	̂[n+	ADP
ejpam-6202	257	2	r	r	NOUN
ejpam-6202	257	3	k	k	NOUN
ejpam-6202	258	1	+	+	CCONJ
ejpam-6202	258	2	r	r	NOUN
ejpam-6202	258	3	]	]	PUNCT
ejpam-6202	258	4	r	r	NOUN
ejpam-6202	258	5	tn	tn	PROPN
ejpam-6202	258	6	n	n	CCONJ
ejpam-6202	258	7	!	!	PUNCT
ejpam-6202	258	8	)	)	PUNCT
ejpam-6202	259	1	(	(	PUNCT
ejpam-6202	259	2	∞∑	∞∑	NUM
ejpam-6202	259	3	n=0	n=0	NUM
ejpam-6202	259	4	gn(x	gn(x	NUM
ejpam-6202	259	5	)	)	PUNCT
ejpam-6202	259	6	tn	tn	NOUN
ejpam-6202	259	7	n	n	CCONJ
ejpam-6202	259	8	!	!	PUNCT
ejpam-6202	259	9	)	)	PUNCT
ejpam-6202	260	1	=	=	PUNCT
ejpam-6202	261	1	∞∑	∞∑	NUM
ejpam-6202	261	2	n=0	n=0	NUM
ejpam-6202	261	3	n∑	n∑	ADV
ejpam-6202	261	4	j=0	j=0	PROPN
ejpam-6202	261	5	̂[j	̂[j	NOUN
ejpam-6202	261	6	+	+	CCONJ
ejpam-6202	261	7	r	r	X
ejpam-6202	261	8	k	k	NOUN
ejpam-6202	262	1	+	+	CCONJ
ejpam-6202	262	2	r	r	NOUN
ejpam-6202	262	3	]	]	PUNCT
ejpam-6202	262	4	r	r	NOUN
ejpam-6202	262	5	tj	tj	PROPN
ejpam-6202	262	6	j	j	PROPN
ejpam-6202	262	7	!	!	PUNCT
ejpam-6202	262	8	gn−j(x	gn−j(x	PROPN
ejpam-6202	262	9	)	)	PUNCT
ejpam-6202	262	10	tn−j	tn−j	NOUN
ejpam-6202	262	11	(	(	PUNCT
ejpam-6202	262	12	n−	n−	NOUN
ejpam-6202	262	13	j	j	NOUN
ejpam-6202	262	14	)	)	PUNCT
ejpam-6202	262	15	!	!	PUNCT
ejpam-6202	263	1	=	=	PUNCT
ejpam-6202	264	1	∞∑	∞∑	PRON
ejpam-6202	264	2	n=0	n=0	NUM
ejpam-6202	264	3	n∑	n∑	PRON
ejpam-6202	264	4	j=0	j=0	PROPN
ejpam-6202	265	1	̂	̂	PROPN
ejpam-6202	265	2	[	[	PUNCT
ejpam-6202	265	3	n−	n−	NOUN
ejpam-6202	265	4	j	j	NOUN
ejpam-6202	266	1	+	+	CCONJ
ejpam-6202	266	2	r	r	NOUN
ejpam-6202	266	3	k	k	NOUN
ejpam-6202	267	1	+	+	CCONJ
ejpam-6202	267	2	r	r	NOUN
ejpam-6202	267	3	]	]	PUNCT
ejpam-6202	267	4	r	r	NOUN
ejpam-6202	267	5	tn−j	tn−j	NOUN
ejpam-6202	267	6	(	(	PUNCT
ejpam-6202	267	7	n−	n−	NOUN
ejpam-6202	267	8	j	j	PROPN
ejpam-6202	267	9	)	)	PUNCT
ejpam-6202	267	10	!	!	PUNCT
ejpam-6202	267	11	gj(x	gj(x	PUNCT
ejpam-6202	267	12	)	)	PUNCT
ejpam-6202	267	13	tj	tj	PROPN
ejpam-6202	267	14	j	j	PROPN
ejpam-6202	267	15	!	!	PUNCT
ejpam-6202	268	1	since	since	SCONJ
ejpam-6202	268	2	gj(x	gj(x	PRON
ejpam-6202	268	3	)	)	PUNCT
ejpam-6202	268	4	=	=	PUNCT
ejpam-6202	268	5	∑j	∑j	PROPN
ejpam-6202	268	6	i=0	i=0	PROPN
ejpam-6202	268	7	(	(	PUNCT
ejpam-6202	268	8	j	j	PROPN
ejpam-6202	268	9	i	i	PROPN
ejpam-6202	268	10	)	)	PUNCT
ejpam-6202	268	11	gix	gix	PROPN
ejpam-6202	268	12	j−i	j−i	PROPN
ejpam-6202	268	13	,	,	PUNCT
ejpam-6202	268	14	then	then	ADV
ejpam-6202	268	15	it	it	PRON
ejpam-6202	268	16	follows	follow	VERB
ejpam-6202	268	17	∞∑	∞∑	NUM
ejpam-6202	268	18	n=0	n=0	NUM
ejpam-6202	268	19	sg1	sg1	NOUN
ejpam-6202	268	20	n(x	n(x	PROPN
ejpam-6202	268	21	;	;	PUNCT
ejpam-6202	268	22	k	k	X
ejpam-6202	268	23	,	,	PUNCT
ejpam-6202	268	24	r	r	NOUN
ejpam-6202	268	25	)	)	PUNCT
ejpam-6202	268	26	tn	tn	NOUN
ejpam-6202	268	27	n	n	NOUN
ejpam-6202	268	28	!	!	PUNCT
ejpam-6202	269	1	=	=	NOUN
ejpam-6202	270	1	∞∑	∞∑	PRON
ejpam-6202	270	2	n=0	n=0	PROPN
ejpam-6202	270	3	n∑	n∑	PRON
ejpam-6202	270	4	j=0	j=0	PROPN
ejpam-6202	270	5	(	(	PUNCT
ejpam-6202	270	6	n	n	X
ejpam-6202	270	7	j	j	PROPN
ejpam-6202	270	8	)	)	PUNCT
ejpam-6202	271	1	̂	̂	VERB
ejpam-6202	271	2	[	[	PUNCT
ejpam-6202	271	3	n−	n−	NOUN
ejpam-6202	271	4	j	j	NOUN
ejpam-6202	271	5	+	+	CCONJ
ejpam-6202	271	6	r	r	NOUN
ejpam-6202	271	7	k	k	NOUN
ejpam-6202	272	1	+	+	CCONJ
ejpam-6202	272	2	r	r	NOUN
ejpam-6202	272	3	]	]	PUNCT
ejpam-6202	272	4	r	r	NOUN
ejpam-6202	272	5	j∑	j∑	PROPN
ejpam-6202	272	6	i=0	i=0	PROPN
ejpam-6202	272	7	(	(	PUNCT
ejpam-6202	272	8	j	j	NOUN
ejpam-6202	272	9	i	i	PROPN
ejpam-6202	272	10	)	)	PUNCT
ejpam-6202	272	11	gj−ix	gj−ix	NOUN
ejpam-6202	273	1	i	i	PRON
ejpam-6202	273	2	t	t	PROPN
ejpam-6202	273	3	n	n	CCONJ
ejpam-6202	273	4	n	n	CCONJ
ejpam-6202	273	5	!	!	PUNCT
ejpam-6202	274	1	=	=	NOUN
ejpam-6202	275	1	∞∑	∞∑	PRON
ejpam-6202	275	2	n=0	n=0	NUM
ejpam-6202	275	3			PUNCT
ejpam-6202	275	4	n∑	n∑	PROPN
ejpam-6202	275	5	i=0	i=0	PROPN
ejpam-6202	275	6	n∑	n∑	PROPN
ejpam-6202	275	7	j	j	PROPN
ejpam-6202	276	1	=	=	NOUN
ejpam-6202	276	2	i	i	PROPN
ejpam-6202	276	3	̂	̂	PROPN
ejpam-6202	276	4	[	[	PUNCT
ejpam-6202	276	5	n−	n−	NOUN
ejpam-6202	276	6	j	j	NOUN
ejpam-6202	277	1	+	+	CCONJ
ejpam-6202	277	2	r	r	NOUN
ejpam-6202	277	3	k	k	NOUN
ejpam-6202	278	1	+	+	CCONJ
ejpam-6202	278	2	r	r	NOUN
ejpam-6202	278	3	]	]	X
ejpam-6202	278	4	r	r	NOUN
ejpam-6202	278	5	(	(	PUNCT
ejpam-6202	278	6	n	n	NOUN
ejpam-6202	278	7	j	j	PROPN
ejpam-6202	278	8	)	)	PUNCT
ejpam-6202	278	9	(	(	PUNCT
ejpam-6202	278	10	j	j	PROPN
ejpam-6202	278	11	i	i	PROPN
ejpam-6202	278	12	)	)	PUNCT
ejpam-6202	278	13	gj−ix	gj−ix	NOUN
ejpam-6202	279	1	i	i	PRON
ejpam-6202	279	2			PROPN
ejpam-6202	279	3	tn	tn	PROPN
ejpam-6202	279	4	n	n	CCONJ
ejpam-6202	279	5	!	!	PUNCT
ejpam-6202	280	1	comparing	compare	VERB
ejpam-6202	280	2	the	the	DET
ejpam-6202	280	3	coefficients	coefficient	NOUN
ejpam-6202	280	4	of	of	ADP
ejpam-6202	280	5	tn	tn	NOUN
ejpam-6202	280	6	n	n	X
ejpam-6202	280	7	!	!	PUNCT
ejpam-6202	281	1	yields	yield	VERB
ejpam-6202	281	2	the	the	DET
ejpam-6202	281	3	desired	desire	VERB
ejpam-6202	281	4	convolution	convolution	NOUN
ejpam-6202	281	5	formula	formula	NOUN
ejpam-6202	281	6	in	in	ADP
ejpam-6202	281	7	(	(	PUNCT
ejpam-6202	281	8	9	9	NUM
ejpam-6202	281	9	)	)	PUNCT
ejpam-6202	281	10	.	.	PUNCT
ejpam-6202	282	1	on	on	ADP
ejpam-6202	282	2	the	the	DET
ejpam-6202	282	3	other	other	ADJ
ejpam-6202	282	4	hand	hand	NOUN
ejpam-6202	282	5	,	,	PUNCT
ejpam-6202	282	6	the	the	DET
ejpam-6202	282	7	exponential	exponential	ADJ
ejpam-6202	282	8	generating	generating	NOUN
ejpam-6202	282	9	function	function	NOUN
ejpam-6202	282	10	in	in	ADP
ejpam-6202	282	11	(	(	PUNCT
ejpam-6202	282	12	8)	8)	NUM
ejpam-6202	282	13	can	can	AUX
ejpam-6202	282	14	be	be	AUX
ejpam-6202	282	15	written	write	VERB
ejpam-6202	282	16	as	as	ADP
ejpam-6202	282	17	∞∑	∞∑	NUM
ejpam-6202	282	18	n=0	n=0	NUM
ejpam-6202	282	19	sg2	sg2	PROPN
ejpam-6202	282	20	n(x	n(x	PROPN
ejpam-6202	282	21	;	;	PUNCT
ejpam-6202	282	22	k	k	X
ejpam-6202	282	23	,	,	PUNCT
ejpam-6202	282	24	r	r	NOUN
ejpam-6202	282	25	)	)	PUNCT
ejpam-6202	282	26	tn	tn	NOUN
ejpam-6202	282	27	n	n	NOUN
ejpam-6202	282	28	!	!	PUNCT
ejpam-6202	283	1	=	=	SYM
ejpam-6202	283	2	2textert(et	2textert(et	NUM
ejpam-6202	283	3	−	−	PRON
ejpam-6202	283	4	1)k	1)k	NUM
ejpam-6202	283	5	k!(et	k!(et	NOUN
ejpam-6202	283	6	+	+	CCONJ
ejpam-6202	283	7	1	1	X
ejpam-6202	283	8	)	)	PUNCT
ejpam-6202	283	9	=	=	NOUN
ejpam-6202	283	10	ert(et	ert(et	X
ejpam-6202	283	11	−	−	PROPN
ejpam-6202	283	12	1)k	1)k	NUM
ejpam-6202	283	13	k	k	NOUN
ejpam-6202	283	14	!	!	PUNCT
ejpam-6202	284	1	2text	2text	NUM
ejpam-6202	284	2	(	(	PUNCT
ejpam-6202	284	3	et	et	NOUN
ejpam-6202	284	4	+	+	NOUN
ejpam-6202	284	5	1	1	X
ejpam-6202	284	6	)	)	PUNCT
ejpam-6202	284	7	=	=	NOUN
ejpam-6202	285	1	(	(	PUNCT
ejpam-6202	285	2	∞∑	∞∑	NUM
ejpam-6202	285	3	n=0	n=0	NUM
ejpam-6202	285	4	{	{	PUNCT
ejpam-6202	285	5	n+	n+	ADP
ejpam-6202	285	6	r	r	NOUN
ejpam-6202	285	7	k	k	NOUN
ejpam-6202	285	8	+	+	CCONJ
ejpam-6202	285	9	r	r	NOUN
ejpam-6202	285	10	}	}	PUNCT
ejpam-6202	285	11	r	r	NOUN
ejpam-6202	285	12	tn	tn	NOUN
ejpam-6202	285	13	n	n	CCONJ
ejpam-6202	285	14	!	!	PUNCT
ejpam-6202	285	15	)	)	PUNCT
ejpam-6202	286	1	(	(	PUNCT
ejpam-6202	286	2	∞∑	∞∑	NUM
ejpam-6202	286	3	n=0	n=0	NUM
ejpam-6202	286	4	gn(x	gn(x	NUM
ejpam-6202	286	5	)	)	PUNCT
ejpam-6202	286	6	tn	tn	NOUN
ejpam-6202	286	7	n	n	CCONJ
ejpam-6202	286	8	!	!	PUNCT
ejpam-6202	286	9	)	)	PUNCT
ejpam-6202	287	1	=	=	PUNCT
ejpam-6202	288	1	∞∑	∞∑	NUM
ejpam-6202	288	2	n=0	n=0	PROPN
ejpam-6202	288	3	n∑	n∑	PRON
ejpam-6202	288	4	j=0	j=0	PROPN
ejpam-6202	288	5	{	{	PUNCT
ejpam-6202	288	6	j	j	PROPN
ejpam-6202	289	1	+	+	CCONJ
ejpam-6202	289	2	r	r	NOUN
ejpam-6202	289	3	k	k	NOUN
ejpam-6202	290	1	+	+	CCONJ
ejpam-6202	290	2	r	r	NOUN
ejpam-6202	290	3	}	}	PUNCT
ejpam-6202	290	4	r	r	PROPN
ejpam-6202	290	5	tj	tj	PROPN
ejpam-6202	290	6	j	j	PROPN
ejpam-6202	290	7	!	!	PUNCT
ejpam-6202	290	8	gn−j(x	gn−j(x	PROPN
ejpam-6202	290	9	)	)	PUNCT
ejpam-6202	290	10	tn−j	tn−j	NOUN
ejpam-6202	290	11	(	(	PUNCT
ejpam-6202	290	12	n−	n−	NOUN
ejpam-6202	290	13	j	j	NOUN
ejpam-6202	290	14	)	)	PUNCT
ejpam-6202	290	15	!	!	PUNCT
ejpam-6202	291	1	=	=	PUNCT
ejpam-6202	292	1	∞∑	∞∑	PRON
ejpam-6202	292	2	n=0	n=0	PROPN
ejpam-6202	292	3	n∑	n∑	PRON
ejpam-6202	292	4	j=0	j=0	PROPN
ejpam-6202	292	5	{	{	PUNCT
ejpam-6202	292	6	n−	n−	NOUN
ejpam-6202	292	7	j	j	NOUN
ejpam-6202	293	1	+	+	CCONJ
ejpam-6202	293	2	r	r	NOUN
ejpam-6202	293	3	k	k	NOUN
ejpam-6202	294	1	+	+	CCONJ
ejpam-6202	294	2	r	r	NOUN
ejpam-6202	294	3	}	}	PUNCT
ejpam-6202	294	4	r	r	NOUN
ejpam-6202	294	5	tn−j	tn−j	NOUN
ejpam-6202	294	6	(	(	PUNCT
ejpam-6202	294	7	n−	n−	NOUN
ejpam-6202	294	8	j	j	PROPN
ejpam-6202	294	9	)	)	PUNCT
ejpam-6202	294	10	!	!	PUNCT
ejpam-6202	294	11	gj(x	gj(x	PUNCT
ejpam-6202	294	12	)	)	PUNCT
ejpam-6202	294	13	tj	tj	PROPN
ejpam-6202	294	14	j	j	PROPN
ejpam-6202	294	15	!	!	PUNCT
ejpam-6202	294	16	=	=	PUNCT
ejpam-6202	295	1	∞∑	∞∑	PRON
ejpam-6202	295	2	n=0	n=0	PROPN
ejpam-6202	295	3	n∑	n∑	PRON
ejpam-6202	295	4	j=0	j=0	PROPN
ejpam-6202	295	5	{	{	PUNCT
ejpam-6202	295	6	n−	n−	NOUN
ejpam-6202	295	7	j	j	NOUN
ejpam-6202	296	1	+	+	CCONJ
ejpam-6202	296	2	r	r	NOUN
ejpam-6202	296	3	k	k	NOUN
ejpam-6202	297	1	+	+	CCONJ
ejpam-6202	297	2	r	r	NOUN
ejpam-6202	297	3	}	}	PUNCT
ejpam-6202	297	4	r	r	NOUN
ejpam-6202	297	5	tn−j	tn−j	NOUN
ejpam-6202	297	6	(	(	PUNCT
ejpam-6202	297	7	n−	n−	NOUN
ejpam-6202	297	8	j	j	PROPN
ejpam-6202	297	9	)	)	PUNCT
ejpam-6202	297	10	!	!	PUNCT
ejpam-6202	298	1	j∑	j∑	PROPN
ejpam-6202	299	1	i=0	i=0	PROPN
ejpam-6202	299	2	(	(	PUNCT
ejpam-6202	299	3	j	j	PROPN
ejpam-6202	299	4	i	i	PROPN
ejpam-6202	299	5	)	)	PUNCT
ejpam-6202	300	1	gix	gix	PROPN
ejpam-6202	300	2	j−i	j−i	PROPN
ejpam-6202	300	3	t	t	PROPN
ejpam-6202	300	4	j	j	PROPN
ejpam-6202	300	5	j	j	PROPN
ejpam-6202	300	6	!	!	PROPN
ejpam-6202	300	7	12	12	NUM
ejpam-6202	300	8	of	of	ADP
ejpam-6202	300	9	26	26	NUM
ejpam-6202	300	10	=	=	NOUN
ejpam-6202	301	1	∞∑	∞∑	NUM
ejpam-6202	301	2	n=0	n=0	NUM
ejpam-6202	301	3			PUNCT
ejpam-6202	301	4	n∑	n∑	PROPN
ejpam-6202	301	5	i=0	i=0	PROPN
ejpam-6202	301	6	n∑	n∑	PROPN
ejpam-6202	301	7	j	j	PROPN
ejpam-6202	302	1	=	=	PRON
ejpam-6202	302	2	i	i	PROPN
ejpam-6202	302	3	{	{	PUNCT
ejpam-6202	302	4	n−	n−	NOUN
ejpam-6202	302	5	j	j	PROPN
ejpam-6202	302	6	+	+	CCONJ
ejpam-6202	302	7	r	r	NOUN
ejpam-6202	302	8	k	k	NOUN
ejpam-6202	302	9	+	+	CCONJ
ejpam-6202	302	10	r	r	NOUN
ejpam-6202	302	11	}	}	PUNCT
ejpam-6202	302	12	r	r	NOUN
ejpam-6202	302	13	(	(	PUNCT
ejpam-6202	302	14	n	n	NOUN
ejpam-6202	302	15	j	j	PROPN
ejpam-6202	302	16	)	)	PUNCT
ejpam-6202	302	17	(	(	PUNCT
ejpam-6202	302	18	j	j	PROPN
ejpam-6202	302	19	i	i	PROPN
ejpam-6202	302	20	)	)	PUNCT
ejpam-6202	302	21	gj−ix	gj−ix	NOUN
ejpam-6202	302	22	i	i	PRON
ejpam-6202	302	23			PROPN
ejpam-6202	302	24	tn	tn	PROPN
ejpam-6202	302	25	n	n	CCONJ
ejpam-6202	302	26	!	!	PUNCT
ejpam-6202	302	27	comparing	compare	VERB
ejpam-6202	302	28	the	the	DET
ejpam-6202	302	29	coefficients	coefficient	NOUN
ejpam-6202	302	30	of	of	ADP
ejpam-6202	302	31	tn	tn	NOUN
ejpam-6202	302	32	n	n	X
ejpam-6202	302	33	!	!	PUNCT
ejpam-6202	302	34	yields	yield	VERB
ejpam-6202	302	35	the	the	DET
ejpam-6202	302	36	desired	desire	VERB
ejpam-6202	302	37	convolution	convolution	NOUN
ejpam-6202	302	38	formula	formula	NOUN
ejpam-6202	302	39	in	in	ADP
ejpam-6202	302	40	(	(	PUNCT
ejpam-6202	302	41	10	10	NUM
ejpam-6202	302	42	)	)	PUNCT
ejpam-6202	302	43	.	.	PUNCT
ejpam-6202	303	1	theorem	theorem	VERB
ejpam-6202	303	2	2.2	2.2	NUM
ejpam-6202	303	3	.	.	PUNCT
ejpam-6202	304	1	the	the	DET
ejpam-6202	304	2	horizontal	horizontal	ADJ
ejpam-6202	304	3	generating	generate	VERB
ejpam-6202	304	4	function	function	NOUN
ejpam-6202	304	5	for	for	ADP
ejpam-6202	304	6	both	both	DET
ejpam-6202	304	7	kinds	kind	NOUN
ejpam-6202	304	8	of	of	ADP
ejpam-6202	304	9	r	r	NOUN
ejpam-6202	304	10	-	-	PUNCT
ejpam-6202	304	11	stirling	stirling	NOUN
ejpam-6202	304	12	genocchi	genocchi	PROPN
ejpam-6202	304	13	polynomials	polynomial	NOUN
ejpam-6202	304	14	are	be	AUX
ejpam-6202	304	15	given	give	VERB
ejpam-6202	304	16	as	as	SCONJ
ejpam-6202	304	17	follows	follow	VERB
ejpam-6202	304	18	:	:	PUNCT
ejpam-6202	305	1	gn(x+	gn(x+	SCONJ
ejpam-6202	305	2	z	z	NOUN
ejpam-6202	306	1	−	−	NOUN
ejpam-6202	306	2	r	r	NOUN
ejpam-6202	306	3	)	)	PUNCT
ejpam-6202	306	4	=	=	SYM
ejpam-6202	307	1	n∑	n∑	PROPN
ejpam-6202	307	2	k=0	k=0	PROPN
ejpam-6202	307	3	sg1	sg1	PROPN
ejpam-6202	307	4	n(x	n(x	PROPN
ejpam-6202	307	5	;	;	PUNCT
ejpam-6202	307	6	k	k	X
ejpam-6202	307	7	,	,	PUNCT
ejpam-6202	307	8	r)z	r)z	X
ejpam-6202	307	9	k	k	X
ejpam-6202	307	10	(	(	PUNCT
ejpam-6202	307	11	11	11	NUM
ejpam-6202	307	12	)	)	PUNCT
ejpam-6202	308	1	gn(x+	gn(x+	NOUN
ejpam-6202	308	2	z	z	NOUN
ejpam-6202	309	1	+	+	NOUN
ejpam-6202	309	2	r	r	X
ejpam-6202	309	3	)	)	PUNCT
ejpam-6202	309	4	=	=	SYM
ejpam-6202	310	1	n∑	n∑	PROPN
ejpam-6202	310	2	k=0	k=0	PROPN
ejpam-6202	310	3	sg2	sg2	PROPN
ejpam-6202	310	4	n(x	n(x	PROPN
ejpam-6202	310	5	;	;	PUNCT
ejpam-6202	310	6	k	k	X
ejpam-6202	310	7	,	,	PUNCT
ejpam-6202	310	8	r)z	r)z	X
ejpam-6202	310	9	k	k	X
ejpam-6202	310	10	(	(	PUNCT
ejpam-6202	310	11	12	12	NUM
ejpam-6202	310	12	)	)	PUNCT
ejpam-6202	310	13	proof	proof	NOUN
ejpam-6202	310	14	.	.	PUNCT
ejpam-6202	311	1	the	the	DET
ejpam-6202	311	2	exponential	exponential	ADJ
ejpam-6202	311	3	generating	generating	NOUN
ejpam-6202	311	4	function	function	NOUN
ejpam-6202	311	5	of	of	ADP
ejpam-6202	311	6	(	(	PUNCT
ejpam-6202	311	7	7	7	X
ejpam-6202	311	8	)	)	PUNCT
ejpam-6202	311	9	can	can	AUX
ejpam-6202	311	10	be	be	AUX
ejpam-6202	311	11	written	write	VERB
ejpam-6202	311	12	as	as	ADP
ejpam-6202	311	13	∞∑	∞∑	NUM
ejpam-6202	311	14	k=0	k=0	PROPN
ejpam-6202	311	15	{	{	PUNCT
ejpam-6202	311	16	∞∑	∞∑	PROPN
ejpam-6202	311	17	n	n	CCONJ
ejpam-6202	311	18	=	=	SYM
ejpam-6202	311	19	k	k	NOUN
ejpam-6202	311	20	sg1	sg1	PROPN
ejpam-6202	311	21	n(x	n(x	PROPN
ejpam-6202	311	22	;	;	PUNCT
ejpam-6202	311	23	k	k	X
ejpam-6202	311	24	,	,	PUNCT
ejpam-6202	311	25	r	r	NOUN
ejpam-6202	311	26	)	)	PUNCT
ejpam-6202	311	27	tn	tn	NOUN
ejpam-6202	311	28	n	n	NOUN
ejpam-6202	311	29	!	!	PUNCT
ejpam-6202	311	30	}	}	PUNCT
ejpam-6202	312	1	zk	zk	PROPN
ejpam-6202	313	1	=	=	PUNCT
ejpam-6202	314	1	(	(	PUNCT
ejpam-6202	314	2	1	1	NUM
ejpam-6202	314	3	1	1	NUM
ejpam-6202	314	4	+	+	NUM
ejpam-6202	314	5	t	t	NOUN
ejpam-6202	314	6	)	)	PUNCT
ejpam-6202	314	7	r	r	NOUN
ejpam-6202	314	8	2text	2text	NUM
ejpam-6202	314	9	(	(	PUNCT
ejpam-6202	314	10	et	et	NOUN
ejpam-6202	314	11	+	+	NOUN
ejpam-6202	314	12	1	1	X
ejpam-6202	314	13	)	)	PUNCT
ejpam-6202	314	14	∑	∑	PUNCT
ejpam-6202	314	15	k≥0	k≥0	VERB
ejpam-6202	314	16	lnk(1	lnk(1	NOUN
ejpam-6202	314	17	+	+	CCONJ
ejpam-6202	314	18	t	t	X
ejpam-6202	314	19	)	)	PUNCT
ejpam-6202	314	20	k	k	NOUN
ejpam-6202	314	21	!	!	PUNCT
ejpam-6202	314	22	zk	zk	X
ejpam-6202	315	1	=	=	PUNCT
ejpam-6202	315	2	(	(	PUNCT
ejpam-6202	315	3	1	1	NUM
ejpam-6202	315	4	1	1	NUM
ejpam-6202	315	5	+	+	NUM
ejpam-6202	315	6	t	t	NOUN
ejpam-6202	315	7	)	)	PUNCT
ejpam-6202	315	8	r	r	NOUN
ejpam-6202	315	9	2text	2text	NUM
ejpam-6202	315	10	(	(	PUNCT
ejpam-6202	315	11	et	et	NOUN
ejpam-6202	315	12	+	+	NOUN
ejpam-6202	315	13	1	1	X
ejpam-6202	315	14	)	)	PUNCT
ejpam-6202	315	15	∑	∑	PUNCT
ejpam-6202	315	16	k≥0	k≥0	PROPN
ejpam-6202	315	17	[	[	X
ejpam-6202	315	18	z	z	X
ejpam-6202	315	19	ln(1	ln(1	NOUN
ejpam-6202	315	20	+	+	NOUN
ejpam-6202	315	21	t)]k	t)]k	NOUN
ejpam-6202	315	22	k	k	NOUN
ejpam-6202	315	23	!	!	PUNCT
ejpam-6202	316	1	=	=	PUNCT
ejpam-6202	317	1	(	(	PUNCT
ejpam-6202	317	2	1	1	NUM
ejpam-6202	317	3	1	1	NUM
ejpam-6202	317	4	+	+	NUM
ejpam-6202	317	5	t	t	NOUN
ejpam-6202	317	6	)	)	PUNCT
ejpam-6202	317	7	r	r	NOUN
ejpam-6202	317	8	eln(1+t)z	eln(1+t)z	PROPN
ejpam-6202	317	9	2text	2text	NUM
ejpam-6202	317	10	(	(	PUNCT
ejpam-6202	317	11	et	et	NOUN
ejpam-6202	317	12	+	+	NOUN
ejpam-6202	317	13	1	1	X
ejpam-6202	317	14	)	)	PUNCT
ejpam-6202	317	15	=	=	PUNCT
ejpam-6202	317	16	∑	∑	PUNCT
ejpam-6202	317	17	n≥0	n≥0	PROPN
ejpam-6202	317	18	(	(	PUNCT
ejpam-6202	317	19	z	z	NOUN
ejpam-6202	317	20	−	−	PROPN
ejpam-6202	317	21	r	r	NOUN
ejpam-6202	317	22	n	n	NOUN
ejpam-6202	317	23	)	)	PUNCT
ejpam-6202	317	24	tn	tn	NOUN
ejpam-6202	317	25	∞∑	∞∑	NUM
ejpam-6202	317	26	n=0	n=0	NUM
ejpam-6202	317	27	gn(x	gn(x	PUNCT
ejpam-6202	317	28	)	)	PUNCT
ejpam-6202	317	29	tn	tn	NOUN
ejpam-6202	317	30	n	n	CCONJ
ejpam-6202	317	31	!	!	PUNCT
ejpam-6202	318	1	=	=	PUNCT
ejpam-6202	319	1	∑	∑	NOUN
ejpam-6202	319	2	n≥0	n≥0	PROPN
ejpam-6202	319	3	(	(	PUNCT
ejpam-6202	319	4	z	z	NOUN
ejpam-6202	319	5	−	−	NOUN
ejpam-6202	319	6	r)n	r)n	NOUN
ejpam-6202	319	7	tn	tn	NOUN
ejpam-6202	319	8	n	n	X
ejpam-6202	319	9	!	!	PUNCT
ejpam-6202	320	1			PROPN
ejpam-6202	320	2	(	(	PUNCT
ejpam-6202	320	3	∞∑	∞∑	NUM
ejpam-6202	320	4	n=0	n=0	NUM
ejpam-6202	320	5	gn(x	gn(x	NOUN
ejpam-6202	320	6	)	)	PUNCT
ejpam-6202	320	7	tn	tn	NOUN
ejpam-6202	320	8	n	n	CCONJ
ejpam-6202	320	9	!	!	PUNCT
ejpam-6202	320	10	)	)	PUNCT
ejpam-6202	321	1	=	=	PUNCT
ejpam-6202	322	1	∞∑	∞∑	NUM
ejpam-6202	322	2	n=0	n=0	NUM
ejpam-6202	322	3	n∑	n∑	NOUN
ejpam-6202	322	4	m=0	m=0	PROPN
ejpam-6202	322	5	(	(	PUNCT
ejpam-6202	322	6	z	z	NOUN
ejpam-6202	322	7	−	−	NOUN
ejpam-6202	322	8	r)m	r)m	NOUN
ejpam-6202	322	9	tm	tm	PROPN
ejpam-6202	322	10	m	m	PROPN
ejpam-6202	322	11	!	!	PUNCT
ejpam-6202	322	12	gn−m(x	gn−m(x	NOUN
ejpam-6202	322	13	)	)	PUNCT
ejpam-6202	323	1	tn−m	tn−m	PROPN
ejpam-6202	323	2	(	(	PUNCT
ejpam-6202	323	3	n−m	n−m	PROPN
ejpam-6202	323	4	)	)	PUNCT
ejpam-6202	323	5	!	!	PUNCT
ejpam-6202	324	1	=	=	PUNCT
ejpam-6202	325	1	∞∑	∞∑	PRON
ejpam-6202	325	2	n=0	n=0	NUM
ejpam-6202	325	3	{	{	PUNCT
ejpam-6202	325	4	n∑	n∑	PROPN
ejpam-6202	325	5	m=0	m=0	PROPN
ejpam-6202	325	6	(	(	PUNCT
ejpam-6202	325	7	z	z	NOUN
ejpam-6202	325	8	−	−	NOUN
ejpam-6202	325	9	r)m	r)m	NOUN
ejpam-6202	325	10	1	1	NUM
ejpam-6202	325	11	(	(	PUNCT
ejpam-6202	325	12	n−m)!m	n−m)!m	PROPN
ejpam-6202	325	13	!	!	PUNCT
ejpam-6202	325	14	gn−m(x	gn−m(x	PROPN
ejpam-6202	325	15	)	)	PUNCT
ejpam-6202	325	16	}	}	PUNCT
ejpam-6202	325	17	tn	tn	NOUN
ejpam-6202	326	1	=	=	SYM
ejpam-6202	327	1	∞∑	∞∑	NUM
ejpam-6202	327	2	n=0	n=0	PRON
ejpam-6202	327	3	{	{	PUNCT
ejpam-6202	327	4	n∑	n∑	PROPN
ejpam-6202	327	5	m=0	m=0	PROPN
ejpam-6202	327	6	(	(	PUNCT
ejpam-6202	327	7	z	z	NOUN
ejpam-6202	327	8	−	−	NOUN
ejpam-6202	327	9	r)m	r)m	NOUN
ejpam-6202	327	10	(	(	PUNCT
ejpam-6202	327	11	n	n	X
ejpam-6202	327	12	m	m	NOUN
ejpam-6202	327	13	)	)	PUNCT
ejpam-6202	327	14	gn−m(x	gn−m(x	PROPN
ejpam-6202	327	15	)	)	PUNCT
ejpam-6202	327	16	}	}	PUNCT
ejpam-6202	327	17	tn	tn	PROPN
ejpam-6202	327	18	n	n	NOUN
ejpam-6202	327	19	!	!	PUNCT
ejpam-6202	327	20	=	=	NOUN
ejpam-6202	328	1	∞∑	∞∑	PRON
ejpam-6202	328	2	n=0	n=0	NUM
ejpam-6202	328	3	{	{	PUNCT
ejpam-6202	328	4	n∑	n∑	NOUN
ejpam-6202	328	5	m=0	m=0	PROPN
ejpam-6202	328	6	(	(	PUNCT
ejpam-6202	328	7	n	n	NOUN
ejpam-6202	328	8	m	m	PROPN
ejpam-6202	328	9	)	)	PUNCT
ejpam-6202	329	1	gn−m(x)(z	gn−m(x)(z	VERB
ejpam-6202	329	2	−	−	NOUN
ejpam-6202	329	3	r)m	r)m	NOUN
ejpam-6202	329	4	}	}	PUNCT
ejpam-6202	329	5	tn	tn	PROPN
ejpam-6202	329	6	n	n	CCONJ
ejpam-6202	329	7	!	!	PUNCT
ejpam-6202	330	1	rewriting	rewrite	VERB
ejpam-6202	330	2	13	13	NUM
ejpam-6202	330	3	of	of	ADP
ejpam-6202	330	4	26	26	NUM
ejpam-6202	330	5	∞∑	∞∑	NUM
ejpam-6202	330	6	n=0	n=0	PRON
ejpam-6202	330	7	{	{	PUNCT
ejpam-6202	330	8	n∑	n∑	NOUN
ejpam-6202	330	9	k=0	k=0	PROPN
ejpam-6202	330	10	sg1	sg1	PROPN
ejpam-6202	330	11	n(x	n(x	PROPN
ejpam-6202	330	12	;	;	PUNCT
ejpam-6202	330	13	k	k	X
ejpam-6202	330	14	,	,	PUNCT
ejpam-6202	330	15	r)z	r)z	PUNCT
ejpam-6202	330	16	k	k	X
ejpam-6202	330	17	}	}	PUNCT
ejpam-6202	330	18	tn	tn	PROPN
ejpam-6202	330	19	n	n	CCONJ
ejpam-6202	330	20	!	!	PUNCT
ejpam-6202	331	1	=	=	NOUN
ejpam-6202	332	1	∞∑	∞∑	PRON
ejpam-6202	332	2	n=0	n=0	NUM
ejpam-6202	332	3	{	{	PUNCT
ejpam-6202	332	4	n∑	n∑	NOUN
ejpam-6202	332	5	m=0	m=0	PROPN
ejpam-6202	332	6	(	(	PUNCT
ejpam-6202	332	7	n	n	NOUN
ejpam-6202	332	8	m	m	PROPN
ejpam-6202	332	9	)	)	PUNCT
ejpam-6202	333	1	gn−m(x)(z	gn−m(x)(z	VERB
ejpam-6202	333	2	−	−	NOUN
ejpam-6202	333	3	r)m	r)m	NOUN
ejpam-6202	333	4	}	}	PUNCT
ejpam-6202	333	5	tn	tn	PROPN
ejpam-6202	333	6	n	n	X
ejpam-6202	333	7	!	!	PUNCT
ejpam-6202	334	1	comparing	compare	VERB
ejpam-6202	334	2	the	the	DET
ejpam-6202	334	3	coefficients	coefficient	NOUN
ejpam-6202	334	4	of	of	ADP
ejpam-6202	334	5	tn	tn	NOUN
ejpam-6202	334	6	n	n	CCONJ
ejpam-6202	334	7	!	!	PROPN
ejpam-6202	335	1	,	,	PUNCT
ejpam-6202	335	2	we	we	PRON
ejpam-6202	335	3	have	have	VERB
ejpam-6202	335	4	n∑	n∑	ADJ
ejpam-6202	335	5	k=0	k=0	PROPN
ejpam-6202	335	6	sg1	sg1	PROPN
ejpam-6202	335	7	n(x	n(x	PROPN
ejpam-6202	335	8	;	;	PUNCT
ejpam-6202	335	9	k	k	X
ejpam-6202	335	10	,	,	PUNCT
ejpam-6202	335	11	r)z	r)z	PUNCT
ejpam-6202	335	12	k	k	X
ejpam-6202	336	1	=	=	PUNCT
ejpam-6202	336	2	n∑	n∑	PROPN
ejpam-6202	336	3	m=0	m=0	PROPN
ejpam-6202	336	4	(	(	PUNCT
ejpam-6202	336	5	n	n	NOUN
ejpam-6202	336	6	m	m	PROPN
ejpam-6202	336	7	)	)	PUNCT
ejpam-6202	337	1	gn−m(x)(z	gn−m(x)(z	VERB
ejpam-6202	337	2	−	−	NOUN
ejpam-6202	337	3	r)m	r)m	NOUN
ejpam-6202	337	4	applying	apply	VERB
ejpam-6202	337	5	the	the	DET
ejpam-6202	337	6	addition	addition	NOUN
ejpam-6202	337	7	formula	formula	NOUN
ejpam-6202	337	8	,	,	PUNCT
ejpam-6202	337	9	we	we	PRON
ejpam-6202	337	10	have	have	VERB
ejpam-6202	337	11	n∑	n∑	ADJ
ejpam-6202	337	12	k=0	k=0	PROPN
ejpam-6202	337	13	sg1	sg1	PROPN
ejpam-6202	337	14	n(x	n(x	PROPN
ejpam-6202	337	15	;	;	PUNCT
ejpam-6202	337	16	k	k	X
ejpam-6202	337	17	,	,	PUNCT
ejpam-6202	337	18	r)z	r)z	PUNCT
ejpam-6202	337	19	k	k	X
ejpam-6202	338	1	=	=	PUNCT
ejpam-6202	338	2	gn(x+	gn(x+	PROPN
ejpam-6202	338	3	z	z	NOUN
ejpam-6202	339	1	−	−	NOUN
ejpam-6202	339	2	r	r	NOUN
ejpam-6202	339	3	)	)	PUNCT
ejpam-6202	339	4	similarly	similarly	ADV
ejpam-6202	339	5	(	(	PUNCT
ejpam-6202	339	6	8)	8)	NUM
ejpam-6202	339	7	can	can	AUX
ejpam-6202	339	8	be	be	AUX
ejpam-6202	339	9	written	write	VERB
ejpam-6202	339	10	as	as	ADP
ejpam-6202	339	11	∞∑	∞∑	NUM
ejpam-6202	339	12	k=0	k=0	PROPN
ejpam-6202	339	13	{	{	PUNCT
ejpam-6202	339	14	∞∑	∞∑	PROPN
ejpam-6202	339	15	n	n	CCONJ
ejpam-6202	339	16	=	=	SYM
ejpam-6202	339	17	k	k	PROPN
ejpam-6202	339	18	sg2	sg2	PROPN
ejpam-6202	339	19	n(x	n(x	PROPN
ejpam-6202	339	20	;	;	PUNCT
ejpam-6202	339	21	k	k	X
ejpam-6202	339	22	,	,	PUNCT
ejpam-6202	339	23	r	r	NOUN
ejpam-6202	339	24	)	)	PUNCT
ejpam-6202	339	25	tn	tn	NOUN
ejpam-6202	339	26	n	n	NOUN
ejpam-6202	339	27	!	!	PUNCT
ejpam-6202	339	28	}	}	PUNCT
ejpam-6202	339	29	zk	zk	PROPN
ejpam-6202	340	1	=	=	PUNCT
ejpam-6202	341	1	∞∑	∞∑	NUM
ejpam-6202	341	2	k=0	k=0	PROPN
ejpam-6202	341	3	{	{	PUNCT
ejpam-6202	341	4	2textert(et	2textert(et	NUM
ejpam-6202	341	5	−	−	NOUN
ejpam-6202	341	6	1)k	1)k	NUM
ejpam-6202	341	7	k!(et	k!(et	NOUN
ejpam-6202	341	8	+	+	CCONJ
ejpam-6202	341	9	1	1	NUM
ejpam-6202	341	10	)	)	PUNCT
ejpam-6202	341	11	}	}	PUNCT
ejpam-6202	341	12	zk	zk	X
ejpam-6202	342	1	=	=	PUNCT
ejpam-6202	342	2	2textert	2textert	PROPN
ejpam-6202	342	3	(	(	PUNCT
ejpam-6202	342	4	et	et	NOUN
ejpam-6202	342	5	+	+	NOUN
ejpam-6202	342	6	1	1	X
ejpam-6202	342	7	)	)	PUNCT
ejpam-6202	342	8	∞∑	∞∑	PRON
ejpam-6202	342	9	k=0	k=0	PROPN
ejpam-6202	342	10	(	(	PUNCT
ejpam-6202	342	11	z	z	NOUN
ejpam-6202	342	12	k	k	NOUN
ejpam-6202	342	13	)	)	PUNCT
ejpam-6202	342	14	(	(	PUNCT
ejpam-6202	342	15	et	et	NOUN
ejpam-6202	342	16	−	−	PROPN
ejpam-6202	342	17	1)k	1)k	NUM
ejpam-6202	343	1	=	=	SYM
ejpam-6202	343	2	2textert	2textert	NUM
ejpam-6202	343	3	(	(	PUNCT
ejpam-6202	343	4	et	et	NOUN
ejpam-6202	343	5	+	+	NOUN
ejpam-6202	343	6	1	1	X
ejpam-6202	343	7	)	)	PUNCT
ejpam-6202	343	8	(	(	PUNCT
ejpam-6202	343	9	1	1	NUM
ejpam-6202	343	10	+	+	CCONJ
ejpam-6202	343	11	(	(	PUNCT
ejpam-6202	343	12	et	et	NOUN
ejpam-6202	343	13	−	−	PROPN
ejpam-6202	343	14	1))z	1))z	NUM
ejpam-6202	344	1	=	=	SYM
ejpam-6202	344	2	2text	2text	NUM
ejpam-6202	344	3	(	(	PUNCT
ejpam-6202	344	4	et	et	NOUN
ejpam-6202	344	5	+	+	NOUN
ejpam-6202	344	6	1	1	NUM
ejpam-6202	344	7	)	)	PUNCT
ejpam-6202	344	8	ert(1	ert(1	NOUN
ejpam-6202	345	1	+	+	CCONJ
ejpam-6202	345	2	(	(	PUNCT
ejpam-6202	345	3	et	et	NOUN
ejpam-6202	345	4	−	−	PROPN
ejpam-6202	345	5	1))z	1))z	NUM
ejpam-6202	346	1	=	=	SYM
ejpam-6202	346	2	e(z+r)t	e(z+r)t	PROPN
ejpam-6202	347	1	2text	2text	NUM
ejpam-6202	347	2	(	(	PUNCT
ejpam-6202	347	3	et	et	NOUN
ejpam-6202	347	4	+	+	NOUN
ejpam-6202	347	5	1	1	X
ejpam-6202	347	6	)	)	PUNCT
ejpam-6202	347	7	=	=	NOUN
ejpam-6202	347	8	(	(	PUNCT
ejpam-6202	347	9	∞∑	∞∑	NUM
ejpam-6202	347	10	n=0	n=0	NUM
ejpam-6202	347	11	(	(	PUNCT
ejpam-6202	347	12	z	z	NOUN
ejpam-6202	347	13	+	+	NOUN
ejpam-6202	347	14	r)n	r)n	X
ejpam-6202	347	15	tn	tn	NOUN
ejpam-6202	347	16	n	n	CCONJ
ejpam-6202	347	17	!	!	PUNCT
ejpam-6202	347	18	)	)	PUNCT
ejpam-6202	348	1	(	(	PUNCT
ejpam-6202	348	2	∞∑	∞∑	NUM
ejpam-6202	348	3	n=0	n=0	NUM
ejpam-6202	348	4	gn(x	gn(x	NUM
ejpam-6202	348	5	)	)	PUNCT
ejpam-6202	348	6	tn	tn	NOUN
ejpam-6202	348	7	n	n	CCONJ
ejpam-6202	348	8	!	!	PUNCT
ejpam-6202	348	9	)	)	PUNCT
ejpam-6202	349	1	=	=	PUNCT
ejpam-6202	350	1	∞∑	∞∑	NUM
ejpam-6202	350	2	n=0	n=0	NUM
ejpam-6202	350	3	n∑	n∑	NOUN
ejpam-6202	350	4	m=0	m=0	PROPN
ejpam-6202	350	5	(	(	PUNCT
ejpam-6202	350	6	z	z	NOUN
ejpam-6202	350	7	+	+	NOUN
ejpam-6202	350	8	r)m	r)m	NOUN
ejpam-6202	350	9	tm	tm	PROPN
ejpam-6202	350	10	m	m	PROPN
ejpam-6202	350	11	!	!	PUNCT
ejpam-6202	350	12	gn−m(x	gn−m(x	NOUN
ejpam-6202	350	13	)	)	PUNCT
ejpam-6202	351	1	tn−m	tn−m	PROPN
ejpam-6202	351	2	(	(	PUNCT
ejpam-6202	351	3	n−m	n−m	PROPN
ejpam-6202	351	4	)	)	PUNCT
ejpam-6202	351	5	!	!	PUNCT
ejpam-6202	352	1	=	=	PUNCT
ejpam-6202	353	1	∞∑	∞∑	PRON
ejpam-6202	353	2	n=0	n=0	NUM
ejpam-6202	353	3	{	{	PUNCT
ejpam-6202	353	4	n∑	n∑	PROPN
ejpam-6202	353	5	m=0	m=0	PROPN
ejpam-6202	353	6	(	(	PUNCT
ejpam-6202	353	7	z	z	NOUN
ejpam-6202	353	8	+	+	NOUN
ejpam-6202	353	9	r)m	r)m	NOUN
ejpam-6202	353	10	1	1	NUM
ejpam-6202	353	11	(	(	PUNCT
ejpam-6202	353	12	n−m)!m	n−m)!m	PROPN
ejpam-6202	353	13	!	!	PUNCT
ejpam-6202	353	14	gn−m(x	gn−m(x	PROPN
ejpam-6202	353	15	)	)	PUNCT
ejpam-6202	353	16	}	}	PUNCT
ejpam-6202	353	17	tn	tn	NOUN
ejpam-6202	354	1	=	=	SYM
ejpam-6202	355	1	∞∑	∞∑	NUM
ejpam-6202	355	2	n=0	n=0	PRON
ejpam-6202	355	3	{	{	PUNCT
ejpam-6202	355	4	n∑	n∑	PROPN
ejpam-6202	355	5	m=0	m=0	PROPN
ejpam-6202	355	6	(	(	PUNCT
ejpam-6202	355	7	z	z	NOUN
ejpam-6202	355	8	+	+	NOUN
ejpam-6202	355	9	r)m	r)m	NOUN
ejpam-6202	355	10	(	(	PUNCT
ejpam-6202	355	11	n	n	X
ejpam-6202	355	12	m	m	NOUN
ejpam-6202	355	13	)	)	PUNCT
ejpam-6202	355	14	gn−m(x	gn−m(x	PROPN
ejpam-6202	355	15	)	)	PUNCT
ejpam-6202	355	16	}	}	PUNCT
ejpam-6202	355	17	tn	tn	PROPN
ejpam-6202	355	18	n	n	NOUN
ejpam-6202	355	19	!	!	PUNCT
ejpam-6202	355	20	=	=	NOUN
ejpam-6202	356	1	∞∑	∞∑	PRON
ejpam-6202	356	2	n=0	n=0	NUM
ejpam-6202	356	3	{	{	PUNCT
ejpam-6202	356	4	n∑	n∑	NOUN
ejpam-6202	356	5	m=0	m=0	PROPN
ejpam-6202	356	6	(	(	PUNCT
ejpam-6202	356	7	n	n	NOUN
ejpam-6202	356	8	m	m	NOUN
ejpam-6202	356	9	)	)	PUNCT
ejpam-6202	357	1	gn−m(x)(z	gn−m(x)(z	VERB
ejpam-6202	357	2	+	+	CCONJ
ejpam-6202	357	3	r)m	r)m	NOUN
ejpam-6202	357	4	}	}	PUNCT
ejpam-6202	357	5	tn	tn	PROPN
ejpam-6202	357	6	n	n	NOUN
ejpam-6202	357	7	!	!	PROPN
ejpam-6202	357	8	14	14	NUM
ejpam-6202	357	9	of	of	ADP
ejpam-6202	357	10	26	26	NUM
ejpam-6202	357	11	rewriting	rewrite	VERB
ejpam-6202	357	12	∞∑	∞∑	PRON
ejpam-6202	357	13	n=0	n=0	PROPN
ejpam-6202	357	14	{	{	PUNCT
ejpam-6202	357	15	n∑	n∑	PROPN
ejpam-6202	357	16	k=0	k=0	PROPN
ejpam-6202	357	17	sg2	sg2	PROPN
ejpam-6202	357	18	n(x	n(x	PROPN
ejpam-6202	357	19	;	;	PUNCT
ejpam-6202	357	20	k	k	X
ejpam-6202	357	21	,	,	PUNCT
ejpam-6202	357	22	r)z	r)z	PUNCT
ejpam-6202	357	23	k	k	X
ejpam-6202	357	24	}	}	PUNCT
ejpam-6202	357	25	tn	tn	PROPN
ejpam-6202	357	26	n	n	CCONJ
ejpam-6202	357	27	!	!	PUNCT
ejpam-6202	357	28	=	=	NOUN
ejpam-6202	358	1	∞∑	∞∑	PRON
ejpam-6202	358	2	n=0	n=0	NUM
ejpam-6202	358	3	{	{	PUNCT
ejpam-6202	358	4	n∑	n∑	NOUN
ejpam-6202	358	5	m=0	m=0	PROPN
ejpam-6202	358	6	(	(	PUNCT
ejpam-6202	358	7	n	n	NOUN
ejpam-6202	358	8	m	m	NOUN
ejpam-6202	358	9	)	)	PUNCT
ejpam-6202	359	1	gn−m(x)(z	gn−m(x)(z	VERB
ejpam-6202	359	2	+	+	CCONJ
ejpam-6202	359	3	r)m	r)m	NOUN
ejpam-6202	359	4	}	}	PUNCT
ejpam-6202	359	5	tn	tn	PROPN
ejpam-6202	359	6	n	n	NOUN
ejpam-6202	359	7	!	!	PUNCT
ejpam-6202	360	1	comparing	compare	VERB
ejpam-6202	360	2	the	the	DET
ejpam-6202	360	3	coefficients	coefficient	NOUN
ejpam-6202	360	4	of	of	ADP
ejpam-6202	360	5	tn	tn	NOUN
ejpam-6202	360	6	n	n	CCONJ
ejpam-6202	360	7	!	!	PROPN
ejpam-6202	361	1	,	,	PUNCT
ejpam-6202	361	2	we	we	PRON
ejpam-6202	361	3	have	have	VERB
ejpam-6202	361	4	n∑	n∑	PROPN
ejpam-6202	361	5	k=0	k=0	PROPN
ejpam-6202	361	6	sg2	sg2	PROPN
ejpam-6202	361	7	n(x	n(x	PROPN
ejpam-6202	361	8	;	;	PUNCT
ejpam-6202	361	9	k	k	X
ejpam-6202	361	10	,	,	PUNCT
ejpam-6202	361	11	r)z	r)z	PUNCT
ejpam-6202	361	12	k	k	X
ejpam-6202	362	1	=	=	PUNCT
ejpam-6202	362	2	n∑	n∑	PROPN
ejpam-6202	362	3	m=0	m=0	PROPN
ejpam-6202	362	4	(	(	PUNCT
ejpam-6202	362	5	n	n	NOUN
ejpam-6202	362	6	m	m	NOUN
ejpam-6202	362	7	)	)	PUNCT
ejpam-6202	363	1	gn−m(x)(z	gn−m(x)(z	ADJ
ejpam-6202	363	2	+	+	DET
ejpam-6202	363	3	r)m	r)m	NOUN
ejpam-6202	363	4	applying	apply	VERB
ejpam-6202	363	5	the	the	DET
ejpam-6202	363	6	addition	addition	NOUN
ejpam-6202	363	7	formula	formula	NOUN
ejpam-6202	363	8	,	,	PUNCT
ejpam-6202	363	9	we	we	PRON
ejpam-6202	363	10	have	have	VERB
ejpam-6202	363	11	n∑	n∑	PROPN
ejpam-6202	363	12	k=0	k=0	PROPN
ejpam-6202	363	13	sg2	sg2	PROPN
ejpam-6202	363	14	n(x	n(x	PROPN
ejpam-6202	363	15	;	;	PUNCT
ejpam-6202	363	16	k	k	X
ejpam-6202	363	17	,	,	PUNCT
ejpam-6202	363	18	r)z	r)z	PUNCT
ejpam-6202	363	19	k	k	X
ejpam-6202	364	1	=	=	PUNCT
ejpam-6202	364	2	gn(x+	gn(x+	PUNCT
ejpam-6202	364	3	z	z	NOUN
ejpam-6202	365	1	+	+	NOUN
ejpam-6202	365	2	r	r	NOUN
ejpam-6202	365	3	)	)	PUNCT
ejpam-6202	365	4	hence	hence	ADV
ejpam-6202	365	5	,	,	PUNCT
ejpam-6202	365	6	we	we	PRON
ejpam-6202	365	7	proved	prove	VERB
ejpam-6202	365	8	the	the	DET
ejpam-6202	365	9	horizontal	horizontal	ADJ
ejpam-6202	365	10	generating	generating	NOUN
ejpam-6202	365	11	function	function	NOUN
ejpam-6202	365	12	in	in	ADP
ejpam-6202	365	13	(	(	PUNCT
ejpam-6202	365	14	11	11	NUM
ejpam-6202	365	15	)	)	PUNCT
ejpam-6202	365	16	and	and	CCONJ
ejpam-6202	365	17	(	(	PUNCT
ejpam-6202	365	18	12	12	NUM
ejpam-6202	365	19	)	)	PUNCT
ejpam-6202	365	20	.	.	PUNCT
ejpam-6202	366	1	theorem	theorem	VERB
ejpam-6202	366	2	2.3	2.3	NUM
ejpam-6202	366	3	.	.	PUNCT
ejpam-6202	367	1	the	the	DET
ejpam-6202	367	2	formula	formula	NOUN
ejpam-6202	367	3	for	for	ADP
ejpam-6202	367	4	the	the	DET
ejpam-6202	367	5	first	first	ADJ
ejpam-6202	367	6	kind	kind	NOUN
ejpam-6202	367	7	of	of	ADP
ejpam-6202	367	8	r	r	NOUN
ejpam-6202	367	9	-	-	PUNCT
ejpam-6202	367	10	stirling	stirling	NOUN
ejpam-6202	367	11	genocchi	genocchi	PROPN
ejpam-6202	367	12	polynomials	polynomial	NOUN
ejpam-6202	367	13	is	be	AUX
ejpam-6202	367	14	explicitly	explicitly	ADV
ejpam-6202	367	15	stated	state	VERB
ejpam-6202	367	16	as	as	SCONJ
ejpam-6202	367	17	follows	follow	VERB
ejpam-6202	367	18	:	:	PUNCT
ejpam-6202	367	19	sg1	sg1	PROPN
ejpam-6202	367	20	n(x	n(x	PROPN
ejpam-6202	367	21	;	;	PUNCT
ejpam-6202	367	22	k	k	X
ejpam-6202	367	23	,	,	PUNCT
ejpam-6202	367	24	r	r	NOUN
ejpam-6202	367	25	)	)	PUNCT
ejpam-6202	367	26	=	=	SYM
ejpam-6202	368	1	n∑	n∑	PROPN
ejpam-6202	368	2	m=0	m=0	PROPN
ejpam-6202	368	3	n∑	n∑	PROPN
ejpam-6202	368	4	j	j	PROPN
ejpam-6202	369	1	=	=	NOUN
ejpam-6202	369	2	m	m	VERB
ejpam-6202	369	3	j−m∑	j−m∑	ADV
ejpam-6202	369	4	i=0	i=0	PROPN
ejpam-6202	369	5	m−k∑	m−k∑	X
ejpam-6202	369	6	f=0	f=0	PROPN
ejpam-6202	369	7	f∑	f∑	PROPN
ejpam-6202	370	1	d	d	X
ejpam-6202	370	2	=	=	X
ejpam-6202	370	3	i	i	PROPN
ejpam-6202	370	4	(	(	PUNCT
ejpam-6202	370	5	−1)n−j+d+fgj−m−ix	−1)n−j+d+fgj−m−ix	NOUN
ejpam-6202	370	6	i	i	PRON
ejpam-6202	370	7	(	(	PUNCT
ejpam-6202	370	8	j	j	PROPN
ejpam-6202	370	9	m	m	PROPN
ejpam-6202	370	10	)	)	PUNCT
ejpam-6202	370	11	(	(	PUNCT
ejpam-6202	370	12	j	j	PROPN
ejpam-6202	370	13	−m	−m	INTJ
ejpam-6202	370	14	i	i	INTJ
ejpam-6202	370	15	)	)	PUNCT
ejpam-6202	370	16	(	(	PUNCT
ejpam-6202	370	17	n	n	CCONJ
ejpam-6202	370	18	j	j	NOUN
ejpam-6202	370	19	)	)	PUNCT
ejpam-6202	370	20	(	(	PUNCT
ejpam-6202	370	21	f	f	PROPN
ejpam-6202	370	22	d	d	PROPN
ejpam-6202	370	23	)	)	PUNCT
ejpam-6202	370	24	(	(	PUNCT
ejpam-6202	370	25	m−	m−	PROPN
ejpam-6202	370	26	1	1	NUM
ejpam-6202	370	27	+	+	CCONJ
ejpam-6202	370	28	f	f	PROPN
ejpam-6202	370	29	m−	m−	PROPN
ejpam-6202	370	30	k	k	PROPN
ejpam-6202	371	1	+	+	CCONJ
ejpam-6202	371	2	f	f	NOUN
ejpam-6202	371	3	)	)	PUNCT
ejpam-6202	372	1	(	(	PUNCT
ejpam-6202	372	2	2m−	2m−	NUM
ejpam-6202	372	3	k	k	NOUN
ejpam-6202	372	4	m−	m−	PROPN
ejpam-6202	372	5	k	k	PROPN
ejpam-6202	373	1	+	+	CCONJ
ejpam-6202	373	2	f	f	PROPN
ejpam-6202	373	3	)	)	PUNCT
ejpam-6202	374	1	(	(	PUNCT
ejpam-6202	374	2	f	f	X
ejpam-6202	374	3	−	−	PROPN
ejpam-6202	374	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	374	5	f	f	X
ejpam-6202	374	6	!	!	PUNCT
ejpam-6202	375	1	rn−j	rn−j	NOUN
ejpam-6202	375	2	proof	proof	NOUN
ejpam-6202	375	3	the	the	DET
ejpam-6202	375	4	exponential	exponential	ADJ
ejpam-6202	375	5	generating	generating	NOUN
ejpam-6202	375	6	function	function	NOUN
ejpam-6202	375	7	in	in	ADP
ejpam-6202	375	8	(	(	PUNCT
ejpam-6202	375	9	7	7	NUM
ejpam-6202	375	10	)	)	PUNCT
ejpam-6202	375	11	composed	compose	VERB
ejpam-6202	375	12	of	of	ADP
ejpam-6202	375	13	three	three	NUM
ejpam-6202	375	14	functions	function	NOUN
ejpam-6202	375	15	.	.	PUNCT
ejpam-6202	376	1	the	the	DET
ejpam-6202	376	2	first	first	ADJ
ejpam-6202	376	3	function	function	NOUN
ejpam-6202	376	4	can	can	AUX
ejpam-6202	376	5	be	be	AUX
ejpam-6202	376	6	expressed	express	VERB
ejpam-6202	376	7	as	as	ADP
ejpam-6202	376	8	(	(	PUNCT
ejpam-6202	376	9	1	1	NUM
ejpam-6202	376	10	1−	1−	NUM
ejpam-6202	376	11	t	t	NOUN
ejpam-6202	376	12	)	)	PUNCT
ejpam-6202	376	13	r	r	NOUN
ejpam-6202	376	14	=	=	PUNCT
ejpam-6202	376	15	∑	∑	PUNCT
ejpam-6202	376	16	n≥0	n≥0	PROPN
ejpam-6202	376	17	(	(	PUNCT
ejpam-6202	376	18	−1)nrn	−1)nrn	PROPN
ejpam-6202	376	19	tn	tn	PROPN
ejpam-6202	376	20	n	n	NOUN
ejpam-6202	376	21	!	!	PUNCT
ejpam-6202	377	1	where	where	SCONJ
ejpam-6202	377	2	rn	rn	PROPN
ejpam-6202	377	3	=	=	SYM
ejpam-6202	377	4	r(r	r(r	PROPN
ejpam-6202	377	5	+	+	CCONJ
ejpam-6202	377	6	1	1	NUM
ejpam-6202	377	7	)	)	PUNCT
ejpam-6202	377	8	.	.	PUNCT
ejpam-6202	377	9	.	.	PUNCT
ejpam-6202	378	1	.	.	PUNCT
ejpam-6202	379	1	(	(	PUNCT
ejpam-6202	379	2	r	r	NOUN
ejpam-6202	379	3	+	+	NUM
ejpam-6202	379	4	n−	n−	NOUN
ejpam-6202	379	5	1	1	NUM
ejpam-6202	379	6	)	)	PUNCT
ejpam-6202	379	7	the	the	DET
ejpam-6202	379	8	second	second	ADJ
ejpam-6202	379	9	function	function	NOUN
ejpam-6202	379	10	can	can	AUX
ejpam-6202	379	11	be	be	AUX
ejpam-6202	379	12	expresses	express	NOUN
ejpam-6202	379	13	as	as	ADP
ejpam-6202	379	14	the	the	DET
ejpam-6202	379	15	genocchi	genocchi	PROPN
ejpam-6202	379	16	polynomial	polynomial	NOUN
ejpam-6202	379	17	,	,	PUNCT
ejpam-6202	379	18	2	2	NUM
ejpam-6202	379	19	t	t	NOUN
ejpam-6202	379	20	(	(	PUNCT
ejpam-6202	379	21	et	et	NOUN
ejpam-6202	379	22	+	+	NOUN
ejpam-6202	379	23	1	1	X
ejpam-6202	379	24	)	)	PUNCT
ejpam-6202	379	25	ext	ext	NOUN
ejpam-6202	379	26	=	=	NOUN
ejpam-6202	380	1	∞∑	∞∑	NUM
ejpam-6202	380	2	n=0	n=0	NUM
ejpam-6202	380	3	gn(x	gn(x	NOUN
ejpam-6202	380	4	)	)	PUNCT
ejpam-6202	380	5	tn	tn	NOUN
ejpam-6202	380	6	n	n	CCONJ
ejpam-6202	380	7	!	!	PUNCT
ejpam-6202	381	1	lastly	lastly	ADV
ejpam-6202	381	2	the	the	DET
ejpam-6202	381	3	third	third	ADJ
ejpam-6202	381	4	function	function	NOUN
ejpam-6202	381	5	can	can	AUX
ejpam-6202	381	6	be	be	AUX
ejpam-6202	381	7	expressed	express	VERB
ejpam-6202	381	8	1	1	NUM
ejpam-6202	381	9	k	k	NOUN
ejpam-6202	381	10	!	!	PUNCT
ejpam-6202	382	1	[	[	X
ejpam-6202	382	2	ln	ln	X
ejpam-6202	382	3	(	(	PUNCT
ejpam-6202	382	4	1	1	NUM
ejpam-6202	382	5	+	+	NUM
ejpam-6202	382	6	t)]k	t)]k	NOUN
ejpam-6202	382	7	=	=	SYM
ejpam-6202	382	8	∑	∑	PROPN
ejpam-6202	382	9	n≥k	n≥k	PROPN
ejpam-6202	382	10	s(n	s(n	PROPN
ejpam-6202	382	11	,	,	PUNCT
ejpam-6202	382	12	k	k	NOUN
ejpam-6202	382	13	)	)	PUNCT
ejpam-6202	382	14	tn	tn	PROPN
ejpam-6202	382	15	n	n	PROPN
ejpam-6202	382	16	!	!	PUNCT
ejpam-6202	382	17	hence	hence	ADV
ejpam-6202	382	18	,	,	PUNCT
ejpam-6202	382	19	using	use	VERB
ejpam-6202	382	20	cauchy	cauchy	PROPN
ejpam-6202	382	21	’s	’s	PART
ejpam-6202	382	22	rule	rule	NOUN
ejpam-6202	382	23	for	for	ADP
ejpam-6202	382	24	the	the	DET
ejpam-6202	382	25	product	product	NOUN
ejpam-6202	382	26	of	of	ADP
ejpam-6202	382	27	power	power	NOUN
ejpam-6202	382	28	series	series	NOUN
ejpam-6202	382	29	,	,	PUNCT
ejpam-6202	382	30	we	we	PRON
ejpam-6202	382	31	have	have	VERB
ejpam-6202	382	32	n∑	n∑	ADJ
ejpam-6202	382	33	k≥0	k≥0	PROPN
ejpam-6202	382	34	sg1	sg1	PROPN
ejpam-6202	382	35	n(x	n(x	PROPN
ejpam-6202	382	36	;	;	PUNCT
ejpam-6202	382	37	k	k	X
ejpam-6202	382	38	,	,	PUNCT
ejpam-6202	382	39	r	r	NOUN
ejpam-6202	382	40	)	)	PUNCT
ejpam-6202	382	41	tn	tn	NOUN
ejpam-6202	382	42	n	n	CCONJ
ejpam-6202	382	43	!	!	PUNCT
ejpam-6202	383	1	=	=	PUNCT
ejpam-6202	384	1	∑	∑	NOUN
ejpam-6202	384	2	n≥0	n≥0	PROPN
ejpam-6202	384	3	(	(	PUNCT
ejpam-6202	384	4	−1)nrn	−1)nrn	PROPN
ejpam-6202	384	5	tn	tn	PROPN
ejpam-6202	384	6	n	n	ADV
ejpam-6202	384	7	!	!	PUNCT
ejpam-6202	385	1			PROPN
ejpam-6202	385	2	(	(	PUNCT
ejpam-6202	385	3	∞∑	∞∑	NUM
ejpam-6202	385	4	n=0	n=0	NUM
ejpam-6202	385	5	gn(x	gn(x	NOUN
ejpam-6202	385	6	)	)	PUNCT
ejpam-6202	385	7	tn	tn	NOUN
ejpam-6202	385	8	n	n	CCONJ
ejpam-6202	385	9	!	!	PUNCT
ejpam-6202	385	10	)	)	PUNCT
ejpam-6202	386	1	∑	∑	NOUN
ejpam-6202	386	2	n≥k	n≥k	PROPN
ejpam-6202	386	3	s(n	s(n	PROPN
ejpam-6202	386	4	,	,	PUNCT
ejpam-6202	386	5	k	k	NOUN
ejpam-6202	386	6	)	)	PUNCT
ejpam-6202	386	7	tn	tn	PROPN
ejpam-6202	386	8	n	n	AUX
ejpam-6202	386	9	!	!	PUNCT
ejpam-6202	387	1			PROPN
ejpam-6202	387	2	15	15	NUM
ejpam-6202	387	3	of	of	ADP
ejpam-6202	387	4	26	26	NUM
ejpam-6202	387	5	=	=	SYM
ejpam-6202	387	6	∑	∑	NOUN
ejpam-6202	387	7	n≥0	n≥0	PROPN
ejpam-6202	387	8	(	(	PUNCT
ejpam-6202	387	9	−1)nrn	−1)nrn	PROPN
ejpam-6202	387	10	tn	tn	PROPN
ejpam-6202	387	11	n	n	ADV
ejpam-6202	387	12	!	!	PUNCT
ejpam-6202	388	1			PROPN
ejpam-6202	388	2	(	(	PUNCT
ejpam-6202	388	3	∞∑	∞∑	PROPN
ejpam-6202	388	4	n=0	n=0	PROPN
ejpam-6202	388	5	{	{	PUNCT
ejpam-6202	388	6	n∑	n∑	NOUN
ejpam-6202	388	7	m	m	PROPN
ejpam-6202	388	8	=	=	PROPN
ejpam-6202	388	9	k	k	PROPN
ejpam-6202	388	10	s(m	s(m	PROPN
ejpam-6202	388	11	,	,	PUNCT
ejpam-6202	388	12	k	k	NOUN
ejpam-6202	388	13	)	)	PUNCT
ejpam-6202	388	14	(	(	PUNCT
ejpam-6202	388	15	n	n	X
ejpam-6202	388	16	m	m	NOUN
ejpam-6202	388	17	)	)	PUNCT
ejpam-6202	388	18	gn−m(x	gn−m(x	PROPN
ejpam-6202	388	19	)	)	PUNCT
ejpam-6202	388	20	}	}	PUNCT
ejpam-6202	388	21	tn	tn	PROPN
ejpam-6202	388	22	n	n	NOUN
ejpam-6202	388	23	!	!	PUNCT
ejpam-6202	388	24	)	)	PUNCT
ejpam-6202	389	1	=	=	PUNCT
ejpam-6202	390	1	∞∑	∞∑	NUM
ejpam-6202	390	2	n=0	n=0	NUM
ejpam-6202	390	3	n∑	n∑	DET
ejpam-6202	390	4	j=0	j=0	PROPN
ejpam-6202	390	5	j∑	j∑	PROPN
ejpam-6202	390	6	m	m	PROPN
ejpam-6202	390	7	=	=	PROPN
ejpam-6202	390	8	k	k	PROPN
ejpam-6202	390	9	s(m	s(m	PROPN
ejpam-6202	390	10	,	,	PUNCT
ejpam-6202	390	11	k	k	NOUN
ejpam-6202	390	12	)	)	PUNCT
ejpam-6202	390	13	(	(	PUNCT
ejpam-6202	390	14	j	j	PROPN
ejpam-6202	390	15	m	m	NOUN
ejpam-6202	390	16	)	)	PUNCT
ejpam-6202	390	17	gj−m(x	gj−m(x	NOUN
ejpam-6202	390	18	)	)	PUNCT
ejpam-6202	390	19	tj	tj	PROPN
ejpam-6202	390	20	j	j	PROPN
ejpam-6202	390	21	!	!	PUNCT
ejpam-6202	390	22	(	(	PUNCT
ejpam-6202	390	23	−1)n−jrn−j	−1)n−jrn−j	ADV
ejpam-6202	390	24	tn−j	tn−j	NOUN
ejpam-6202	390	25	(	(	PUNCT
ejpam-6202	390	26	n−	n−	NOUN
ejpam-6202	390	27	j	j	NOUN
ejpam-6202	390	28	)	)	PUNCT
ejpam-6202	390	29	!	!	PUNCT
ejpam-6202	391	1	=	=	PUNCT
ejpam-6202	392	1	∞∑	∞∑	DET
ejpam-6202	392	2	n=0	n=0	NUM
ejpam-6202	392	3	n∑	n∑	DET
ejpam-6202	392	4	j=0	j=0	PROPN
ejpam-6202	392	5	j∑	j∑	PROPN
ejpam-6202	392	6	m	m	PROPN
ejpam-6202	392	7	=	=	PROPN
ejpam-6202	392	8	k	k	PROPN
ejpam-6202	392	9	s(m	s(m	PROPN
ejpam-6202	392	10	,	,	PUNCT
ejpam-6202	392	11	k	k	NOUN
ejpam-6202	392	12	)	)	PUNCT
ejpam-6202	392	13	(	(	PUNCT
ejpam-6202	392	14	j	j	PROPN
ejpam-6202	392	15	m	m	NOUN
ejpam-6202	392	16	)	)	PUNCT
ejpam-6202	392	17	gj−m(x	gj−m(x	NOUN
ejpam-6202	392	18	)	)	PUNCT
ejpam-6202	392	19	tj−j+n	tj−j+n	NOUN
ejpam-6202	392	20	(	(	PUNCT
ejpam-6202	392	21	n−	n−	NOUN
ejpam-6202	392	22	j)!j	j)!j	PROPN
ejpam-6202	392	23	!	!	PUNCT
ejpam-6202	393	1	(	(	PUNCT
ejpam-6202	393	2	−1)n−jrn−j	−1)n−jrn−j	ADV
ejpam-6202	393	3	=	=	VERB
ejpam-6202	394	1	∞∑	∞∑	NUM
ejpam-6202	394	2	n=0	n=0	NUM
ejpam-6202	394	3			PUNCT
ejpam-6202	394	4	n∑	n∑	PROPN
ejpam-6202	394	5	m=0	m=0	PROPN
ejpam-6202	394	6	n∑	n∑	PROPN
ejpam-6202	394	7	j	j	PROPN
ejpam-6202	395	1	=	=	PROPN
ejpam-6202	395	2	m	m	PROPN
ejpam-6202	395	3	s(m	s(m	PROPN
ejpam-6202	395	4	,	,	PUNCT
ejpam-6202	395	5	k	k	NOUN
ejpam-6202	395	6	)	)	PUNCT
ejpam-6202	395	7	(	(	PUNCT
ejpam-6202	395	8	j	j	PROPN
ejpam-6202	395	9	m	m	NOUN
ejpam-6202	395	10	)	)	PUNCT
ejpam-6202	395	11	gj−m(x	gj−m(x	NOUN
ejpam-6202	395	12	)	)	PUNCT
ejpam-6202	395	13	1	1	NUM
ejpam-6202	395	14	(	(	PUNCT
ejpam-6202	395	15	n−	n−	NOUN
ejpam-6202	395	16	j)!j	j)!j	PROPN
ejpam-6202	395	17	!	!	PUNCT
ejpam-6202	396	1	(	(	PUNCT
ejpam-6202	396	2	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	396	3			ADV
ejpam-6202	396	4	tn	tn	NOUN
ejpam-6202	397	1	=	=	PUNCT
ejpam-6202	397	2	∞∑	∞∑	NUM
ejpam-6202	397	3	n=0	n=0	NUM
ejpam-6202	397	4			PUNCT
ejpam-6202	397	5	n∑	n∑	PROPN
ejpam-6202	397	6	m=0	m=0	PROPN
ejpam-6202	397	7	n∑	n∑	PROPN
ejpam-6202	397	8	j	j	PROPN
ejpam-6202	398	1	=	=	PROPN
ejpam-6202	398	2	m	m	PROPN
ejpam-6202	398	3	s(m	s(m	PROPN
ejpam-6202	398	4	,	,	PUNCT
ejpam-6202	398	5	k	k	NOUN
ejpam-6202	398	6	)	)	PUNCT
ejpam-6202	398	7	(	(	PUNCT
ejpam-6202	398	8	j	j	PROPN
ejpam-6202	398	9	m	m	VERB
ejpam-6202	398	10	)	)	PUNCT
ejpam-6202	398	11	j−m∑	j−m∑	PROPN
ejpam-6202	399	1	i=0	i=0	PROPN
ejpam-6202	399	2	(	(	PUNCT
ejpam-6202	399	3	j	j	PROPN
ejpam-6202	399	4	−m	−m	VERB
ejpam-6202	399	5	i	i	INTJ
ejpam-6202	399	6	)	)	PUNCT
ejpam-6202	400	1	gj−m−ix	gj−m−ix	VERB
ejpam-6202	400	2	i	i	PRON
ejpam-6202	400	3	(	(	PUNCT
ejpam-6202	400	4	n	n	X
ejpam-6202	400	5	j	j	PROPN
ejpam-6202	400	6	)	)	PUNCT
ejpam-6202	400	7	(	(	PUNCT
ejpam-6202	400	8	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	400	9			PROPN
ejpam-6202	400	10	tn	tn	NOUN
ejpam-6202	400	11	n	n	CCONJ
ejpam-6202	400	12	!	!	PUNCT
ejpam-6202	400	13	=	=	PUNCT
ejpam-6202	401	1	∞∑	∞∑	DET
ejpam-6202	401	2	n=0	n=0	NUM
ejpam-6202	401	3			PUNCT
ejpam-6202	401	4	n∑	n∑	PROPN
ejpam-6202	401	5	m=0	m=0	PROPN
ejpam-6202	401	6	n∑	n∑	PROPN
ejpam-6202	401	7	j	j	PROPN
ejpam-6202	401	8	=	=	NOUN
ejpam-6202	401	9	m	m	PROPN
ejpam-6202	401	10	j−m∑	j−m∑	ADP
ejpam-6202	401	11	i=0	i=0	PROPN
ejpam-6202	401	12	s(m	s(m	PROPN
ejpam-6202	401	13	,	,	PUNCT
ejpam-6202	401	14	k	k	NOUN
ejpam-6202	401	15	)	)	PUNCT
ejpam-6202	401	16	(	(	PUNCT
ejpam-6202	401	17	j	j	PROPN
ejpam-6202	401	18	m	m	VERB
ejpam-6202	401	19	)	)	PUNCT
ejpam-6202	401	20	(	(	PUNCT
ejpam-6202	401	21	j	j	PROPN
ejpam-6202	401	22	−m	−m	NOUN
ejpam-6202	401	23	i	i	INTJ
ejpam-6202	401	24	)	)	PUNCT
ejpam-6202	402	1	gj−m−ix	gj−m−ix	VERB
ejpam-6202	402	2	i	i	PRON
ejpam-6202	402	3	(	(	PUNCT
ejpam-6202	402	4	n	n	X
ejpam-6202	402	5	j	j	PROPN
ejpam-6202	402	6	)	)	PUNCT
ejpam-6202	402	7	(	(	PUNCT
ejpam-6202	402	8	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	402	9			PROPN
ejpam-6202	402	10	tn	tn	PROPN
ejpam-6202	402	11	n	n	CCONJ
ejpam-6202	402	12	!	!	PUNCT
ejpam-6202	402	13	comparing	compare	VERB
ejpam-6202	402	14	the	the	DET
ejpam-6202	402	15	coefficients	coefficient	NOUN
ejpam-6202	402	16	of	of	ADP
ejpam-6202	402	17	tn	tn	NOUN
ejpam-6202	402	18	n	n	CCONJ
ejpam-6202	402	19	!	!	PUNCT
ejpam-6202	402	20	,	,	PUNCT
ejpam-6202	402	21	sg1	sg1	PROPN
ejpam-6202	402	22	n(x	n(x	PROPN
ejpam-6202	402	23	;	;	PUNCT
ejpam-6202	402	24	k	k	X
ejpam-6202	402	25	,	,	PUNCT
ejpam-6202	402	26	r	r	NOUN
ejpam-6202	402	27	)	)	PUNCT
ejpam-6202	402	28	=	=	SYM
ejpam-6202	402	29	n∑	n∑	PROPN
ejpam-6202	402	30	m=0	m=0	PROPN
ejpam-6202	402	31	n∑	n∑	PROPN
ejpam-6202	402	32	j	j	PROPN
ejpam-6202	403	1	=	=	NOUN
ejpam-6202	403	2	m	m	NOUN
ejpam-6202	403	3	m∑	m∑	ADJ
ejpam-6202	403	4	i=0	i=0	PROPN
ejpam-6202	403	5	(	(	PUNCT
ejpam-6202	403	6	j	j	NOUN
ejpam-6202	403	7	m	m	VERB
ejpam-6202	403	8	)	)	PUNCT
ejpam-6202	403	9	(	(	PUNCT
ejpam-6202	403	10	m	m	VERB
ejpam-6202	403	11	i	i	NOUN
ejpam-6202	403	12	)	)	PUNCT
ejpam-6202	403	13	(	(	PUNCT
ejpam-6202	403	14	n	n	CCONJ
ejpam-6202	403	15	j	j	PROPN
ejpam-6202	403	16	)	)	PUNCT
ejpam-6202	403	17	gm−ix	gm−ix	PROPN
ejpam-6202	403	18	is(m	is(m	PROPN
ejpam-6202	403	19	,	,	PUNCT
ejpam-6202	403	20	k)(−1)n−jrn−j	k)(−1)n−jrn−j	ADV
ejpam-6202	403	21	using	use	VERB
ejpam-6202	403	22	the	the	DET
ejpam-6202	403	23	schlömilch	schlömilch	NOUN
ejpam-6202	403	24	formula	formula	NOUN
ejpam-6202	403	25	for	for	ADP
ejpam-6202	403	26	the	the	DET
ejpam-6202	403	27	stirling	stirling	NOUN
ejpam-6202	403	28	numbers	number	NOUN
ejpam-6202	403	29	of	of	ADP
ejpam-6202	403	30	the	the	DET
ejpam-6202	403	31	first	first	ADJ
ejpam-6202	403	32	kind	kind	NOUN
ejpam-6202	403	33	,	,	PUNCT
ejpam-6202	403	34	s(n	s(n	PROPN
ejpam-6202	403	35	,	,	PUNCT
ejpam-6202	403	36	k	k	NOUN
ejpam-6202	403	37	)	)	PUNCT
ejpam-6202	403	38	=	=	PUNCT
ejpam-6202	404	1	n−k∑	n−k∑	NOUN
ejpam-6202	404	2	r=0	r=0	VERB
ejpam-6202	404	3	r∑	r∑	PRON
ejpam-6202	404	4	j	j	X
ejpam-6202	405	1	=	=	NOUN
ejpam-6202	405	2	i	i	PROPN
ejpam-6202	405	3	(	(	PUNCT
ejpam-6202	405	4	−1)j+r	−1)j+r	NOUN
ejpam-6202	405	5	(	(	PUNCT
ejpam-6202	405	6	r	r	NOUN
ejpam-6202	405	7	j	j	PROPN
ejpam-6202	405	8	)	)	PUNCT
ejpam-6202	405	9	(	(	PUNCT
ejpam-6202	405	10	n−	n−	NOUN
ejpam-6202	405	11	1	1	NUM
ejpam-6202	405	12	+	+	CCONJ
ejpam-6202	405	13	r	r	NOUN
ejpam-6202	405	14	n−	n−	NOUN
ejpam-6202	405	15	k	k	NOUN
ejpam-6202	405	16	+	+	CCONJ
ejpam-6202	405	17	r	r	NOUN
ejpam-6202	405	18	)	)	PUNCT
ejpam-6202	405	19	(	(	PUNCT
ejpam-6202	405	20	2n−	2n−	NUM
ejpam-6202	405	21	k	k	NOUN
ejpam-6202	405	22	n−	n−	NOUN
ejpam-6202	405	23	k	k	NOUN
ejpam-6202	406	1	+	+	CCONJ
ejpam-6202	406	2	r	r	NOUN
ejpam-6202	406	3	)	)	PUNCT
ejpam-6202	406	4	(	(	PUNCT
ejpam-6202	406	5	r	r	NOUN
ejpam-6202	406	6	−	−	PROPN
ejpam-6202	406	7	j)n−k+r	j)n−k+r	PROPN
ejpam-6202	406	8	r	r	NOUN
ejpam-6202	406	9	!	!	PUNCT
ejpam-6202	407	1	then	then	ADV
ejpam-6202	407	2	the	the	DET
ejpam-6202	407	3	schlömilch	schlömilch	ADJ
ejpam-6202	407	4	formula	formula	NOUN
ejpam-6202	407	5	for	for	ADP
ejpam-6202	407	6	the	the	DET
ejpam-6202	407	7	r	r	NOUN
ejpam-6202	407	8	-	-	PUNCT
ejpam-6202	407	9	stirling	stirling	NOUN
ejpam-6202	407	10	genocchi	genocchi	PROPN
ejpam-6202	407	11	polynomial	polynomial	NOUN
ejpam-6202	407	12	of	of	ADP
ejpam-6202	407	13	the	the	DET
ejpam-6202	407	14	first	first	ADJ
ejpam-6202	407	15	kind	kind	NOUN
ejpam-6202	407	16	is	be	AUX
ejpam-6202	407	17	given	give	VERB
ejpam-6202	407	18	by	by	ADP
ejpam-6202	407	19	sg1	sg1	NOUN
ejpam-6202	407	20	n(x	n(x	PROPN
ejpam-6202	407	21	;	;	PUNCT
ejpam-6202	407	22	k	k	X
ejpam-6202	407	23	,	,	PUNCT
ejpam-6202	407	24	r	r	NOUN
ejpam-6202	407	25	)	)	PUNCT
ejpam-6202	407	26	=	=	SYM
ejpam-6202	408	1	n∑	n∑	PROPN
ejpam-6202	408	2	m=0	m=0	PROPN
ejpam-6202	408	3	n∑	n∑	PROPN
ejpam-6202	408	4	j	j	PROPN
ejpam-6202	409	1	=	=	NOUN
ejpam-6202	409	2	m	m	VERB
ejpam-6202	409	3	j−m∑	j−m∑	ADJ
ejpam-6202	409	4	i=0	i=0	PROPN
ejpam-6202	409	5	(	(	PUNCT
ejpam-6202	409	6	j	j	NOUN
ejpam-6202	409	7	m	m	PROPN
ejpam-6202	409	8	)	)	PUNCT
ejpam-6202	409	9	(	(	PUNCT
ejpam-6202	409	10	j	j	PROPN
ejpam-6202	409	11	−m	−m	INTJ
ejpam-6202	409	12	i	i	INTJ
ejpam-6202	409	13	)	)	PUNCT
ejpam-6202	409	14	(	(	PUNCT
ejpam-6202	409	15	n	n	CCONJ
ejpam-6202	409	16	j	j	NOUN
ejpam-6202	409	17	)	)	PUNCT
ejpam-6202	409	18	gj−m−ix	gj−m−ix	PROPN
ejpam-6202	409	19	i(−1)n−jrn−j	i(−1)n−jrn−j	ADV
ejpam-6202	409	20	m−k∑	m−k∑	AUX
ejpam-6202	409	21	f=0	f=0	PROPN
ejpam-6202	409	22	f∑	f∑	PROPN
ejpam-6202	409	23	d	d	X
ejpam-6202	410	1	=	=	X
ejpam-6202	410	2	i	i	PROPN
ejpam-6202	410	3	(	(	PUNCT
ejpam-6202	410	4	−1)d+f	−1)d+f	X
ejpam-6202	410	5	(	(	PUNCT
ejpam-6202	410	6	f	f	NOUN
ejpam-6202	410	7	d	d	PROPN
ejpam-6202	410	8	)	)	PUNCT
ejpam-6202	410	9	(	(	PUNCT
ejpam-6202	410	10	m−	m−	PROPN
ejpam-6202	410	11	1	1	NUM
ejpam-6202	410	12	+	+	CCONJ
ejpam-6202	410	13	f	f	PROPN
ejpam-6202	410	14	m−	m−	PROPN
ejpam-6202	410	15	k	k	PROPN
ejpam-6202	411	1	+	+	CCONJ
ejpam-6202	411	2	f	f	NOUN
ejpam-6202	411	3	)	)	PUNCT
ejpam-6202	412	1	(	(	PUNCT
ejpam-6202	412	2	2m−	2m−	NUM
ejpam-6202	412	3	k	k	NOUN
ejpam-6202	412	4	m−	m−	PROPN
ejpam-6202	412	5	k	k	PROPN
ejpam-6202	413	1	+	+	CCONJ
ejpam-6202	413	2	f	f	PROPN
ejpam-6202	413	3	)	)	PUNCT
ejpam-6202	414	1	(	(	PUNCT
ejpam-6202	414	2	f	f	X
ejpam-6202	414	3	−	−	PROPN
ejpam-6202	414	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	414	5	f	f	X
ejpam-6202	414	6	!	!	PUNCT
ejpam-6202	415	1	=	=	PUNCT
ejpam-6202	416	1	n∑	n∑	PROPN
ejpam-6202	416	2	m=0	m=0	PROPN
ejpam-6202	416	3	n∑	n∑	PROPN
ejpam-6202	416	4	j	j	PROPN
ejpam-6202	417	1	=	=	NOUN
ejpam-6202	417	2	m	m	VERB
ejpam-6202	417	3	j−m∑	j−m∑	ADV
ejpam-6202	417	4	i=0	i=0	PROPN
ejpam-6202	417	5	m−k∑	m−k∑	X
ejpam-6202	417	6	f=0	f=0	PROPN
ejpam-6202	417	7	f∑	f∑	PROPN
ejpam-6202	418	1	d	d	X
ejpam-6202	419	1	=	=	X
ejpam-6202	419	2	i	i	PROPN
ejpam-6202	419	3	(	(	PUNCT
ejpam-6202	419	4	j	j	PROPN
ejpam-6202	419	5	−m	−m	INTJ
ejpam-6202	419	6	i	i	INTJ
ejpam-6202	419	7	)	)	PUNCT
ejpam-6202	419	8	(	(	PUNCT
ejpam-6202	419	9	j	j	PROPN
ejpam-6202	419	10	m	m	VERB
ejpam-6202	419	11	)	)	PUNCT
ejpam-6202	419	12	gj−m−ix	gj−m−ix	VERB
ejpam-6202	419	13	i	i	PRON
ejpam-6202	419	14	(	(	PUNCT
ejpam-6202	419	15	n	n	X
ejpam-6202	419	16	j	j	PROPN
ejpam-6202	419	17	)	)	PUNCT
ejpam-6202	419	18	(	(	PUNCT
ejpam-6202	419	19	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	419	20	(	(	PUNCT
ejpam-6202	419	21	−1)d+f	−1)d+f	NUM
ejpam-6202	419	22	(	(	PUNCT
ejpam-6202	419	23	f	f	NOUN
ejpam-6202	419	24	d	d	PROPN
ejpam-6202	419	25	)	)	PUNCT
ejpam-6202	419	26	(	(	PUNCT
ejpam-6202	419	27	m−	m−	PROPN
ejpam-6202	419	28	1	1	NUM
ejpam-6202	419	29	+	+	CCONJ
ejpam-6202	419	30	f	f	PROPN
ejpam-6202	419	31	m−	m−	PROPN
ejpam-6202	419	32	k	k	PROPN
ejpam-6202	420	1	+	+	CCONJ
ejpam-6202	420	2	f	f	NOUN
ejpam-6202	420	3	)	)	PUNCT
ejpam-6202	421	1	(	(	PUNCT
ejpam-6202	421	2	2m−	2m−	NUM
ejpam-6202	421	3	k	k	NOUN
ejpam-6202	421	4	m−	m−	PROPN
ejpam-6202	421	5	k	k	PROPN
ejpam-6202	422	1	+	+	CCONJ
ejpam-6202	422	2	f	f	PROPN
ejpam-6202	422	3	)	)	PUNCT
ejpam-6202	423	1	(	(	PUNCT
ejpam-6202	423	2	f	f	X
ejpam-6202	423	3	−	−	PROPN
ejpam-6202	423	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	423	5	f	f	X
ejpam-6202	423	6	!	!	PUNCT
ejpam-6202	424	1	16	16	NUM
ejpam-6202	424	2	of	of	ADP
ejpam-6202	424	3	26	26	NUM
ejpam-6202	424	4	=	=	SYM
ejpam-6202	424	5	n∑	n∑	PROPN
ejpam-6202	424	6	m=0	m=0	PROPN
ejpam-6202	424	7	n∑	n∑	PROPN
ejpam-6202	424	8	j	j	PROPN
ejpam-6202	425	1	=	=	NOUN
ejpam-6202	425	2	m	m	VERB
ejpam-6202	425	3	j−m∑	j−m∑	ADV
ejpam-6202	425	4	i=0	i=0	PROPN
ejpam-6202	425	5	m−k∑	m−k∑	X
ejpam-6202	425	6	f=0	f=0	PROPN
ejpam-6202	425	7	f∑	f∑	PROPN
ejpam-6202	426	1	d	d	X
ejpam-6202	426	2	=	=	X
ejpam-6202	426	3	i	i	PROPN
ejpam-6202	426	4	(	(	PUNCT
ejpam-6202	426	5	−1)n−j+d+fgj−m−ix	−1)n−j+d+fgj−m−ix	NOUN
ejpam-6202	426	6	i	i	PRON
ejpam-6202	426	7	(	(	PUNCT
ejpam-6202	426	8	j	j	PROPN
ejpam-6202	426	9	m	m	PROPN
ejpam-6202	426	10	)	)	PUNCT
ejpam-6202	426	11	(	(	PUNCT
ejpam-6202	426	12	j	j	PROPN
ejpam-6202	426	13	−m	−m	INTJ
ejpam-6202	426	14	i	i	INTJ
ejpam-6202	426	15	)	)	PUNCT
ejpam-6202	426	16	(	(	PUNCT
ejpam-6202	426	17	n	n	CCONJ
ejpam-6202	426	18	j	j	NOUN
ejpam-6202	426	19	)	)	PUNCT
ejpam-6202	426	20	(	(	PUNCT
ejpam-6202	426	21	f	f	PROPN
ejpam-6202	426	22	d	d	PROPN
ejpam-6202	426	23	)	)	PUNCT
ejpam-6202	426	24	(	(	PUNCT
ejpam-6202	426	25	m−	m−	PROPN
ejpam-6202	426	26	1	1	NUM
ejpam-6202	426	27	+	+	CCONJ
ejpam-6202	426	28	f	f	PROPN
ejpam-6202	426	29	m−	m−	PROPN
ejpam-6202	426	30	k	k	PROPN
ejpam-6202	427	1	+	+	CCONJ
ejpam-6202	427	2	f	f	NOUN
ejpam-6202	427	3	)	)	PUNCT
ejpam-6202	428	1	(	(	PUNCT
ejpam-6202	428	2	2m−	2m−	NUM
ejpam-6202	428	3	k	k	NOUN
ejpam-6202	428	4	m−	m−	PROPN
ejpam-6202	428	5	k	k	PROPN
ejpam-6202	429	1	+	+	CCONJ
ejpam-6202	429	2	f	f	PROPN
ejpam-6202	429	3	)	)	PUNCT
ejpam-6202	430	1	(	(	PUNCT
ejpam-6202	430	2	f	f	X
ejpam-6202	430	3	−	−	PROPN
ejpam-6202	430	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	430	5	f	f	X
ejpam-6202	430	6	!	!	PUNCT
ejpam-6202	431	1	rn−j	rn−j	PROPN
ejpam-6202	431	2	theorem	theorem	VERB
ejpam-6202	431	3	2.4	2.4	NUM
ejpam-6202	431	4	.	.	PUNCT
ejpam-6202	432	1	the	the	DET
ejpam-6202	432	2	formula	formula	NOUN
ejpam-6202	432	3	for	for	ADP
ejpam-6202	432	4	the	the	DET
ejpam-6202	432	5	second	second	ADJ
ejpam-6202	432	6	kind	kind	NOUN
ejpam-6202	432	7	of	of	ADP
ejpam-6202	432	8	r	r	NOUN
ejpam-6202	432	9	-	-	PUNCT
ejpam-6202	432	10	stirling	stirling	NOUN
ejpam-6202	432	11	genocchi	genocchi	PROPN
ejpam-6202	432	12	polynomials	polynomial	NOUN
ejpam-6202	432	13	is	be	AUX
ejpam-6202	432	14	explicitly	explicitly	ADV
ejpam-6202	432	15	defined	define	VERB
ejpam-6202	432	16	by	by	ADP
ejpam-6202	432	17	the	the	DET
ejpam-6202	432	18	following	follow	VERB
ejpam-6202	432	19	formula	formula	NOUN
ejpam-6202	432	20	:	:	PUNCT
ejpam-6202	432	21	sg2	sg2	PROPN
ejpam-6202	432	22	n(x	n(x	PROPN
ejpam-6202	432	23	;	;	PUNCT
ejpam-6202	432	24	k	k	X
ejpam-6202	432	25	,	,	PUNCT
ejpam-6202	432	26	r	r	NOUN
ejpam-6202	432	27	)	)	PUNCT
ejpam-6202	433	1	=	=	SYM
ejpam-6202	433	2	n∑	n∑	PROPN
ejpam-6202	433	3	m=0	m=0	PROPN
ejpam-6202	433	4	j−m∑	j−m∑	PROPN
ejpam-6202	433	5	i=0	i=0	PROPN
ejpam-6202	433	6	{	{	PUNCT
ejpam-6202	433	7	m+	m+	NOUN
ejpam-6202	433	8	r	r	NOUN
ejpam-6202	433	9	k	k	NOUN
ejpam-6202	434	1	+	+	CCONJ
ejpam-6202	434	2	r	r	NOUN
ejpam-6202	434	3	}	}	PUNCT
ejpam-6202	434	4	r	r	NOUN
ejpam-6202	434	5	(	(	PUNCT
ejpam-6202	434	6	n	n	NOUN
ejpam-6202	434	7	m	m	VERB
ejpam-6202	434	8	)	)	PUNCT
ejpam-6202	434	9	(	(	PUNCT
ejpam-6202	434	10	j	j	PROPN
ejpam-6202	434	11	−m	−m	NOUN
ejpam-6202	434	12	i	i	PROPN
ejpam-6202	434	13	)	)	PUNCT
ejpam-6202	435	1	gm−ix	gm−ix	NOUN
ejpam-6202	435	2	i	i	PRON
ejpam-6202	435	3	proof	proof	VERB
ejpam-6202	435	4	the	the	DET
ejpam-6202	435	5	exponential	exponential	ADJ
ejpam-6202	435	6	generating	generating	NOUN
ejpam-6202	435	7	function	function	NOUN
ejpam-6202	435	8	in	in	ADP
ejpam-6202	435	9	(	(	PUNCT
ejpam-6202	435	10	8)	8)	NUM
ejpam-6202	435	11	can	can	AUX
ejpam-6202	435	12	be	be	AUX
ejpam-6202	435	13	written	write	VERB
ejpam-6202	435	14	as	as	ADP
ejpam-6202	435	15	n∑	n∑	PROPN
ejpam-6202	435	16	n≥k	n≥k	PROPN
ejpam-6202	435	17	k!sg2	k!sg2	PROPN
ejpam-6202	435	18	n(x	n(x	PROPN
ejpam-6202	435	19	;	;	PUNCT
ejpam-6202	435	20	k	k	X
ejpam-6202	435	21	,	,	PUNCT
ejpam-6202	435	22	r	r	NOUN
ejpam-6202	435	23	)	)	PUNCT
ejpam-6202	435	24	tn	tn	NOUN
ejpam-6202	435	25	n	n	NOUN
ejpam-6202	435	26	!	!	PUNCT
ejpam-6202	436	1	=	=	PUNCT
ejpam-6202	437	1	2textert	2textert	PROPN
ejpam-6202	437	2	(	(	PUNCT
ejpam-6202	437	3	et	et	NOUN
ejpam-6202	437	4	+	+	NOUN
ejpam-6202	437	5	1	1	X
ejpam-6202	437	6	)	)	PUNCT
ejpam-6202	437	7	k∑	k∑	NOUN
ejpam-6202	438	1	i=0	i=0	PROPN
ejpam-6202	439	1	(	(	PUNCT
ejpam-6202	439	2	k	k	NOUN
ejpam-6202	439	3	i	i	PROPN
ejpam-6202	439	4	)	)	PUNCT
ejpam-6202	439	5	(	(	PUNCT
ejpam-6202	439	6	et)k−i(−1)i	et)k−i(−1)i	X
ejpam-6202	439	7	=	=	SYM
ejpam-6202	439	8	2text	2text	NUM
ejpam-6202	439	9	(	(	PUNCT
ejpam-6202	439	10	et	et	NOUN
ejpam-6202	439	11	+	+	NOUN
ejpam-6202	439	12	1	1	X
ejpam-6202	439	13	)	)	PUNCT
ejpam-6202	439	14	k∑	k∑	NOUN
ejpam-6202	440	1	i=0	i=0	PROPN
ejpam-6202	440	2	(	(	PUNCT
ejpam-6202	440	3	k	k	NOUN
ejpam-6202	440	4	i	i	PROPN
ejpam-6202	440	5	)	)	PUNCT
ejpam-6202	440	6	ert(et)k−i(−1)i	ert(et)k−i(−1)i	PROPN
ejpam-6202	441	1	=	=	SYM
ejpam-6202	441	2	2text	2text	NUM
ejpam-6202	441	3	(	(	PUNCT
ejpam-6202	441	4	et	et	NOUN
ejpam-6202	441	5	+	+	NOUN
ejpam-6202	441	6	1	1	X
ejpam-6202	441	7	)	)	PUNCT
ejpam-6202	441	8	k∑	k∑	NOUN
ejpam-6202	442	1	i=0	i=0	PROPN
ejpam-6202	442	2	(	(	PUNCT
ejpam-6202	442	3	k	k	NOUN
ejpam-6202	442	4	i	i	PROPN
ejpam-6202	442	5	)	)	PUNCT
ejpam-6202	442	6	ert+(k−i)t(−1)i	ert+(k−i)t(−1)i	X
ejpam-6202	443	1	=	=	SYM
ejpam-6202	443	2	k∑	k∑	PROPN
ejpam-6202	443	3	i=0	i=0	PROPN
ejpam-6202	443	4	(	(	PUNCT
ejpam-6202	443	5	k	k	NOUN
ejpam-6202	443	6	i	i	PROPN
ejpam-6202	443	7	)	)	PUNCT
ejpam-6202	443	8	ert(et)k−i(−1)i	ert(et)k−i(−1)i	VERB
ejpam-6202	443	9	∞∑	∞∑	PRON
ejpam-6202	443	10	n=0	n=0	NUM
ejpam-6202	443	11	gn(x	gn(x	PUNCT
ejpam-6202	443	12	)	)	PUNCT
ejpam-6202	443	13	tn	tn	NOUN
ejpam-6202	443	14	n	n	NOUN
ejpam-6202	443	15	!	!	PUNCT
ejpam-6202	444	1	=	=	PUNCT
ejpam-6202	445	1			PROPN
ejpam-6202	445	2	k∑	k∑	PROPN
ejpam-6202	445	3	i=0	i=0	PROPN
ejpam-6202	445	4	(	(	PUNCT
ejpam-6202	445	5	k	k	NOUN
ejpam-6202	445	6	i	i	PROPN
ejpam-6202	445	7	)	)	PUNCT
ejpam-6202	445	8	∑	∑	PROPN
ejpam-6202	445	9	n≥0	n≥0	ADP
ejpam-6202	445	10	[	[	X
ejpam-6202	445	11	(	(	PUNCT
ejpam-6202	445	12	(	(	PUNCT
ejpam-6202	445	13	k	k	NOUN
ejpam-6202	445	14	−	−	PROPN
ejpam-6202	445	15	i	i	PROPN
ejpam-6202	445	16	)	)	PUNCT
ejpam-6202	445	17	+	+	NUM
ejpam-6202	445	18	r)t]n	r)t]n	NOUN
ejpam-6202	445	19	n	n	CCONJ
ejpam-6202	445	20	!	!	PUNCT
ejpam-6202	446	1	(	(	PUNCT
ejpam-6202	446	2	−1)i	−1)i	X
ejpam-6202	446	3			PROPN
ejpam-6202	446	4	(	(	PUNCT
ejpam-6202	446	5	∞∑	∞∑	NUM
ejpam-6202	446	6	n=0	n=0	NUM
ejpam-6202	446	7	gn(x	gn(x	NOUN
ejpam-6202	446	8	)	)	PUNCT
ejpam-6202	446	9	tn	tn	NOUN
ejpam-6202	446	10	n	n	CCONJ
ejpam-6202	446	11	!	!	PUNCT
ejpam-6202	446	12	)	)	PUNCT
ejpam-6202	447	1	=	=	PUNCT
ejpam-6202	448	1			PROPN
ejpam-6202	448	2	∞∑	∞∑	NUM
ejpam-6202	448	3	n≥0	n≥0	PROPN
ejpam-6202	448	4	{	{	PUNCT
ejpam-6202	448	5	k∑	k∑	NOUN
ejpam-6202	448	6	i=0	i=0	PROPN
ejpam-6202	448	7	(	(	PUNCT
ejpam-6202	448	8	−1)i	−1)i	X
ejpam-6202	448	9	(	(	PUNCT
ejpam-6202	448	10	k	k	X
ejpam-6202	448	11	i	i	PROPN
ejpam-6202	448	12	)	)	PUNCT
ejpam-6202	448	13	(	(	PUNCT
ejpam-6202	448	14	(	(	PUNCT
ejpam-6202	448	15	k	k	X
ejpam-6202	448	16	−	−	PROPN
ejpam-6202	448	17	i	i	PROPN
ejpam-6202	448	18	)	)	PUNCT
ejpam-6202	448	19	+	+	PUNCT
ejpam-6202	448	20	r)n	r)n	X
ejpam-6202	448	21	}	}	PUNCT
ejpam-6202	448	22	tn	tn	PROPN
ejpam-6202	448	23	n	n	NOUN
ejpam-6202	448	24	!	!	PUNCT
ejpam-6202	449	1			PROPN
ejpam-6202	449	2	(	(	PUNCT
ejpam-6202	449	3	∞∑	∞∑	NUM
ejpam-6202	449	4	n=0	n=0	NUM
ejpam-6202	449	5	gn(x	gn(x	NOUN
ejpam-6202	449	6	)	)	PUNCT
ejpam-6202	449	7	tn	tn	NOUN
ejpam-6202	449	8	n	n	CCONJ
ejpam-6202	449	9	!	!	PUNCT
ejpam-6202	449	10	)	)	PUNCT
ejpam-6202	450	1	=	=	PUNCT
ejpam-6202	451	1			PROPN
ejpam-6202	451	2	∞∑	∞∑	NUM
ejpam-6202	451	3	n≥0	n≥0	PROPN
ejpam-6202	451	4	k	k	NOUN
ejpam-6202	451	5	!	!	PUNCT
ejpam-6202	451	6	{	{	PUNCT
ejpam-6202	452	1	n+	n+	ADP
ejpam-6202	452	2	r	r	NOUN
ejpam-6202	452	3	k	k	NOUN
ejpam-6202	453	1	+	+	CCONJ
ejpam-6202	453	2	r	r	NOUN
ejpam-6202	453	3	}	}	PUNCT
ejpam-6202	453	4	r	r	NOUN
ejpam-6202	453	5	tn	tn	NOUN
ejpam-6202	453	6	n	n	ADV
ejpam-6202	453	7	!	!	PUNCT
ejpam-6202	454	1			PROPN
ejpam-6202	454	2	(	(	PUNCT
ejpam-6202	454	3	∞∑	∞∑	NUM
ejpam-6202	454	4	n=0	n=0	NUM
ejpam-6202	454	5	gn(x	gn(x	NOUN
ejpam-6202	454	6	)	)	PUNCT
ejpam-6202	454	7	tn	tn	NOUN
ejpam-6202	454	8	n	n	CCONJ
ejpam-6202	454	9	!	!	PUNCT
ejpam-6202	454	10	)	)	PUNCT
ejpam-6202	455	1	=	=	PUNCT
ejpam-6202	456	1	∞∑	∞∑	NUM
ejpam-6202	456	2	n=0	n=0	NUM
ejpam-6202	456	3	n∑	n∑	NOUN
ejpam-6202	456	4	m=0	m=0	PROPN
ejpam-6202	456	5	k	k	PROPN
ejpam-6202	456	6	!	!	PUNCT
ejpam-6202	456	7	{	{	PUNCT
ejpam-6202	457	1	m+	m+	NOUN
ejpam-6202	458	1	r	r	NOUN
ejpam-6202	458	2	k	k	PROPN
ejpam-6202	459	1	+	+	CCONJ
ejpam-6202	459	2	r	r	NOUN
ejpam-6202	459	3	}	}	PUNCT
ejpam-6202	459	4	r	r	NOUN
ejpam-6202	459	5	tm	tm	NOUN
ejpam-6202	459	6	m	m	PROPN
ejpam-6202	459	7	!	!	PUNCT
ejpam-6202	459	8	gn−m(x	gn−m(x	NOUN
ejpam-6202	459	9	)	)	PUNCT
ejpam-6202	460	1	tn−m	tn−m	PROPN
ejpam-6202	460	2	(	(	PUNCT
ejpam-6202	460	3	n−m	n−m	PROPN
ejpam-6202	460	4	)	)	PUNCT
ejpam-6202	460	5	!	!	PUNCT
ejpam-6202	461	1	=	=	PUNCT
ejpam-6202	462	1	∞∑	∞∑	PRON
ejpam-6202	462	2	n=0	n=0	PRON
ejpam-6202	462	3	{	{	PUNCT
ejpam-6202	462	4	n∑	n∑	NOUN
ejpam-6202	462	5	m=0	m=0	PROPN
ejpam-6202	462	6	k	k	PROPN
ejpam-6202	462	7	!	!	PUNCT
ejpam-6202	462	8	{	{	PUNCT
ejpam-6202	463	1	m+	m+	NOUN
ejpam-6202	464	1	r	r	NOUN
ejpam-6202	464	2	k	k	PROPN
ejpam-6202	465	1	+	+	CCONJ
ejpam-6202	465	2	r	r	NOUN
ejpam-6202	465	3	}	}	PUNCT
ejpam-6202	465	4	r	r	NOUN
ejpam-6202	465	5	1	1	NUM
ejpam-6202	465	6	(	(	PUNCT
ejpam-6202	465	7	n−m)!m	n−m)!m	PROPN
ejpam-6202	465	8	!	!	PUNCT
ejpam-6202	465	9	gn−m(x	gn−m(x	PROPN
ejpam-6202	465	10	)	)	PUNCT
ejpam-6202	465	11	}	}	PUNCT
ejpam-6202	465	12	tn	tn	NOUN
ejpam-6202	466	1	=	=	SYM
ejpam-6202	466	2	∞∑	∞∑	NUM
ejpam-6202	466	3	n=0	n=0	PRON
ejpam-6202	466	4	{	{	PUNCT
ejpam-6202	466	5	n∑	n∑	NOUN
ejpam-6202	466	6	m=0	m=0	PROPN
ejpam-6202	466	7	k	k	PROPN
ejpam-6202	466	8	!	!	PUNCT
ejpam-6202	466	9	{	{	PUNCT
ejpam-6202	467	1	m+	m+	NOUN
ejpam-6202	468	1	r	r	NOUN
ejpam-6202	468	2	k	k	PROPN
ejpam-6202	469	1	+	+	CCONJ
ejpam-6202	469	2	r	r	NOUN
ejpam-6202	469	3	}	}	PUNCT
ejpam-6202	469	4	r	r	NOUN
ejpam-6202	469	5	(	(	PUNCT
ejpam-6202	469	6	n	n	NOUN
ejpam-6202	469	7	m	m	VERB
ejpam-6202	469	8	)	)	PUNCT
ejpam-6202	469	9	j−m∑	j−m∑	X
ejpam-6202	469	10	i=0	i=0	PROPN
ejpam-6202	470	1	(	(	PUNCT
ejpam-6202	470	2	j	j	PROPN
ejpam-6202	470	3	−m	−m	VERB
ejpam-6202	470	4	i	i	PROPN
ejpam-6202	470	5	)	)	PUNCT
ejpam-6202	471	1	gm−ix	gm−ix	PROPN
ejpam-6202	471	2	i	i	PRON
ejpam-6202	471	3	}	}	PUNCT
ejpam-6202	471	4	tn	tn	PROPN
ejpam-6202	471	5	n	n	PROPN
ejpam-6202	471	6	!	!	PROPN
ejpam-6202	471	7	17	17	NUM
ejpam-6202	471	8	of	of	ADP
ejpam-6202	471	9	26	26	NUM
ejpam-6202	471	10	=	=	NOUN
ejpam-6202	471	11	∞∑	∞∑	NUM
ejpam-6202	471	12	n=0	n=0	PRON
ejpam-6202	471	13	{	{	PUNCT
ejpam-6202	471	14	n∑	n∑	NOUN
ejpam-6202	471	15	m=0	m=0	PROPN
ejpam-6202	471	16	j−m∑	j−m∑	PROPN
ejpam-6202	471	17	i=0	i=0	PROPN
ejpam-6202	471	18	k	k	X
ejpam-6202	471	19	!	!	PUNCT
ejpam-6202	471	20	{	{	PUNCT
ejpam-6202	472	1	m+	m+	NOUN
ejpam-6202	473	1	r	r	NOUN
ejpam-6202	473	2	k	k	PROPN
ejpam-6202	474	1	+	+	CCONJ
ejpam-6202	474	2	r	r	NOUN
ejpam-6202	474	3	}	}	PUNCT
ejpam-6202	474	4	r	r	NOUN
ejpam-6202	474	5	(	(	PUNCT
ejpam-6202	474	6	n	n	NOUN
ejpam-6202	474	7	m	m	VERB
ejpam-6202	474	8	)	)	PUNCT
ejpam-6202	474	9	(	(	PUNCT
ejpam-6202	474	10	j	j	PROPN
ejpam-6202	474	11	−m	−m	NOUN
ejpam-6202	474	12	i	i	PROPN
ejpam-6202	474	13	)	)	PUNCT
ejpam-6202	475	1	gm−ix	gm−ix	PROPN
ejpam-6202	475	2	i	i	PRON
ejpam-6202	475	3	}	}	PUNCT
ejpam-6202	475	4	tn	tn	PROPN
ejpam-6202	475	5	n	n	ADP
ejpam-6202	475	6	!	!	PUNCT
ejpam-6202	476	1	comparing	compare	VERB
ejpam-6202	476	2	the	the	DET
ejpam-6202	476	3	coefficients	coefficient	NOUN
ejpam-6202	476	4	of	of	ADP
ejpam-6202	476	5	tn	tn	NOUN
ejpam-6202	476	6	n	n	CCONJ
ejpam-6202	476	7	!	!	PROPN
ejpam-6202	477	1	,	,	PUNCT
ejpam-6202	477	2	we	we	PRON
ejpam-6202	477	3	have	have	VERB
ejpam-6202	477	4	k!sg2	k!sg2	PROPN
ejpam-6202	477	5	n(x	n(x	PROPN
ejpam-6202	477	6	;	;	PUNCT
ejpam-6202	477	7	k	k	X
ejpam-6202	477	8	,	,	PUNCT
ejpam-6202	477	9	r	r	NOUN
ejpam-6202	477	10	)	)	PUNCT
ejpam-6202	477	11	=	=	SYM
ejpam-6202	477	12	n∑	n∑	NOUN
ejpam-6202	477	13	m=0	m=0	PROPN
ejpam-6202	477	14	j−m∑	j−m∑	PROPN
ejpam-6202	477	15	i=0	i=0	PROPN
ejpam-6202	477	16	k	k	X
ejpam-6202	477	17	!	!	PUNCT
ejpam-6202	477	18	{	{	PUNCT
ejpam-6202	478	1	m+	m+	NOUN
ejpam-6202	479	1	r	r	NOUN
ejpam-6202	479	2	k	k	PROPN
ejpam-6202	480	1	+	+	CCONJ
ejpam-6202	480	2	r	r	NOUN
ejpam-6202	480	3	}	}	PUNCT
ejpam-6202	480	4	r	r	NOUN
ejpam-6202	480	5	(	(	PUNCT
ejpam-6202	480	6	n	n	NOUN
ejpam-6202	480	7	m	m	VERB
ejpam-6202	480	8	)	)	PUNCT
ejpam-6202	480	9	(	(	PUNCT
ejpam-6202	480	10	j	j	PROPN
ejpam-6202	480	11	−m	−m	NOUN
ejpam-6202	480	12	i	i	PROPN
ejpam-6202	480	13	)	)	PUNCT
ejpam-6202	481	1	gm−ix	gm−ix	PROPN
ejpam-6202	482	1	i	i	PRON
ejpam-6202	482	2	sg2	sg2	PROPN
ejpam-6202	482	3	n(x	n(x	PROPN
ejpam-6202	482	4	;	;	PUNCT
ejpam-6202	482	5	k	k	X
ejpam-6202	482	6	,	,	PUNCT
ejpam-6202	482	7	r	r	NOUN
ejpam-6202	482	8	)	)	PUNCT
ejpam-6202	482	9	=	=	SYM
ejpam-6202	482	10	n∑	n∑	PROPN
ejpam-6202	482	11	m=0	m=0	PROPN
ejpam-6202	482	12	j−m∑	j−m∑	PROPN
ejpam-6202	482	13	i=0	i=0	PROPN
ejpam-6202	482	14	{	{	PUNCT
ejpam-6202	483	1	m+	m+	NOUN
ejpam-6202	483	2	r	r	NOUN
ejpam-6202	483	3	k	k	NOUN
ejpam-6202	484	1	+	+	CCONJ
ejpam-6202	484	2	r	r	NOUN
ejpam-6202	484	3	}	}	PUNCT
ejpam-6202	484	4	r	r	NOUN
ejpam-6202	484	5	(	(	PUNCT
ejpam-6202	484	6	n	n	NOUN
ejpam-6202	484	7	m	m	VERB
ejpam-6202	484	8	)	)	PUNCT
ejpam-6202	484	9	(	(	PUNCT
ejpam-6202	484	10	j	j	PROPN
ejpam-6202	484	11	−m	−m	NOUN
ejpam-6202	484	12	i	i	PROPN
ejpam-6202	484	13	)	)	PUNCT
ejpam-6202	485	1	gm−ix	gm−ix	PROPN
ejpam-6202	485	2	i	i	PRON
ejpam-6202	485	3	3	3	NUM
ejpam-6202	485	4	.	.	PUNCT
ejpam-6202	486	1	r	r	X
ejpam-6202	486	2	-	-	PUNCT
ejpam-6202	486	3	stirling	stirling	NOUN
ejpam-6202	486	4	genocchi	genocchi	PROPN
ejpam-6202	486	5	polynomials	polynomial	NOUN
ejpam-6202	486	6	of	of	ADP
ejpam-6202	486	7	higher	high	ADJ
ejpam-6202	486	8	order	order	NOUN
ejpam-6202	486	9	the	the	DET
ejpam-6202	486	10	genocchi	genocchi	PROPN
ejpam-6202	486	11	polynomials	polynomial	NOUN
ejpam-6202	486	12	of	of	ADP
ejpam-6202	486	13	higher	high	ADJ
ejpam-6202	486	14	order	order	NOUN
ejpam-6202	486	15	satisfy	satisfy	VERB
ejpam-6202	486	16	the	the	DET
ejpam-6202	486	17	relation	relation	NOUN
ejpam-6202	486	18	∞∑	∞∑	PROPN
ejpam-6202	486	19	n=0	n=0	NUM
ejpam-6202	486	20	gw	gw	PROPN
ejpam-6202	486	21	n	n	PROPN
ejpam-6202	486	22	(	(	PUNCT
ejpam-6202	486	23	x	x	NOUN
ejpam-6202	486	24	)	)	PUNCT
ejpam-6202	486	25	tn	tn	PROPN
ejpam-6202	486	26	n	n	NOUN
ejpam-6202	486	27	!	!	PUNCT
ejpam-6202	487	1	=	=	PUNCT
ejpam-6202	487	2	(	(	PUNCT
ejpam-6202	487	3	2	2	NUM
ejpam-6202	487	4	t	t	NOUN
ejpam-6202	487	5	et	et	NOUN
ejpam-6202	487	6	+	+	CCONJ
ejpam-6202	487	7	1	1	X
ejpam-6202	487	8	)	)	PUNCT
ejpam-6202	487	9	w	w	PROPN
ejpam-6202	487	10	ext	ext	NOUN
ejpam-6202	487	11	,	,	PUNCT
ejpam-6202	487	12	(	(	PUNCT
ejpam-6202	487	13	see	see	VERB
ejpam-6202	487	14	[	[	X
ejpam-6202	487	15	4	4	NUM
ejpam-6202	487	16	]	]	NUM
ejpam-6202	487	17	)	)	PUNCT
ejpam-6202	487	18	.	.	PUNCT
ejpam-6202	488	1	now	now	ADV
ejpam-6202	488	2	,	,	PUNCT
ejpam-6202	488	3	we	we	PRON
ejpam-6202	488	4	define	define	VERB
ejpam-6202	488	5	the	the	DET
ejpam-6202	488	6	r	r	NOUN
ejpam-6202	488	7	-	-	PUNCT
ejpam-6202	488	8	stirling	stirling	NOUN
ejpam-6202	488	9	genocchi	genocchi	PROPN
ejpam-6202	488	10	polynomials	polynomial	NOUN
ejpam-6202	488	11	of	of	ADP
ejpam-6202	488	12	higher	high	ADJ
ejpam-6202	488	13	order	order	NOUN
ejpam-6202	488	14	by	by	ADP
ejpam-6202	488	15	means	mean	NOUN
ejpam-6202	488	16	of	of	ADP
ejpam-6202	488	17	exponential	exponential	ADJ
ejpam-6202	488	18	generating	generating	NOUN
ejpam-6202	488	19	function	function	NOUN
ejpam-6202	488	20	are	be	AUX
ejpam-6202	488	21	as	as	SCONJ
ejpam-6202	488	22	follows	follow	VERB
ejpam-6202	488	23	:	:	PUNCT
ejpam-6202	488	24	∞∑	∞∑	NUM
ejpam-6202	488	25	n=0	n=0	NUM
ejpam-6202	488	26	sg1w	sg1w	PROPN
ejpam-6202	488	27	n	n	CCONJ
ejpam-6202	488	28	(	(	PUNCT
ejpam-6202	488	29	x	x	X
ejpam-6202	488	30	;	;	PUNCT
ejpam-6202	488	31	k	k	X
ejpam-6202	488	32	,	,	PUNCT
ejpam-6202	488	33	r	r	NOUN
ejpam-6202	488	34	)	)	PUNCT
ejpam-6202	488	35	tn	tn	NOUN
ejpam-6202	488	36	n	n	NOUN
ejpam-6202	488	37	!	!	PUNCT
ejpam-6202	489	1	=	=	PUNCT
ejpam-6202	489	2	(	(	PUNCT
ejpam-6202	489	3	1	1	NUM
ejpam-6202	489	4	1	1	NUM
ejpam-6202	489	5	+	+	NUM
ejpam-6202	489	6	t	t	NOUN
ejpam-6202	489	7	)	)	PUNCT
ejpam-6202	489	8	r	r	NOUN
ejpam-6202	489	9	(	(	PUNCT
ejpam-6202	489	10	2	2	NUM
ejpam-6202	489	11	t	t	NOUN
ejpam-6202	489	12	et	et	NOUN
ejpam-6202	490	1	+	+	CCONJ
ejpam-6202	490	2	1	1	X
ejpam-6202	490	3	)	)	PUNCT
ejpam-6202	490	4	w	w	NOUN
ejpam-6202	490	5	ext	ext	NOUN
ejpam-6202	490	6	lnk(1	lnk(1	NOUN
ejpam-6202	490	7	+	+	CCONJ
ejpam-6202	490	8	t	t	X
ejpam-6202	490	9	)	)	PUNCT
ejpam-6202	491	1	k	k	NOUN
ejpam-6202	491	2	!	!	PUNCT
ejpam-6202	492	1	(	(	PUNCT
ejpam-6202	492	2	13	13	NUM
ejpam-6202	492	3	)	)	PUNCT
ejpam-6202	492	4	∞∑	∞∑	PRON
ejpam-6202	492	5	n=0	n=0	PROPN
ejpam-6202	492	6	sg2w	sg2w	PROPN
ejpam-6202	492	7	n	n	CCONJ
ejpam-6202	492	8	(	(	PUNCT
ejpam-6202	492	9	x	x	X
ejpam-6202	492	10	;	;	PUNCT
ejpam-6202	492	11	k	k	X
ejpam-6202	492	12	,	,	PUNCT
ejpam-6202	492	13	r	r	NOUN
ejpam-6202	492	14	)	)	PUNCT
ejpam-6202	492	15	tn	tn	NOUN
ejpam-6202	492	16	n	n	NOUN
ejpam-6202	492	17	!	!	PUNCT
ejpam-6202	492	18	=	=	PUNCT
ejpam-6202	493	1	(	(	PUNCT
ejpam-6202	493	2	2	2	NUM
ejpam-6202	493	3	t	t	NOUN
ejpam-6202	493	4	et	et	NOUN
ejpam-6202	493	5	+	+	CCONJ
ejpam-6202	493	6	1	1	X
ejpam-6202	493	7	)	)	PUNCT
ejpam-6202	493	8	w	w	NOUN
ejpam-6202	493	9	extert(et	extert(et	PROPN
ejpam-6202	493	10	−	−	PROPN
ejpam-6202	493	11	1)k	1)k	NUM
ejpam-6202	493	12	k!(et	k!(et	NOUN
ejpam-6202	493	13	+	+	CCONJ
ejpam-6202	493	14	1	1	NUM
ejpam-6202	493	15	)	)	PUNCT
ejpam-6202	493	16	(	(	PUNCT
ejpam-6202	493	17	14	14	NUM
ejpam-6202	493	18	)	)	PUNCT
ejpam-6202	493	19	we	we	PRON
ejpam-6202	493	20	can	can	AUX
ejpam-6202	493	21	also	also	ADV
ejpam-6202	493	22	establish	establish	VERB
ejpam-6202	493	23	some	some	DET
ejpam-6202	493	24	properties	property	NOUN
ejpam-6202	493	25	parallel	parallel	ADJ
ejpam-6202	493	26	to	to	ADP
ejpam-6202	493	27	those	those	PRON
ejpam-6202	493	28	of	of	ADP
ejpam-6202	493	29	r	r	NOUN
ejpam-6202	493	30	-	-	PUNCT
ejpam-6202	493	31	stirling	stirling	NOUN
ejpam-6202	493	32	genocchi	genocchi	PROPN
ejpam-6202	493	33	polynomials	polynomial	NOUN
ejpam-6202	493	34	.	.	PUNCT
ejpam-6202	494	1	theorem	theorem	VERB
ejpam-6202	494	2	3.1	3.1	NUM
ejpam-6202	494	3	.	.	PUNCT
ejpam-6202	494	4	convolution	convolution	NOUN
ejpam-6202	494	5	formula	formula	NOUN
ejpam-6202	494	6	of	of	ADP
ejpam-6202	494	7	the	the	DET
ejpam-6202	494	8	r	r	NOUN
ejpam-6202	494	9	-	-	PUNCT
ejpam-6202	494	10	stirling	stirling	NOUN
ejpam-6202	494	11	numbers	number	NOUN
ejpam-6202	494	12	and	and	CCONJ
ejpam-6202	494	13	genocchi	genocchi	PROPN
ejpam-6202	494	14	polynomials	polynomial	NOUN
ejpam-6202	494	15	of	of	ADP
ejpam-6202	494	16	higher	high	ADJ
ejpam-6202	494	17	order	order	NOUN
ejpam-6202	494	18	are	be	AUX
ejpam-6202	494	19	given	give	VERB
ejpam-6202	494	20	as	as	SCONJ
ejpam-6202	494	21	follows	follow	VERB
ejpam-6202	494	22	:	:	PUNCT
ejpam-6202	494	23	sg1w	sg1w	PROPN
ejpam-6202	494	24	n	n	CCONJ
ejpam-6202	494	25	(	(	PUNCT
ejpam-6202	494	26	x	x	X
ejpam-6202	494	27	;	;	PUNCT
ejpam-6202	494	28	k	k	X
ejpam-6202	494	29	,	,	PUNCT
ejpam-6202	494	30	r	r	NOUN
ejpam-6202	494	31	)	)	PUNCT
ejpam-6202	494	32	=	=	SYM
ejpam-6202	494	33	n∑	n∑	PROPN
ejpam-6202	494	34	j	j	PROPN
ejpam-6202	495	1	=	=	PROPN
ejpam-6202	495	2	k	k	PROPN
ejpam-6202	495	3	̂[j	̂[j	PROPN
ejpam-6202	496	1	+	+	CCONJ
ejpam-6202	497	1	r	r	X
ejpam-6202	497	2	k	k	NOUN
ejpam-6202	498	1	+	+	CCONJ
ejpam-6202	498	2	r	r	NOUN
ejpam-6202	498	3	]	]	X
ejpam-6202	498	4	r	r	NOUN
ejpam-6202	498	5	(	(	PUNCT
ejpam-6202	498	6	n	n	X
ejpam-6202	498	7	j	j	PROPN
ejpam-6202	498	8	)	)	PUNCT
ejpam-6202	498	9	gw	gw	PROPN
ejpam-6202	498	10	n−j(x	n−j(x	NOUN
ejpam-6202	498	11	)	)	PUNCT
ejpam-6202	498	12	(	(	PUNCT
ejpam-6202	498	13	15	15	NUM
ejpam-6202	498	14	)	)	PUNCT
ejpam-6202	498	15	sg2w	sg2w	PROPN
ejpam-6202	498	16	n	n	CCONJ
ejpam-6202	498	17	(	(	PUNCT
ejpam-6202	498	18	x	x	X
ejpam-6202	498	19	;	;	PUNCT
ejpam-6202	498	20	k	k	X
ejpam-6202	498	21	,	,	PUNCT
ejpam-6202	498	22	r	r	NOUN
ejpam-6202	498	23	)	)	PUNCT
ejpam-6202	498	24	=	=	SYM
ejpam-6202	499	1	n∑	n∑	PROPN
ejpam-6202	499	2	j	j	PROPN
ejpam-6202	500	1	=	=	PROPN
ejpam-6202	500	2	k	k	PROPN
ejpam-6202	500	3	{	{	PUNCT
ejpam-6202	500	4	j	j	PROPN
ejpam-6202	500	5	+	+	CCONJ
ejpam-6202	500	6	r	r	NOUN
ejpam-6202	500	7	k	k	NOUN
ejpam-6202	500	8	+	+	CCONJ
ejpam-6202	500	9	r	r	NOUN
ejpam-6202	500	10	}	}	PUNCT
ejpam-6202	500	11	r	r	NOUN
ejpam-6202	500	12	(	(	PUNCT
ejpam-6202	500	13	n	n	X
ejpam-6202	500	14	j	j	PROPN
ejpam-6202	500	15	)	)	PUNCT
ejpam-6202	500	16	gw	gw	PROPN
ejpam-6202	500	17	n−j(x	n−j(x	PROPN
ejpam-6202	500	18	)	)	PUNCT
ejpam-6202	500	19	(	(	PUNCT
ejpam-6202	500	20	16	16	NUM
ejpam-6202	500	21	)	)	PUNCT
ejpam-6202	501	1	where	where	SCONJ
ejpam-6202	501	2	n	n	PRON
ejpam-6202	501	3	≥	≥	AUX
ejpam-6202	501	4	k	k	NOUN
ejpam-6202	501	5	otherwise	otherwise	ADV
ejpam-6202	501	6	sg1w	sg1w	VERB
ejpam-6202	501	7	n	n	CCONJ
ejpam-6202	501	8	(	(	PUNCT
ejpam-6202	501	9	x	x	X
ejpam-6202	501	10	;	;	PUNCT
ejpam-6202	501	11	k	k	X
ejpam-6202	501	12	,	,	PUNCT
ejpam-6202	501	13	r	r	NOUN
ejpam-6202	501	14	)	)	PUNCT
ejpam-6202	501	15	=	=	SYM
ejpam-6202	502	1	sg2w	sg2w	PROPN
ejpam-6202	502	2	n	n	CCONJ
ejpam-6202	502	3	(	(	PUNCT
ejpam-6202	502	4	x	x	X
ejpam-6202	502	5	;	;	PUNCT
ejpam-6202	502	6	k	k	X
ejpam-6202	502	7	,	,	PUNCT
ejpam-6202	502	8	r	r	NOUN
ejpam-6202	502	9	)	)	PUNCT
ejpam-6202	502	10	=	=	SYM
ejpam-6202	502	11	0	0	NUM
ejpam-6202	502	12	proof	proof	NOUN
ejpam-6202	502	13	.	.	PUNCT
ejpam-6202	503	1	the	the	DET
ejpam-6202	503	2	exponential	exponential	ADJ
ejpam-6202	503	3	generating	generating	NOUN
ejpam-6202	503	4	function	function	NOUN
ejpam-6202	503	5	in	in	ADP
ejpam-6202	503	6	(	(	PUNCT
ejpam-6202	503	7	13	13	NUM
ejpam-6202	503	8	)	)	PUNCT
ejpam-6202	503	9	can	can	AUX
ejpam-6202	503	10	be	be	AUX
ejpam-6202	503	11	written	write	VERB
ejpam-6202	503	12	as	as	ADP
ejpam-6202	503	13	∞∑	∞∑	NUM
ejpam-6202	503	14	n=0	n=0	NUM
ejpam-6202	503	15	sg1w	sg1w	PROPN
ejpam-6202	503	16	n	n	CCONJ
ejpam-6202	503	17	(	(	PUNCT
ejpam-6202	503	18	x	x	X
ejpam-6202	503	19	;	;	PUNCT
ejpam-6202	503	20	k	k	X
ejpam-6202	503	21	,	,	PUNCT
ejpam-6202	503	22	r	r	NOUN
ejpam-6202	503	23	)	)	PUNCT
ejpam-6202	503	24	tn	tn	NOUN
ejpam-6202	503	25	n	n	NOUN
ejpam-6202	503	26	!	!	PUNCT
ejpam-6202	504	1	=	=	PUNCT
ejpam-6202	504	2	(	(	PUNCT
ejpam-6202	504	3	1	1	NUM
ejpam-6202	504	4	1	1	NUM
ejpam-6202	504	5	+	+	NUM
ejpam-6202	504	6	t	t	NOUN
ejpam-6202	504	7	)	)	PUNCT
ejpam-6202	504	8	r	r	NOUN
ejpam-6202	504	9	(	(	PUNCT
ejpam-6202	504	10	2	2	NUM
ejpam-6202	504	11	t	t	NOUN
ejpam-6202	504	12	et	et	NOUN
ejpam-6202	505	1	+	+	CCONJ
ejpam-6202	505	2	1	1	X
ejpam-6202	505	3	)	)	PUNCT
ejpam-6202	505	4	w	w	NOUN
ejpam-6202	505	5	ext	ext	NOUN
ejpam-6202	505	6	lnk(1	lnk(1	NOUN
ejpam-6202	505	7	+	+	CCONJ
ejpam-6202	505	8	t	t	X
ejpam-6202	505	9	)	)	PUNCT
ejpam-6202	506	1	k	k	NOUN
ejpam-6202	506	2	!	!	PROPN
ejpam-6202	506	3	18	18	NUM
ejpam-6202	506	4	of	of	ADP
ejpam-6202	506	5	26	26	NUM
ejpam-6202	506	6	=	=	SYM
ejpam-6202	506	7	(	(	PUNCT
ejpam-6202	506	8	1	1	NUM
ejpam-6202	506	9	1	1	NUM
ejpam-6202	506	10	+	+	NUM
ejpam-6202	506	11	t	t	NOUN
ejpam-6202	506	12	)	)	PUNCT
ejpam-6202	506	13	r	r	NOUN
ejpam-6202	506	14	lnk(1	lnk(1	NOUN
ejpam-6202	506	15	+	+	CCONJ
ejpam-6202	506	16	t	t	X
ejpam-6202	506	17	)	)	PUNCT
ejpam-6202	507	1	k	k	NOUN
ejpam-6202	507	2	!	!	PUNCT
ejpam-6202	508	1	(	(	PUNCT
ejpam-6202	508	2	2	2	NUM
ejpam-6202	508	3	t	t	NOUN
ejpam-6202	508	4	et	et	NOUN
ejpam-6202	508	5	+	+	CCONJ
ejpam-6202	508	6	1	1	X
ejpam-6202	508	7	)	)	PUNCT
ejpam-6202	508	8	w	w	NOUN
ejpam-6202	508	9	ext	ext	NOUN
ejpam-6202	508	10	=	=	PUNCT
ejpam-6202	509	1	(	(	PUNCT
ejpam-6202	509	2	∞∑	∞∑	NUM
ejpam-6202	509	3	n=0	n=0	NUM
ejpam-6202	509	4	̂[n+	̂[n+	ADP
ejpam-6202	509	5	r	r	NOUN
ejpam-6202	509	6	k	k	NOUN
ejpam-6202	510	1	+	+	CCONJ
ejpam-6202	510	2	r	r	NOUN
ejpam-6202	510	3	]	]	PUNCT
ejpam-6202	510	4	r	r	NOUN
ejpam-6202	510	5	tn	tn	PROPN
ejpam-6202	510	6	n	n	CCONJ
ejpam-6202	510	7	!	!	PUNCT
ejpam-6202	510	8	)	)	PUNCT
ejpam-6202	511	1	(	(	PUNCT
ejpam-6202	511	2	∞∑	∞∑	PROPN
ejpam-6202	511	3	n=0	n=0	NUM
ejpam-6202	511	4	gw	gw	PROPN
ejpam-6202	511	5	n	n	PROPN
ejpam-6202	511	6	(	(	PUNCT
ejpam-6202	511	7	x	x	NOUN
ejpam-6202	511	8	)	)	PUNCT
ejpam-6202	511	9	tn	tn	PROPN
ejpam-6202	511	10	n	n	NOUN
ejpam-6202	511	11	!	!	PUNCT
ejpam-6202	511	12	)	)	PUNCT
ejpam-6202	512	1	=	=	PUNCT
ejpam-6202	513	1	∞∑	∞∑	NUM
ejpam-6202	513	2	n=0	n=0	NUM
ejpam-6202	513	3	n∑	n∑	ADV
ejpam-6202	513	4	j=0	j=0	PROPN
ejpam-6202	513	5	̂[j	̂[j	NOUN
ejpam-6202	513	6	+	+	CCONJ
ejpam-6202	513	7	r	r	X
ejpam-6202	513	8	k	k	NOUN
ejpam-6202	514	1	+	+	CCONJ
ejpam-6202	514	2	r	r	NOUN
ejpam-6202	514	3	]	]	PUNCT
ejpam-6202	515	1	r	r	NOUN
ejpam-6202	515	2	tj	tj	PROPN
ejpam-6202	515	3	j	j	PROPN
ejpam-6202	515	4	!	!	PUNCT
ejpam-6202	516	1	gw	gw	PROPN
ejpam-6202	516	2	n−j(x	n−j(x	NOUN
ejpam-6202	516	3	)	)	PUNCT
ejpam-6202	516	4	tn−j	tn−j	NOUN
ejpam-6202	516	5	(	(	PUNCT
ejpam-6202	516	6	n−	n−	NOUN
ejpam-6202	516	7	j	j	NOUN
ejpam-6202	516	8	)	)	PUNCT
ejpam-6202	516	9	!	!	PUNCT
ejpam-6202	517	1	=	=	PUNCT
ejpam-6202	518	1	∞∑	∞∑	PRON
ejpam-6202	518	2	n=0	n=0	NUM
ejpam-6202	518	3			PUNCT
ejpam-6202	518	4	n∑	n∑	NOUN
ejpam-6202	518	5	j=0	j=0	PROPN
ejpam-6202	518	6	̂[j	̂[j	NOUN
ejpam-6202	518	7	+	+	CCONJ
ejpam-6202	518	8	r	r	X
ejpam-6202	518	9	k	k	NOUN
ejpam-6202	519	1	+	+	CCONJ
ejpam-6202	519	2	r	r	NOUN
ejpam-6202	519	3	]	]	PUNCT
ejpam-6202	519	4	r	r	NOUN
ejpam-6202	519	5	n	n	NOUN
ejpam-6202	519	6	!	!	PUNCT
ejpam-6202	520	1	(	(	PUNCT
ejpam-6202	520	2	n−	n−	NOUN
ejpam-6202	520	3	j)!j	j)!j	PROPN
ejpam-6202	520	4	!	!	PUNCT
ejpam-6202	521	1	gw	gw	PROPN
ejpam-6202	521	2	n−j(x	n−j(x	NOUN
ejpam-6202	521	3	)	)	PUNCT
ejpam-6202	522	1			PROPN
ejpam-6202	522	2	tn	tn	NOUN
ejpam-6202	522	3	n	n	CCONJ
ejpam-6202	522	4	!	!	PUNCT
ejpam-6202	522	5	=	=	PUNCT
ejpam-6202	523	1	∞∑	∞∑	PRON
ejpam-6202	523	2	n=0	n=0	NUM
ejpam-6202	523	3			PUNCT
ejpam-6202	523	4	n∑	n∑	NOUN
ejpam-6202	523	5	j=0	j=0	PROPN
ejpam-6202	523	6	̂[j	̂[j	NOUN
ejpam-6202	523	7	+	+	CCONJ
ejpam-6202	523	8	r	r	X
ejpam-6202	523	9	k	k	NOUN
ejpam-6202	524	1	+	+	CCONJ
ejpam-6202	524	2	r	r	NOUN
ejpam-6202	524	3	]	]	X
ejpam-6202	524	4	r	r	NOUN
ejpam-6202	524	5	(	(	PUNCT
ejpam-6202	524	6	n	n	X
ejpam-6202	524	7	j	j	PROPN
ejpam-6202	524	8	)	)	PUNCT
ejpam-6202	524	9	gw	gw	PROPN
ejpam-6202	524	10	n−j(x	n−j(x	NOUN
ejpam-6202	524	11	)	)	PUNCT
ejpam-6202	525	1			PROPN
ejpam-6202	525	2	tn	tn	PROPN
ejpam-6202	525	3	n	n	CCONJ
ejpam-6202	525	4	!	!	PUNCT
ejpam-6202	525	5	comparing	compare	VERB
ejpam-6202	525	6	the	the	DET
ejpam-6202	525	7	coefficients	coefficient	NOUN
ejpam-6202	525	8	of	of	ADP
ejpam-6202	525	9	tn	tn	NOUN
ejpam-6202	525	10	n	n	X
ejpam-6202	525	11	!	!	PUNCT
ejpam-6202	525	12	yields	yield	VERB
ejpam-6202	525	13	the	the	DET
ejpam-6202	525	14	desired	desire	VERB
ejpam-6202	525	15	convolution	convolution	NOUN
ejpam-6202	525	16	formula	formula	NOUN
ejpam-6202	525	17	in	in	ADP
ejpam-6202	525	18	(	(	PUNCT
ejpam-6202	525	19	15	15	NUM
ejpam-6202	525	20	)	)	PUNCT
ejpam-6202	525	21	.	.	PUNCT
ejpam-6202	526	1	on	on	ADP
ejpam-6202	526	2	the	the	DET
ejpam-6202	526	3	other	other	ADJ
ejpam-6202	526	4	hand	hand	NOUN
ejpam-6202	526	5	,	,	PUNCT
ejpam-6202	526	6	the	the	DET
ejpam-6202	526	7	exponential	exponential	ADJ
ejpam-6202	526	8	generating	generating	NOUN
ejpam-6202	526	9	function	function	NOUN
ejpam-6202	526	10	in	in	ADP
ejpam-6202	526	11	(	(	PUNCT
ejpam-6202	526	12	14	14	NUM
ejpam-6202	526	13	)	)	PUNCT
ejpam-6202	526	14	can	can	AUX
ejpam-6202	526	15	be	be	AUX
ejpam-6202	526	16	written	write	VERB
ejpam-6202	526	17	as	as	ADP
ejpam-6202	526	18	∞∑	∞∑	NUM
ejpam-6202	526	19	n=0	n=0	PROPN
ejpam-6202	526	20	sg2w	sg2w	PROPN
ejpam-6202	526	21	n	n	CCONJ
ejpam-6202	526	22	(	(	PUNCT
ejpam-6202	526	23	x	x	X
ejpam-6202	526	24	;	;	PUNCT
ejpam-6202	526	25	k	k	X
ejpam-6202	526	26	,	,	PUNCT
ejpam-6202	526	27	r	r	NOUN
ejpam-6202	526	28	)	)	PUNCT
ejpam-6202	526	29	tn	tn	NOUN
ejpam-6202	526	30	n	n	NOUN
ejpam-6202	526	31	!	!	PUNCT
ejpam-6202	527	1	=	=	PUNCT
ejpam-6202	527	2	(	(	PUNCT
ejpam-6202	527	3	2	2	NUM
ejpam-6202	527	4	t	t	NOUN
ejpam-6202	527	5	et	et	NOUN
ejpam-6202	527	6	+	+	CCONJ
ejpam-6202	527	7	1	1	X
ejpam-6202	527	8	)	)	PUNCT
ejpam-6202	527	9	w	w	NOUN
ejpam-6202	527	10	extert(et	extert(et	PROPN
ejpam-6202	527	11	−	−	PROPN
ejpam-6202	527	12	1)k	1)k	NUM
ejpam-6202	527	13	k!(et	k!(et	NOUN
ejpam-6202	527	14	+	+	CCONJ
ejpam-6202	527	15	1	1	X
ejpam-6202	527	16	)	)	PUNCT
ejpam-6202	527	17	=	=	NOUN
ejpam-6202	527	18	ert(et	ert(et	X
ejpam-6202	527	19	−	−	PROPN
ejpam-6202	527	20	1)k	1)k	NUM
ejpam-6202	527	21	k	k	NOUN
ejpam-6202	527	22	!	!	PUNCT
ejpam-6202	528	1	(	(	PUNCT
ejpam-6202	528	2	2	2	NUM
ejpam-6202	528	3	t	t	NOUN
ejpam-6202	528	4	et	et	NOUN
ejpam-6202	528	5	+	+	CCONJ
ejpam-6202	528	6	1	1	X
ejpam-6202	528	7	)	)	PUNCT
ejpam-6202	528	8	w	w	NOUN
ejpam-6202	528	9	ext	ext	NOUN
ejpam-6202	528	10	=	=	PUNCT
ejpam-6202	529	1	(	(	PUNCT
ejpam-6202	529	2	∞∑	∞∑	PROPN
ejpam-6202	529	3	n=0	n=0	NUM
ejpam-6202	529	4	{	{	PUNCT
ejpam-6202	529	5	n+	n+	ADP
ejpam-6202	529	6	r	r	NOUN
ejpam-6202	529	7	k	k	NOUN
ejpam-6202	529	8	+	+	CCONJ
ejpam-6202	529	9	r	r	NOUN
ejpam-6202	529	10	}	}	PUNCT
ejpam-6202	529	11	r	r	NOUN
ejpam-6202	529	12	tn	tn	NOUN
ejpam-6202	529	13	n	n	CCONJ
ejpam-6202	529	14	!	!	PUNCT
ejpam-6202	529	15	)	)	PUNCT
ejpam-6202	530	1	(	(	PUNCT
ejpam-6202	530	2	∞∑	∞∑	PROPN
ejpam-6202	530	3	n=0	n=0	NUM
ejpam-6202	530	4	gw	gw	PROPN
ejpam-6202	530	5	n	n	PROPN
ejpam-6202	530	6	(	(	PUNCT
ejpam-6202	530	7	x	x	NOUN
ejpam-6202	530	8	)	)	PUNCT
ejpam-6202	530	9	tn	tn	PROPN
ejpam-6202	530	10	n	n	NOUN
ejpam-6202	530	11	!	!	PUNCT
ejpam-6202	530	12	)	)	PUNCT
ejpam-6202	531	1	=	=	PUNCT
ejpam-6202	532	1	∞∑	∞∑	NUM
ejpam-6202	532	2	n=0	n=0	PROPN
ejpam-6202	532	3	n∑	n∑	PRON
ejpam-6202	532	4	j=0	j=0	PROPN
ejpam-6202	532	5	{	{	PUNCT
ejpam-6202	532	6	j	j	PROPN
ejpam-6202	533	1	+	+	CCONJ
ejpam-6202	533	2	r	r	NOUN
ejpam-6202	533	3	k	k	NOUN
ejpam-6202	534	1	+	+	CCONJ
ejpam-6202	534	2	r	r	NOUN
ejpam-6202	534	3	}	}	PUNCT
ejpam-6202	534	4	r	r	PROPN
ejpam-6202	534	5	tj	tj	NOUN
ejpam-6202	534	6	j	j	PROPN
ejpam-6202	534	7	!	!	PUNCT
ejpam-6202	535	1	gw	gw	PROPN
ejpam-6202	535	2	n−j(x	n−j(x	NOUN
ejpam-6202	535	3	)	)	PUNCT
ejpam-6202	535	4	tn−j	tn−j	NOUN
ejpam-6202	535	5	(	(	PUNCT
ejpam-6202	535	6	n−	n−	NOUN
ejpam-6202	535	7	j	j	NOUN
ejpam-6202	535	8	)	)	PUNCT
ejpam-6202	535	9	!	!	PUNCT
ejpam-6202	536	1	=	=	PUNCT
ejpam-6202	537	1	∞∑	∞∑	PRON
ejpam-6202	537	2	n=0	n=0	NUM
ejpam-6202	537	3			PUNCT
ejpam-6202	537	4	n∑	n∑	NOUN
ejpam-6202	537	5	j=0	j=0	PROPN
ejpam-6202	537	6	{	{	PUNCT
ejpam-6202	537	7	j	j	PROPN
ejpam-6202	537	8	+	+	CCONJ
ejpam-6202	537	9	r	r	NOUN
ejpam-6202	537	10	k	k	NOUN
ejpam-6202	538	1	+	+	CCONJ
ejpam-6202	538	2	r	r	NOUN
ejpam-6202	538	3	}	}	PUNCT
ejpam-6202	538	4	r	r	NOUN
ejpam-6202	538	5	n	n	NOUN
ejpam-6202	538	6	!	!	PUNCT
ejpam-6202	539	1	(	(	PUNCT
ejpam-6202	539	2	n−	n−	NOUN
ejpam-6202	539	3	j)!j	j)!j	PROPN
ejpam-6202	539	4	!	!	PUNCT
ejpam-6202	540	1	gw	gw	PROPN
ejpam-6202	540	2	n−j(x	n−j(x	NOUN
ejpam-6202	540	3	)	)	PUNCT
ejpam-6202	541	1			PROPN
ejpam-6202	541	2	tn	tn	NOUN
ejpam-6202	541	3	n	n	CCONJ
ejpam-6202	541	4	!	!	PUNCT
ejpam-6202	541	5	=	=	PUNCT
ejpam-6202	542	1	∞∑	∞∑	PRON
ejpam-6202	542	2	n=0	n=0	NUM
ejpam-6202	542	3			PUNCT
ejpam-6202	542	4	n∑	n∑	NOUN
ejpam-6202	542	5	j=0	j=0	PROPN
ejpam-6202	542	6	{	{	PUNCT
ejpam-6202	542	7	j	j	PROPN
ejpam-6202	543	1	+	+	CCONJ
ejpam-6202	543	2	r	r	NOUN
ejpam-6202	543	3	k	k	NOUN
ejpam-6202	544	1	+	+	CCONJ
ejpam-6202	544	2	r	r	NOUN
ejpam-6202	544	3	}	}	PUNCT
ejpam-6202	544	4	r	r	NOUN
ejpam-6202	544	5	(	(	PUNCT
ejpam-6202	544	6	n	n	X
ejpam-6202	544	7	j	j	PROPN
ejpam-6202	544	8	)	)	PUNCT
ejpam-6202	544	9	gw	gw	PROPN
ejpam-6202	544	10	n−j(x	n−j(x	NOUN
ejpam-6202	544	11	)	)	PUNCT
ejpam-6202	545	1			PROPN
ejpam-6202	545	2	tn	tn	PROPN
ejpam-6202	545	3	n	n	CCONJ
ejpam-6202	545	4	!	!	PUNCT
ejpam-6202	545	5	comparing	compare	VERB
ejpam-6202	545	6	the	the	DET
ejpam-6202	545	7	coefficients	coefficient	NOUN
ejpam-6202	545	8	of	of	ADP
ejpam-6202	545	9	tn	tn	NOUN
ejpam-6202	545	10	n	n	X
ejpam-6202	545	11	!	!	PUNCT
ejpam-6202	545	12	yields	yield	VERB
ejpam-6202	545	13	the	the	DET
ejpam-6202	545	14	desired	desire	VERB
ejpam-6202	545	15	convolution	convolution	NOUN
ejpam-6202	545	16	formula	formula	NOUN
ejpam-6202	545	17	in	in	ADP
ejpam-6202	545	18	(	(	PUNCT
ejpam-6202	545	19	16	16	NUM
ejpam-6202	545	20	)	)	PUNCT
ejpam-6202	545	21	.	.	PUNCT
ejpam-6202	546	1	theorem	theorem	VERB
ejpam-6202	546	2	3.2	3.2	NUM
ejpam-6202	546	3	.	.	PUNCT
ejpam-6202	547	1	the	the	DET
ejpam-6202	547	2	horizontal	horizontal	ADJ
ejpam-6202	547	3	generating	generate	VERB
ejpam-6202	547	4	function	function	NOUN
ejpam-6202	547	5	for	for	ADP
ejpam-6202	547	6	both	both	DET
ejpam-6202	547	7	kinds	kind	NOUN
ejpam-6202	547	8	of	of	ADP
ejpam-6202	547	9	r	r	NOUN
ejpam-6202	547	10	-	-	PUNCT
ejpam-6202	547	11	stirling	stirling	NOUN
ejpam-6202	547	12	genocchi	genocchi	PROPN
ejpam-6202	547	13	polynomials	polynomial	NOUN
ejpam-6202	547	14	of	of	ADP
ejpam-6202	547	15	higher	high	ADJ
ejpam-6202	547	16	order	order	NOUN
ejpam-6202	547	17	are	be	AUX
ejpam-6202	547	18	given	give	VERB
ejpam-6202	547	19	as	as	SCONJ
ejpam-6202	547	20	follows	follow	VERB
ejpam-6202	547	21	:	:	PUNCT
ejpam-6202	548	1	gw	gw	PROPN
ejpam-6202	548	2	n	n	PROPN
ejpam-6202	548	3	(	(	PUNCT
ejpam-6202	548	4	x+	x+	X
ejpam-6202	548	5	z	z	NOUN
ejpam-6202	548	6	−	−	NOUN
ejpam-6202	548	7	r	r	NOUN
ejpam-6202	548	8	)	)	PUNCT
ejpam-6202	548	9	=	=	SYM
ejpam-6202	548	10	n∑	n∑	NOUN
ejpam-6202	548	11	k=0	k=0	PROPN
ejpam-6202	548	12	sg1w	sg1w	PROPN
ejpam-6202	548	13	n	n	PROPN
ejpam-6202	548	14	(	(	PUNCT
ejpam-6202	548	15	x	x	X
ejpam-6202	548	16	;	;	PUNCT
ejpam-6202	548	17	k	k	X
ejpam-6202	548	18	,	,	PUNCT
ejpam-6202	548	19	r)zk	r)zk	PROPN
ejpam-6202	548	20	(	(	PUNCT
ejpam-6202	548	21	17	17	NUM
ejpam-6202	548	22	)	)	PUNCT
ejpam-6202	548	23	19	19	NUM
ejpam-6202	548	24	of	of	ADP
ejpam-6202	548	25	26	26	NUM
ejpam-6202	548	26	gw	gw	PROPN
ejpam-6202	548	27	n	n	PROPN
ejpam-6202	548	28	(	(	PUNCT
ejpam-6202	548	29	x+	x+	X
ejpam-6202	548	30	z	z	NOUN
ejpam-6202	548	31	+	+	NOUN
ejpam-6202	548	32	r	r	X
ejpam-6202	548	33	)	)	PUNCT
ejpam-6202	548	34	=	=	SYM
ejpam-6202	549	1	n∑	n∑	PROPN
ejpam-6202	549	2	k=0	k=0	PROPN
ejpam-6202	549	3	sg2w	sg2w	PROPN
ejpam-6202	549	4	n	n	CCONJ
ejpam-6202	549	5	(	(	PUNCT
ejpam-6202	549	6	x	x	X
ejpam-6202	549	7	;	;	PUNCT
ejpam-6202	549	8	k	k	X
ejpam-6202	549	9	,	,	PUNCT
ejpam-6202	549	10	r)zk	r)zk	PROPN
ejpam-6202	549	11	(	(	PUNCT
ejpam-6202	549	12	18	18	NUM
ejpam-6202	549	13	)	)	PUNCT
ejpam-6202	549	14	proof	proof	NOUN
ejpam-6202	549	15	.	.	PUNCT
ejpam-6202	550	1	the	the	DET
ejpam-6202	550	2	exponential	exponential	ADJ
ejpam-6202	550	3	generating	generating	NOUN
ejpam-6202	550	4	function	function	NOUN
ejpam-6202	550	5	of	of	ADP
ejpam-6202	550	6	(	(	PUNCT
ejpam-6202	550	7	13	13	NUM
ejpam-6202	550	8	)	)	PUNCT
ejpam-6202	550	9	can	can	AUX
ejpam-6202	550	10	be	be	AUX
ejpam-6202	550	11	written	write	VERB
ejpam-6202	550	12	as	as	ADP
ejpam-6202	550	13	∞∑	∞∑	NUM
ejpam-6202	550	14	k=0	k=0	PROPN
ejpam-6202	550	15	{	{	PUNCT
ejpam-6202	550	16	∞∑	∞∑	PROPN
ejpam-6202	550	17	n	n	CCONJ
ejpam-6202	550	18	=	=	SYM
ejpam-6202	550	19	k	k	X
ejpam-6202	550	20	sg1w	sg1w	PROPN
ejpam-6202	550	21	n	n	PROPN
ejpam-6202	550	22	(	(	PUNCT
ejpam-6202	550	23	x	x	X
ejpam-6202	550	24	;	;	PUNCT
ejpam-6202	550	25	k	k	X
ejpam-6202	550	26	,	,	PUNCT
ejpam-6202	550	27	r	r	NOUN
ejpam-6202	550	28	)	)	PUNCT
ejpam-6202	550	29	tn	tn	NOUN
ejpam-6202	550	30	n	n	NOUN
ejpam-6202	550	31	!	!	PUNCT
ejpam-6202	550	32	}	}	PUNCT
ejpam-6202	551	1	zk	zk	PROPN
ejpam-6202	552	1	=	=	PUNCT
ejpam-6202	553	1	(	(	PUNCT
ejpam-6202	553	2	1	1	NUM
ejpam-6202	553	3	1	1	NUM
ejpam-6202	553	4	+	+	NUM
ejpam-6202	553	5	t	t	NOUN
ejpam-6202	553	6	)	)	PUNCT
ejpam-6202	553	7	r	r	NOUN
ejpam-6202	553	8	(	(	PUNCT
ejpam-6202	553	9	2	2	NUM
ejpam-6202	553	10	t	t	NOUN
ejpam-6202	553	11	et	et	NOUN
ejpam-6202	553	12	+	+	CCONJ
ejpam-6202	553	13	1	1	X
ejpam-6202	553	14	)	)	PUNCT
ejpam-6202	553	15	w	w	NOUN
ejpam-6202	553	16	ext	ext	NOUN
ejpam-6202	553	17	∑	∑	ADV
ejpam-6202	553	18	k≥0	k≥0	PROPN
ejpam-6202	553	19	lnk(1	lnk(1	NOUN
ejpam-6202	553	20	+	+	CCONJ
ejpam-6202	553	21	t	t	X
ejpam-6202	553	22	)	)	PUNCT
ejpam-6202	554	1	k	k	NOUN
ejpam-6202	554	2	!	!	PUNCT
ejpam-6202	554	3	zk	zk	X
ejpam-6202	555	1	=	=	PUNCT
ejpam-6202	555	2	(	(	PUNCT
ejpam-6202	555	3	1	1	NUM
ejpam-6202	555	4	1	1	NUM
ejpam-6202	555	5	+	+	NUM
ejpam-6202	555	6	t	t	NOUN
ejpam-6202	555	7	)	)	PUNCT
ejpam-6202	555	8	r	r	NOUN
ejpam-6202	555	9	(	(	PUNCT
ejpam-6202	555	10	2	2	NUM
ejpam-6202	555	11	t	t	NOUN
ejpam-6202	555	12	et	et	NOUN
ejpam-6202	555	13	+	+	CCONJ
ejpam-6202	555	14	1	1	X
ejpam-6202	555	15	)	)	PUNCT
ejpam-6202	555	16	w	w	NOUN
ejpam-6202	555	17	ext	ext	NOUN
ejpam-6202	555	18	∑	∑	PROPN
ejpam-6202	555	19	k≥0	k≥0	PROPN
ejpam-6202	555	20	[	[	X
ejpam-6202	555	21	z	z	X
ejpam-6202	555	22	ln(1	ln(1	NOUN
ejpam-6202	555	23	+	+	NOUN
ejpam-6202	555	24	t)]k	t)]k	NOUN
ejpam-6202	555	25	k	k	NOUN
ejpam-6202	555	26	!	!	PUNCT
ejpam-6202	556	1	=	=	PUNCT
ejpam-6202	556	2	(	(	PUNCT
ejpam-6202	556	3	1	1	NUM
ejpam-6202	556	4	1	1	NUM
ejpam-6202	556	5	+	+	NUM
ejpam-6202	556	6	t	t	NOUN
ejpam-6202	556	7	)	)	PUNCT
ejpam-6202	556	8	r	r	NOUN
ejpam-6202	556	9	eln(1+t)z	eln(1+t)z	NOUN
ejpam-6202	556	10	(	(	PUNCT
ejpam-6202	556	11	2	2	NUM
ejpam-6202	556	12	t	t	NOUN
ejpam-6202	556	13	et	et	NOUN
ejpam-6202	556	14	+	+	CCONJ
ejpam-6202	556	15	1	1	X
ejpam-6202	556	16	)	)	PUNCT
ejpam-6202	556	17	w	w	NOUN
ejpam-6202	556	18	ext	ext	NOUN
ejpam-6202	556	19	=	=	PUNCT
ejpam-6202	556	20	∑	∑	PUNCT
ejpam-6202	556	21	n≥0	n≥0	PROPN
ejpam-6202	556	22	(	(	PUNCT
ejpam-6202	556	23	z	z	NOUN
ejpam-6202	556	24	−	−	PROPN
ejpam-6202	556	25	r	r	NOUN
ejpam-6202	556	26	n	n	NOUN
ejpam-6202	556	27	)	)	PUNCT
ejpam-6202	556	28	tn	tn	NOUN
ejpam-6202	556	29	∞∑	∞∑	NUM
ejpam-6202	556	30	n=0	n=0	PUNCT
ejpam-6202	556	31	gw	gw	PROPN
ejpam-6202	556	32	n	n	PROPN
ejpam-6202	556	33	(	(	PUNCT
ejpam-6202	556	34	x	x	NOUN
ejpam-6202	556	35	)	)	PUNCT
ejpam-6202	556	36	tn	tn	PROPN
ejpam-6202	556	37	n	n	NOUN
ejpam-6202	556	38	!	!	PUNCT
ejpam-6202	557	1	=	=	PUNCT
ejpam-6202	558	1	∑	∑	NOUN
ejpam-6202	558	2	n≥0	n≥0	PROPN
ejpam-6202	558	3	(	(	PUNCT
ejpam-6202	558	4	z	z	NOUN
ejpam-6202	558	5	−	−	NOUN
ejpam-6202	558	6	r)n	r)n	NOUN
ejpam-6202	558	7	tn	tn	NOUN
ejpam-6202	558	8	n	n	X
ejpam-6202	558	9	!	!	PUNCT
ejpam-6202	559	1			PROPN
ejpam-6202	559	2	(	(	PUNCT
ejpam-6202	559	3	∞∑	∞∑	PROPN
ejpam-6202	559	4	n=0	n=0	NUM
ejpam-6202	559	5	gw	gw	PROPN
ejpam-6202	559	6	n	n	PROPN
ejpam-6202	559	7	(	(	PUNCT
ejpam-6202	559	8	x	x	NOUN
ejpam-6202	559	9	)	)	PUNCT
ejpam-6202	559	10	tn	tn	PROPN
ejpam-6202	559	11	n	n	NOUN
ejpam-6202	559	12	!	!	PUNCT
ejpam-6202	559	13	)	)	PUNCT
ejpam-6202	560	1	=	=	PUNCT
ejpam-6202	561	1	∞∑	∞∑	NUM
ejpam-6202	561	2	n=0	n=0	NUM
ejpam-6202	561	3	n∑	n∑	NOUN
ejpam-6202	561	4	m=0	m=0	PROPN
ejpam-6202	561	5	(	(	PUNCT
ejpam-6202	561	6	z	z	NOUN
ejpam-6202	561	7	−	−	NOUN
ejpam-6202	561	8	r)m	r)m	NOUN
ejpam-6202	561	9	tm	tm	PROPN
ejpam-6202	561	10	m	m	PROPN
ejpam-6202	561	11	!	!	PUNCT
ejpam-6202	562	1	gw	gw	PROPN
ejpam-6202	562	2	n−m(x	n−m(x	PROPN
ejpam-6202	562	3	)	)	PUNCT
ejpam-6202	563	1	tn−m	tn−m	PROPN
ejpam-6202	563	2	(	(	PUNCT
ejpam-6202	563	3	n−m	n−m	PROPN
ejpam-6202	563	4	)	)	PUNCT
ejpam-6202	563	5	!	!	PUNCT
ejpam-6202	564	1	=	=	PUNCT
ejpam-6202	565	1	∞∑	∞∑	PRON
ejpam-6202	565	2	n=0	n=0	NUM
ejpam-6202	565	3	{	{	PUNCT
ejpam-6202	565	4	n∑	n∑	PROPN
ejpam-6202	565	5	m=0	m=0	PROPN
ejpam-6202	565	6	(	(	PUNCT
ejpam-6202	565	7	z	z	NOUN
ejpam-6202	565	8	−	−	NOUN
ejpam-6202	565	9	r)m	r)m	NOUN
ejpam-6202	565	10	1	1	NUM
ejpam-6202	565	11	(	(	PUNCT
ejpam-6202	565	12	n−m)!m	n−m)!m	PROPN
ejpam-6202	565	13	!	!	PUNCT
ejpam-6202	565	14	gw	gw	PROPN
ejpam-6202	565	15	n−m(x	n−m(x	PROPN
ejpam-6202	565	16	)	)	PUNCT
ejpam-6202	565	17	}	}	PUNCT
ejpam-6202	566	1	tn	tn	NOUN
ejpam-6202	567	1	=	=	SYM
ejpam-6202	567	2	∞∑	∞∑	NUM
ejpam-6202	567	3	n=0	n=0	PRON
ejpam-6202	567	4	{	{	PUNCT
ejpam-6202	567	5	n∑	n∑	PROPN
ejpam-6202	567	6	m=0	m=0	PROPN
ejpam-6202	567	7	(	(	PUNCT
ejpam-6202	567	8	z	z	NOUN
ejpam-6202	567	9	−	−	NOUN
ejpam-6202	567	10	r)m	r)m	NOUN
ejpam-6202	567	11	(	(	PUNCT
ejpam-6202	567	12	n	n	X
ejpam-6202	567	13	m	m	VERB
ejpam-6202	567	14	)	)	PUNCT
ejpam-6202	567	15	gw	gw	PROPN
ejpam-6202	567	16	n−m(x	n−m(x	PROPN
ejpam-6202	567	17	)	)	PUNCT
ejpam-6202	567	18	}	}	PUNCT
ejpam-6202	567	19	tn	tn	PROPN
ejpam-6202	567	20	n	n	NOUN
ejpam-6202	567	21	!	!	PUNCT
ejpam-6202	567	22	=	=	NOUN
ejpam-6202	568	1	∞∑	∞∑	PRON
ejpam-6202	568	2	n=0	n=0	NUM
ejpam-6202	568	3	{	{	PUNCT
ejpam-6202	568	4	n∑	n∑	NOUN
ejpam-6202	568	5	m=0	m=0	PROPN
ejpam-6202	568	6	(	(	PUNCT
ejpam-6202	568	7	n	n	NOUN
ejpam-6202	568	8	m	m	VERB
ejpam-6202	568	9	)	)	PUNCT
ejpam-6202	569	1	gw	gw	ADP
ejpam-6202	569	2	n−m(x)(z	n−m(x)(z	PUNCT
ejpam-6202	570	1	−	−	NOUN
ejpam-6202	570	2	r)m	r)m	NOUN
ejpam-6202	570	3	}	}	PUNCT
ejpam-6202	570	4	tn	tn	PROPN
ejpam-6202	570	5	n	n	CCONJ
ejpam-6202	570	6	!	!	PUNCT
ejpam-6202	571	1	rewriting	rewrite	VERB
ejpam-6202	571	2	∞∑	∞∑	PRON
ejpam-6202	571	3	n=0	n=0	PROPN
ejpam-6202	571	4	{	{	PUNCT
ejpam-6202	571	5	n∑	n∑	NOUN
ejpam-6202	571	6	k=0	k=0	PROPN
ejpam-6202	571	7	sg1w	sg1w	PROPN
ejpam-6202	571	8	n	n	PROPN
ejpam-6202	571	9	(	(	PUNCT
ejpam-6202	571	10	x	x	X
ejpam-6202	571	11	;	;	PUNCT
ejpam-6202	571	12	k	k	X
ejpam-6202	571	13	,	,	PUNCT
ejpam-6202	571	14	r)zk	r)zk	PROPN
ejpam-6202	571	15	}	}	PUNCT
ejpam-6202	571	16	tn	tn	PROPN
ejpam-6202	571	17	n	n	NOUN
ejpam-6202	571	18	!	!	PUNCT
ejpam-6202	572	1	=	=	NOUN
ejpam-6202	573	1	∞∑	∞∑	PRON
ejpam-6202	573	2	n=0	n=0	NUM
ejpam-6202	573	3	{	{	PUNCT
ejpam-6202	573	4	n∑	n∑	NOUN
ejpam-6202	573	5	m=0	m=0	PROPN
ejpam-6202	573	6	(	(	PUNCT
ejpam-6202	573	7	n	n	NOUN
ejpam-6202	573	8	m	m	VERB
ejpam-6202	573	9	)	)	PUNCT
ejpam-6202	574	1	gw	gw	ADP
ejpam-6202	574	2	n−m(x)(z	n−m(x)(z	PUNCT
ejpam-6202	575	1	−	−	NOUN
ejpam-6202	575	2	r)m	r)m	NOUN
ejpam-6202	575	3	}	}	PUNCT
ejpam-6202	575	4	tn	tn	PROPN
ejpam-6202	575	5	n	n	X
ejpam-6202	575	6	!	!	PUNCT
ejpam-6202	576	1	comparing	compare	VERB
ejpam-6202	576	2	the	the	DET
ejpam-6202	576	3	coefficients	coefficient	NOUN
ejpam-6202	576	4	of	of	ADP
ejpam-6202	576	5	tn	tn	NOUN
ejpam-6202	576	6	n	n	CCONJ
ejpam-6202	576	7	!	!	PROPN
ejpam-6202	577	1	,	,	PUNCT
ejpam-6202	577	2	we	we	PRON
ejpam-6202	577	3	have	have	VERB
ejpam-6202	577	4	n∑	n∑	ADJ
ejpam-6202	577	5	k=0	k=0	PROPN
ejpam-6202	577	6	sg1w	sg1w	PROPN
ejpam-6202	577	7	n	n	PROPN
ejpam-6202	577	8	(	(	PUNCT
ejpam-6202	577	9	x	x	X
ejpam-6202	577	10	;	;	PUNCT
ejpam-6202	577	11	k	k	X
ejpam-6202	577	12	,	,	PUNCT
ejpam-6202	577	13	r)zk	r)zk	PROPN
ejpam-6202	577	14	=	=	SYM
ejpam-6202	577	15	n∑	n∑	PROPN
ejpam-6202	577	16	m=0	m=0	PROPN
ejpam-6202	577	17	(	(	PUNCT
ejpam-6202	577	18	n	n	NOUN
ejpam-6202	577	19	m	m	VERB
ejpam-6202	577	20	)	)	PUNCT
ejpam-6202	578	1	gw	gw	ADP
ejpam-6202	578	2	n−m(x)(z	n−m(x)(z	PUNCT
ejpam-6202	579	1	−	−	NOUN
ejpam-6202	579	2	r)m	r)m	NOUN
ejpam-6202	579	3	applying	apply	VERB
ejpam-6202	579	4	the	the	DET
ejpam-6202	579	5	addition	addition	NOUN
ejpam-6202	579	6	formula	formula	NOUN
ejpam-6202	579	7	,	,	PUNCT
ejpam-6202	579	8	we	we	PRON
ejpam-6202	579	9	have	have	VERB
ejpam-6202	579	10	n∑	n∑	ADJ
ejpam-6202	579	11	k=0	k=0	PROPN
ejpam-6202	579	12	sg1w	sg1w	PROPN
ejpam-6202	579	13	n	n	PROPN
ejpam-6202	579	14	(	(	PUNCT
ejpam-6202	579	15	x	x	X
ejpam-6202	579	16	;	;	PUNCT
ejpam-6202	579	17	k	k	X
ejpam-6202	579	18	,	,	PUNCT
ejpam-6202	579	19	r)zk	r)zk	PROPN
ejpam-6202	579	20	=	=	SYM
ejpam-6202	579	21	gw	gw	PROPN
ejpam-6202	579	22	n	n	PROPN
ejpam-6202	579	23	(	(	PUNCT
ejpam-6202	579	24	x+	x+	X
ejpam-6202	579	25	z	z	NOUN
ejpam-6202	580	1	−	−	NOUN
ejpam-6202	580	2	r	r	NOUN
ejpam-6202	580	3	)	)	PUNCT
ejpam-6202	580	4	20	20	NUM
ejpam-6202	580	5	of	of	ADP
ejpam-6202	580	6	26	26	NUM
ejpam-6202	580	7	similarly	similarly	ADV
ejpam-6202	580	8	(	(	PUNCT
ejpam-6202	580	9	14	14	NUM
ejpam-6202	580	10	)	)	PUNCT
ejpam-6202	580	11	can	can	AUX
ejpam-6202	580	12	be	be	AUX
ejpam-6202	580	13	written	write	VERB
ejpam-6202	580	14	as	as	ADP
ejpam-6202	580	15	∞∑	∞∑	NUM
ejpam-6202	580	16	k=0	k=0	PROPN
ejpam-6202	580	17	{	{	PUNCT
ejpam-6202	580	18	∞∑	∞∑	PROPN
ejpam-6202	580	19	n	n	CCONJ
ejpam-6202	580	20	=	=	SYM
ejpam-6202	580	21	k	k	PROPN
ejpam-6202	580	22	sg2w	sg2w	PROPN
ejpam-6202	580	23	n	n	PROPN
ejpam-6202	580	24	(	(	PUNCT
ejpam-6202	580	25	x	x	X
ejpam-6202	580	26	;	;	PUNCT
ejpam-6202	580	27	k	k	X
ejpam-6202	580	28	,	,	PUNCT
ejpam-6202	580	29	r	r	NOUN
ejpam-6202	580	30	)	)	PUNCT
ejpam-6202	580	31	tn	tn	NOUN
ejpam-6202	580	32	n	n	NOUN
ejpam-6202	580	33	!	!	PUNCT
ejpam-6202	580	34	}	}	PUNCT
ejpam-6202	580	35	zk	zk	PROPN
ejpam-6202	581	1	=	=	PUNCT
ejpam-6202	582	1	∞∑	∞∑	NUM
ejpam-6202	582	2	k=0	k=0	PROPN
ejpam-6202	582	3	{	{	PUNCT
ejpam-6202	582	4	(	(	PUNCT
ejpam-6202	582	5	2	2	NUM
ejpam-6202	582	6	t	t	NOUN
ejpam-6202	582	7	et	et	NOUN
ejpam-6202	582	8	+	+	CCONJ
ejpam-6202	582	9	1	1	X
ejpam-6202	582	10	)	)	PUNCT
ejpam-6202	582	11	w	w	NOUN
ejpam-6202	582	12	ext	ext	NOUN
ejpam-6202	582	13	ert(et	ert(et	NOUN
ejpam-6202	582	14	−	−	PROPN
ejpam-6202	582	15	1)k	1)k	NUM
ejpam-6202	582	16	k	k	NOUN
ejpam-6202	582	17	!	!	PUNCT
ejpam-6202	582	18	}	}	PUNCT
ejpam-6202	582	19	zk	zk	PROPN
ejpam-6202	583	1	=	=	PUNCT
ejpam-6202	583	2	(	(	PUNCT
ejpam-6202	583	3	2	2	NUM
ejpam-6202	583	4	t	t	NOUN
ejpam-6202	583	5	et	et	NOUN
ejpam-6202	583	6	+	+	CCONJ
ejpam-6202	583	7	1	1	X
ejpam-6202	583	8	)	)	PUNCT
ejpam-6202	583	9	w	w	NOUN
ejpam-6202	583	10	extert	extert	NOUN
ejpam-6202	583	11	∞∑	∞∑	PROPN
ejpam-6202	583	12	k=0	k=0	PROPN
ejpam-6202	584	1	(	(	PUNCT
ejpam-6202	584	2	z	z	NOUN
ejpam-6202	584	3	k	k	NOUN
ejpam-6202	584	4	)	)	PUNCT
ejpam-6202	584	5	(	(	PUNCT
ejpam-6202	584	6	et	et	NOUN
ejpam-6202	584	7	−	−	PROPN
ejpam-6202	584	8	1)k	1)k	NUM
ejpam-6202	584	9	=	=	SYM
ejpam-6202	584	10	(	(	PUNCT
ejpam-6202	584	11	2	2	NUM
ejpam-6202	584	12	t	t	NOUN
ejpam-6202	584	13	et	et	NOUN
ejpam-6202	585	1	+	+	CCONJ
ejpam-6202	585	2	1	1	X
ejpam-6202	585	3	)	)	PUNCT
ejpam-6202	585	4	w	w	PROPN
ejpam-6202	585	5	extert(1	extert(1	PROPN
ejpam-6202	586	1	+	+	CCONJ
ejpam-6202	586	2	(	(	PUNCT
ejpam-6202	586	3	et	et	NOUN
ejpam-6202	586	4	−	−	PROPN
ejpam-6202	586	5	1))z	1))z	NUM
ejpam-6202	587	1	=	=	SYM
ejpam-6202	587	2	e(z+r)t	e(z+r)t	PROPN
ejpam-6202	587	3	(	(	PUNCT
ejpam-6202	587	4	2	2	NUM
ejpam-6202	587	5	t	t	NOUN
ejpam-6202	587	6	et	et	NOUN
ejpam-6202	587	7	+	+	CCONJ
ejpam-6202	587	8	1	1	X
ejpam-6202	587	9	)	)	PUNCT
ejpam-6202	587	10	w	w	NOUN
ejpam-6202	587	11	ext	ext	NOUN
ejpam-6202	587	12	=	=	PUNCT
ejpam-6202	587	13	(	(	PUNCT
ejpam-6202	587	14	∞∑	∞∑	NUM
ejpam-6202	587	15	n=0	n=0	NUM
ejpam-6202	587	16	(	(	PUNCT
ejpam-6202	587	17	z	z	NOUN
ejpam-6202	587	18	+	+	NOUN
ejpam-6202	587	19	r)n	r)n	X
ejpam-6202	587	20	tn	tn	NOUN
ejpam-6202	587	21	n	n	CCONJ
ejpam-6202	587	22	!	!	PUNCT
ejpam-6202	587	23	)	)	PUNCT
ejpam-6202	588	1	(	(	PUNCT
ejpam-6202	588	2	∞∑	∞∑	PROPN
ejpam-6202	588	3	n=0	n=0	NUM
ejpam-6202	588	4	gw	gw	PROPN
ejpam-6202	588	5	n	n	PROPN
ejpam-6202	588	6	(	(	PUNCT
ejpam-6202	588	7	x	x	NOUN
ejpam-6202	588	8	)	)	PUNCT
ejpam-6202	588	9	tn	tn	PROPN
ejpam-6202	588	10	n	n	NOUN
ejpam-6202	588	11	!	!	PUNCT
ejpam-6202	588	12	)	)	PUNCT
ejpam-6202	589	1	=	=	PUNCT
ejpam-6202	590	1	∞∑	∞∑	NUM
ejpam-6202	590	2	n=0	n=0	NUM
ejpam-6202	590	3	n∑	n∑	NOUN
ejpam-6202	590	4	m=0	m=0	PROPN
ejpam-6202	590	5	(	(	PUNCT
ejpam-6202	590	6	z	z	NOUN
ejpam-6202	590	7	+	+	NOUN
ejpam-6202	590	8	r)m	r)m	NOUN
ejpam-6202	590	9	tm	tm	PROPN
ejpam-6202	590	10	m	m	PROPN
ejpam-6202	590	11	!	!	PUNCT
ejpam-6202	591	1	gw	gw	PROPN
ejpam-6202	591	2	n−m(x	n−m(x	PROPN
ejpam-6202	591	3	)	)	PUNCT
ejpam-6202	592	1	tn−m	tn−m	PROPN
ejpam-6202	592	2	(	(	PUNCT
ejpam-6202	592	3	n−m	n−m	PROPN
ejpam-6202	592	4	)	)	PUNCT
ejpam-6202	592	5	!	!	PUNCT
ejpam-6202	593	1	=	=	PUNCT
ejpam-6202	594	1	∞∑	∞∑	PRON
ejpam-6202	594	2	n=0	n=0	NUM
ejpam-6202	594	3	{	{	PUNCT
ejpam-6202	594	4	n∑	n∑	PROPN
ejpam-6202	594	5	m=0	m=0	PROPN
ejpam-6202	594	6	(	(	PUNCT
ejpam-6202	594	7	z	z	NOUN
ejpam-6202	594	8	+	+	NOUN
ejpam-6202	594	9	r)m	r)m	NOUN
ejpam-6202	594	10	1	1	NUM
ejpam-6202	594	11	(	(	PUNCT
ejpam-6202	594	12	n−m)!m	n−m)!m	PROPN
ejpam-6202	594	13	!	!	PUNCT
ejpam-6202	594	14	gw	gw	PROPN
ejpam-6202	594	15	n−m(x	n−m(x	PROPN
ejpam-6202	594	16	)	)	PUNCT
ejpam-6202	594	17	}	}	PUNCT
ejpam-6202	594	18	tn	tn	NOUN
ejpam-6202	595	1	=	=	SYM
ejpam-6202	595	2	∞∑	∞∑	NUM
ejpam-6202	595	3	n=0	n=0	PRON
ejpam-6202	595	4	{	{	PUNCT
ejpam-6202	595	5	n∑	n∑	PROPN
ejpam-6202	595	6	m=0	m=0	PROPN
ejpam-6202	595	7	(	(	PUNCT
ejpam-6202	595	8	z	z	NOUN
ejpam-6202	595	9	+	+	NOUN
ejpam-6202	595	10	r)m	r)m	NOUN
ejpam-6202	595	11	(	(	PUNCT
ejpam-6202	595	12	n	n	X
ejpam-6202	595	13	m	m	VERB
ejpam-6202	595	14	)	)	PUNCT
ejpam-6202	595	15	gw	gw	PROPN
ejpam-6202	595	16	n−m(x	n−m(x	PROPN
ejpam-6202	595	17	)	)	PUNCT
ejpam-6202	595	18	}	}	PUNCT
ejpam-6202	595	19	tn	tn	PROPN
ejpam-6202	595	20	n	n	NOUN
ejpam-6202	595	21	!	!	PUNCT
ejpam-6202	595	22	=	=	NOUN
ejpam-6202	596	1	∞∑	∞∑	PRON
ejpam-6202	596	2	n=0	n=0	NUM
ejpam-6202	596	3	{	{	PUNCT
ejpam-6202	596	4	n∑	n∑	NOUN
ejpam-6202	596	5	m=0	m=0	PROPN
ejpam-6202	596	6	(	(	PUNCT
ejpam-6202	596	7	n	n	NOUN
ejpam-6202	596	8	m	m	VERB
ejpam-6202	596	9	)	)	PUNCT
ejpam-6202	597	1	gw	gw	ADP
ejpam-6202	597	2	n−m(x)(z	n−m(x)(z	PUNCT
ejpam-6202	598	1	+	+	NUM
ejpam-6202	598	2	r)m	r)m	NOUN
ejpam-6202	598	3	}	}	PUNCT
ejpam-6202	598	4	tn	tn	PROPN
ejpam-6202	598	5	n	n	CCONJ
ejpam-6202	598	6	!	!	PUNCT
ejpam-6202	599	1	rewriting	rewrite	VERB
ejpam-6202	599	2	∞∑	∞∑	PRON
ejpam-6202	599	3	n=0	n=0	PROPN
ejpam-6202	599	4	{	{	PUNCT
ejpam-6202	599	5	n∑	n∑	NOUN
ejpam-6202	599	6	k=0	k=0	PROPN
ejpam-6202	599	7	sg2w	sg2w	PROPN
ejpam-6202	599	8	n	n	CCONJ
ejpam-6202	599	9	(	(	PUNCT
ejpam-6202	599	10	x	x	X
ejpam-6202	599	11	;	;	PUNCT
ejpam-6202	599	12	k	k	X
ejpam-6202	599	13	,	,	PUNCT
ejpam-6202	599	14	r)zk	r)zk	PROPN
ejpam-6202	599	15	}	}	PUNCT
ejpam-6202	599	16	tn	tn	PROPN
ejpam-6202	599	17	n	n	NOUN
ejpam-6202	599	18	!	!	PUNCT
ejpam-6202	600	1	=	=	NOUN
ejpam-6202	601	1	∞∑	∞∑	PRON
ejpam-6202	601	2	n=0	n=0	NUM
ejpam-6202	601	3	{	{	PUNCT
ejpam-6202	601	4	n∑	n∑	NOUN
ejpam-6202	601	5	m=0	m=0	PROPN
ejpam-6202	601	6	(	(	PUNCT
ejpam-6202	601	7	n	n	NOUN
ejpam-6202	601	8	m	m	VERB
ejpam-6202	601	9	)	)	PUNCT
ejpam-6202	602	1	gw	gw	ADP
ejpam-6202	602	2	n−m(x)(z	n−m(x)(z	PUNCT
ejpam-6202	603	1	+	+	NUM
ejpam-6202	603	2	r)m	r)m	NOUN
ejpam-6202	603	3	}	}	PUNCT
ejpam-6202	603	4	tn	tn	PROPN
ejpam-6202	603	5	n	n	NOUN
ejpam-6202	603	6	!	!	PUNCT
ejpam-6202	603	7	comparing	compare	VERB
ejpam-6202	603	8	the	the	DET
ejpam-6202	603	9	coefficients	coefficient	NOUN
ejpam-6202	603	10	of	of	ADP
ejpam-6202	603	11	tn	tn	NOUN
ejpam-6202	603	12	n	n	CCONJ
ejpam-6202	603	13	!	!	PROPN
ejpam-6202	603	14	,	,	PUNCT
ejpam-6202	603	15	we	we	PRON
ejpam-6202	603	16	have	have	VERB
ejpam-6202	603	17	n∑	n∑	ADJ
ejpam-6202	603	18	k=0	k=0	PROPN
ejpam-6202	603	19	sg2w	sg2w	PROPN
ejpam-6202	603	20	n	n	CCONJ
ejpam-6202	603	21	(	(	PUNCT
ejpam-6202	603	22	x	x	X
ejpam-6202	603	23	;	;	PUNCT
ejpam-6202	603	24	k	k	X
ejpam-6202	603	25	,	,	PUNCT
ejpam-6202	603	26	r)zk	r)zk	PROPN
ejpam-6202	603	27	=	=	SYM
ejpam-6202	603	28	n∑	n∑	PROPN
ejpam-6202	603	29	m=0	m=0	PROPN
ejpam-6202	603	30	(	(	PUNCT
ejpam-6202	603	31	n	n	NOUN
ejpam-6202	603	32	m	m	VERB
ejpam-6202	603	33	)	)	PUNCT
ejpam-6202	604	1	gw	gw	ADP
ejpam-6202	604	2	n−m(x)(z	n−m(x)(z	PUNCT
ejpam-6202	605	1	+	+	NUM
ejpam-6202	605	2	r)m	r)m	NOUN
ejpam-6202	605	3	applying	apply	VERB
ejpam-6202	605	4	the	the	DET
ejpam-6202	605	5	addition	addition	NOUN
ejpam-6202	605	6	formula	formula	NOUN
ejpam-6202	605	7	,	,	PUNCT
ejpam-6202	605	8	we	we	PRON
ejpam-6202	605	9	have	have	VERB
ejpam-6202	605	10	n∑	n∑	ADJ
ejpam-6202	605	11	k=0	k=0	PROPN
ejpam-6202	605	12	sg2w	sg2w	PROPN
ejpam-6202	605	13	n	n	CCONJ
ejpam-6202	605	14	(	(	PUNCT
ejpam-6202	605	15	x	x	X
ejpam-6202	605	16	;	;	PUNCT
ejpam-6202	605	17	k	k	X
ejpam-6202	605	18	,	,	PUNCT
ejpam-6202	605	19	r)zk	r)zk	PROPN
ejpam-6202	605	20	=	=	SYM
ejpam-6202	605	21	gw	gw	PROPN
ejpam-6202	605	22	n	n	PROPN
ejpam-6202	605	23	(	(	PUNCT
ejpam-6202	605	24	x+	x+	X
ejpam-6202	605	25	z	z	NOUN
ejpam-6202	605	26	+	+	CCONJ
ejpam-6202	605	27	r	r	NOUN
ejpam-6202	605	28	)	)	PUNCT
ejpam-6202	605	29	hence	hence	ADV
ejpam-6202	605	30	,	,	PUNCT
ejpam-6202	605	31	we	we	PRON
ejpam-6202	605	32	proved	prove	VERB
ejpam-6202	605	33	the	the	DET
ejpam-6202	605	34	horizontal	horizontal	ADJ
ejpam-6202	605	35	generating	generating	NOUN
ejpam-6202	605	36	function	function	NOUN
ejpam-6202	605	37	in	in	ADP
ejpam-6202	605	38	(	(	PUNCT
ejpam-6202	605	39	17	17	NUM
ejpam-6202	605	40	)	)	PUNCT
ejpam-6202	605	41	and	and	CCONJ
ejpam-6202	605	42	(	(	PUNCT
ejpam-6202	605	43	18	18	NUM
ejpam-6202	605	44	)	)	PUNCT
ejpam-6202	605	45	.	.	PUNCT
ejpam-6202	606	1	21	21	NUM
ejpam-6202	606	2	of	of	ADP
ejpam-6202	606	3	26	26	NUM
ejpam-6202	606	4	theorem	theorem	VERB
ejpam-6202	606	5	3.3	3.3	NUM
ejpam-6202	606	6	.	.	PUNCT
ejpam-6202	607	1	the	the	DET
ejpam-6202	607	2	formula	formula	NOUN
ejpam-6202	607	3	for	for	ADP
ejpam-6202	607	4	the	the	DET
ejpam-6202	607	5	first	first	ADJ
ejpam-6202	607	6	kind	kind	NOUN
ejpam-6202	607	7	of	of	ADP
ejpam-6202	607	8	r	r	NOUN
ejpam-6202	607	9	-	-	PUNCT
ejpam-6202	607	10	stirling	stirling	NOUN
ejpam-6202	607	11	genocchi	genocchi	PROPN
ejpam-6202	607	12	polynomials	polynomial	NOUN
ejpam-6202	607	13	of	of	ADP
ejpam-6202	607	14	higher	high	ADJ
ejpam-6202	607	15	order	order	NOUN
ejpam-6202	607	16	is	be	AUX
ejpam-6202	607	17	explicitly	explicitly	ADV
ejpam-6202	607	18	stated	state	VERB
ejpam-6202	607	19	as	as	SCONJ
ejpam-6202	607	20	follows	follow	VERB
ejpam-6202	607	21	:	:	PUNCT
ejpam-6202	607	22	sg1w	sg1w	PROPN
ejpam-6202	607	23	n	n	CCONJ
ejpam-6202	607	24	(	(	PUNCT
ejpam-6202	607	25	x	x	X
ejpam-6202	607	26	;	;	PUNCT
ejpam-6202	607	27	k	k	X
ejpam-6202	607	28	,	,	PUNCT
ejpam-6202	607	29	r	r	NOUN
ejpam-6202	607	30	)	)	PUNCT
ejpam-6202	607	31	=	=	SYM
ejpam-6202	607	32	n∑	n∑	PROPN
ejpam-6202	607	33	m=0	m=0	PROPN
ejpam-6202	607	34	n∑	n∑	PROPN
ejpam-6202	607	35	j	j	PROPN
ejpam-6202	608	1	=	=	NOUN
ejpam-6202	608	2	m	m	VERB
ejpam-6202	608	3	m−k∑	m−k∑	X
ejpam-6202	609	1	f=0	f=0	X
ejpam-6202	609	2	f∑	f∑	PROPN
ejpam-6202	610	1	d	d	X
ejpam-6202	611	1	=	=	X
ejpam-6202	611	2	i	i	PROPN
ejpam-6202	611	3	(	(	PUNCT
ejpam-6202	611	4	−1)n−j+d+fgw	−1)n−j+d+fgw	PROPN
ejpam-6202	611	5	j−m(x	j−m(x	PROPN
ejpam-6202	611	6	)	)	PUNCT
ejpam-6202	611	7	(	(	PUNCT
ejpam-6202	611	8	j	j	NOUN
ejpam-6202	611	9	m	m	VERB
ejpam-6202	611	10	)	)	PUNCT
ejpam-6202	611	11	(	(	PUNCT
ejpam-6202	611	12	n	n	X
ejpam-6202	611	13	j	j	NOUN
ejpam-6202	611	14	)	)	PUNCT
ejpam-6202	611	15	(	(	PUNCT
ejpam-6202	611	16	f	f	PROPN
ejpam-6202	611	17	d	d	PROPN
ejpam-6202	611	18	)	)	PUNCT
ejpam-6202	611	19	(	(	PUNCT
ejpam-6202	611	20	m−	m−	PROPN
ejpam-6202	611	21	1	1	NUM
ejpam-6202	611	22	+	+	CCONJ
ejpam-6202	611	23	f	f	PROPN
ejpam-6202	611	24	m−	m−	PROPN
ejpam-6202	611	25	k	k	PROPN
ejpam-6202	612	1	+	+	CCONJ
ejpam-6202	612	2	f	f	NOUN
ejpam-6202	612	3	)	)	PUNCT
ejpam-6202	613	1	(	(	PUNCT
ejpam-6202	613	2	2m−	2m−	NUM
ejpam-6202	613	3	k	k	NOUN
ejpam-6202	613	4	m−	m−	PROPN
ejpam-6202	613	5	k	k	PROPN
ejpam-6202	614	1	+	+	CCONJ
ejpam-6202	614	2	f	f	PROPN
ejpam-6202	614	3	)	)	PUNCT
ejpam-6202	615	1	(	(	PUNCT
ejpam-6202	615	2	f	f	X
ejpam-6202	615	3	−	−	PROPN
ejpam-6202	615	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	615	5	f	f	X
ejpam-6202	615	6	!	!	PUNCT
ejpam-6202	616	1	rn−j	rn−j	NOUN
ejpam-6202	616	2	proof	proof	NOUN
ejpam-6202	616	3	.	.	PUNCT
ejpam-6202	617	1	the	the	DET
ejpam-6202	617	2	exponential	exponential	ADJ
ejpam-6202	617	3	generating	generating	NOUN
ejpam-6202	617	4	function	function	NOUN
ejpam-6202	617	5	in	in	ADP
ejpam-6202	617	6	(	(	PUNCT
ejpam-6202	617	7	13	13	NUM
ejpam-6202	617	8	)	)	PUNCT
ejpam-6202	617	9	composed	compose	VERB
ejpam-6202	617	10	of	of	ADP
ejpam-6202	617	11	three	three	NUM
ejpam-6202	617	12	functions	function	NOUN
ejpam-6202	617	13	.	.	PUNCT
ejpam-6202	618	1	the	the	DET
ejpam-6202	618	2	first	first	ADJ
ejpam-6202	618	3	function	function	NOUN
ejpam-6202	618	4	can	can	AUX
ejpam-6202	618	5	be	be	AUX
ejpam-6202	618	6	expressed	express	VERB
ejpam-6202	618	7	as	as	ADP
ejpam-6202	618	8	(	(	PUNCT
ejpam-6202	618	9	1	1	NUM
ejpam-6202	618	10	1−	1−	NUM
ejpam-6202	618	11	t	t	NOUN
ejpam-6202	618	12	)	)	PUNCT
ejpam-6202	618	13	r	r	NOUN
ejpam-6202	618	14	=	=	PUNCT
ejpam-6202	618	15	∑	∑	PUNCT
ejpam-6202	618	16	n≥0	n≥0	PROPN
ejpam-6202	618	17	(	(	PUNCT
ejpam-6202	618	18	−1)nrn	−1)nrn	PROPN
ejpam-6202	618	19	tn	tn	PROPN
ejpam-6202	618	20	n	n	NOUN
ejpam-6202	618	21	!	!	PUNCT
ejpam-6202	619	1	where	where	SCONJ
ejpam-6202	619	2	rn	rn	PROPN
ejpam-6202	619	3	=	=	SYM
ejpam-6202	619	4	r(r	r(r	PROPN
ejpam-6202	619	5	+	+	CCONJ
ejpam-6202	619	6	1	1	NUM
ejpam-6202	619	7	)	)	PUNCT
ejpam-6202	619	8	.	.	PUNCT
ejpam-6202	619	9	.	.	PUNCT
ejpam-6202	620	1	.	.	PUNCT
ejpam-6202	621	1	(	(	PUNCT
ejpam-6202	621	2	r	r	NOUN
ejpam-6202	621	3	+	+	NUM
ejpam-6202	621	4	n−	n−	NOUN
ejpam-6202	621	5	1	1	NUM
ejpam-6202	621	6	)	)	PUNCT
ejpam-6202	621	7	the	the	DET
ejpam-6202	621	8	second	second	ADJ
ejpam-6202	621	9	function	function	NOUN
ejpam-6202	621	10	can	can	AUX
ejpam-6202	621	11	be	be	AUX
ejpam-6202	621	12	expresses	express	NOUN
ejpam-6202	621	13	as	as	ADP
ejpam-6202	621	14	the	the	DET
ejpam-6202	621	15	genocchi	genocchi	PROPN
ejpam-6202	621	16	polynomial	polynomial	NOUN
ejpam-6202	621	17	of	of	ADP
ejpam-6202	621	18	higher	high	ADJ
ejpam-6202	621	19	order	order	NOUN
ejpam-6202	621	20	,	,	PUNCT
ejpam-6202	621	21	(	(	PUNCT
ejpam-6202	621	22	2	2	NUM
ejpam-6202	621	23	t	t	NOUN
ejpam-6202	621	24	et	et	NOUN
ejpam-6202	622	1	+	+	CCONJ
ejpam-6202	622	2	1	1	X
ejpam-6202	622	3	)	)	PUNCT
ejpam-6202	622	4	w	w	NOUN
ejpam-6202	622	5	ext	ext	NOUN
ejpam-6202	622	6	=	=	PUNCT
ejpam-6202	623	1	∞∑	∞∑	PROPN
ejpam-6202	623	2	n=0	n=0	PUNCT
ejpam-6202	623	3	gw	gw	PROPN
ejpam-6202	623	4	n	n	PROPN
ejpam-6202	623	5	(	(	PUNCT
ejpam-6202	623	6	x	x	NOUN
ejpam-6202	623	7	)	)	PUNCT
ejpam-6202	623	8	tn	tn	PROPN
ejpam-6202	623	9	n	n	AUX
ejpam-6202	623	10	!	!	PUNCT
ejpam-6202	624	1	lastly	lastly	ADV
ejpam-6202	624	2	the	the	DET
ejpam-6202	624	3	third	third	ADJ
ejpam-6202	624	4	function	function	NOUN
ejpam-6202	624	5	can	can	AUX
ejpam-6202	624	6	be	be	AUX
ejpam-6202	624	7	expressed	express	VERB
ejpam-6202	624	8	1	1	NUM
ejpam-6202	624	9	k	k	NOUN
ejpam-6202	624	10	!	!	PUNCT
ejpam-6202	625	1	[	[	X
ejpam-6202	625	2	ln	ln	X
ejpam-6202	625	3	(	(	PUNCT
ejpam-6202	625	4	1	1	NUM
ejpam-6202	625	5	+	+	NUM
ejpam-6202	625	6	t)]k	t)]k	NOUN
ejpam-6202	625	7	=	=	SYM
ejpam-6202	625	8	∑	∑	PROPN
ejpam-6202	625	9	n≥k	n≥k	PROPN
ejpam-6202	625	10	s(n	s(n	PROPN
ejpam-6202	625	11	,	,	PUNCT
ejpam-6202	625	12	k	k	NOUN
ejpam-6202	625	13	)	)	PUNCT
ejpam-6202	625	14	tn	tn	PROPN
ejpam-6202	625	15	n	n	PROPN
ejpam-6202	625	16	!	!	PUNCT
ejpam-6202	625	17	hence	hence	ADV
ejpam-6202	625	18	,	,	PUNCT
ejpam-6202	625	19	using	use	VERB
ejpam-6202	625	20	cauchy	cauchy	PROPN
ejpam-6202	625	21	’s	’s	PART
ejpam-6202	625	22	rule	rule	NOUN
ejpam-6202	625	23	for	for	ADP
ejpam-6202	625	24	the	the	DET
ejpam-6202	625	25	product	product	NOUN
ejpam-6202	625	26	of	of	ADP
ejpam-6202	625	27	power	power	NOUN
ejpam-6202	625	28	series	series	NOUN
ejpam-6202	625	29	,	,	PUNCT
ejpam-6202	625	30	we	we	PRON
ejpam-6202	625	31	have	have	VERB
ejpam-6202	625	32	n∑	n∑	PROPN
ejpam-6202	625	33	k≥0	k≥0	PROPN
ejpam-6202	625	34	sg1w	sg1w	PROPN
ejpam-6202	625	35	n	n	CCONJ
ejpam-6202	625	36	(	(	PUNCT
ejpam-6202	625	37	x	x	X
ejpam-6202	625	38	;	;	PUNCT
ejpam-6202	625	39	k	k	X
ejpam-6202	625	40	,	,	PUNCT
ejpam-6202	625	41	r	r	NOUN
ejpam-6202	625	42	)	)	PUNCT
ejpam-6202	625	43	tn	tn	NOUN
ejpam-6202	625	44	n	n	CCONJ
ejpam-6202	625	45	!	!	PUNCT
ejpam-6202	626	1	=	=	PUNCT
ejpam-6202	627	1	∑	∑	NOUN
ejpam-6202	627	2	n≥0	n≥0	PROPN
ejpam-6202	627	3	(	(	PUNCT
ejpam-6202	627	4	−1)nrn	−1)nrn	PROPN
ejpam-6202	627	5	tn	tn	PROPN
ejpam-6202	627	6	n	n	ADV
ejpam-6202	627	7	!	!	PUNCT
ejpam-6202	628	1			PROPN
ejpam-6202	628	2	(	(	PUNCT
ejpam-6202	628	3	∞∑	∞∑	PROPN
ejpam-6202	628	4	n=0	n=0	NUM
ejpam-6202	628	5	gw	gw	PROPN
ejpam-6202	628	6	n	n	PROPN
ejpam-6202	628	7	(	(	PUNCT
ejpam-6202	628	8	x	x	NOUN
ejpam-6202	628	9	)	)	PUNCT
ejpam-6202	628	10	tn	tn	PROPN
ejpam-6202	628	11	n	n	PROPN
ejpam-6202	628	12	!	!	PUNCT
ejpam-6202	628	13	)	)	PUNCT
ejpam-6202	628	14	∑	∑	NOUN
ejpam-6202	628	15	n≥k	n≥k	PROPN
ejpam-6202	628	16	s(n	s(n	PROPN
ejpam-6202	628	17	,	,	PUNCT
ejpam-6202	628	18	k	k	NOUN
ejpam-6202	628	19	)	)	PUNCT
ejpam-6202	628	20	tn	tn	PROPN
ejpam-6202	629	1	n	n	NOUN
ejpam-6202	629	2	!	!	PUNCT
ejpam-6202	630	1			PROPN
ejpam-6202	631	1	=	=	PUNCT
ejpam-6202	631	2	∑	∑	NOUN
ejpam-6202	631	3	n≥0	n≥0	PROPN
ejpam-6202	631	4	(	(	PUNCT
ejpam-6202	631	5	−1)nrn	−1)nrn	PROPN
ejpam-6202	631	6	tn	tn	PROPN
ejpam-6202	631	7	n	n	ADV
ejpam-6202	631	8	!	!	PUNCT
ejpam-6202	632	1			PROPN
ejpam-6202	632	2	(	(	PUNCT
ejpam-6202	632	3	∞∑	∞∑	PROPN
ejpam-6202	632	4	n=0	n=0	PROPN
ejpam-6202	632	5	{	{	PUNCT
ejpam-6202	632	6	n∑	n∑	NOUN
ejpam-6202	632	7	m	m	PROPN
ejpam-6202	632	8	=	=	PROPN
ejpam-6202	632	9	k	k	PROPN
ejpam-6202	632	10	s(m	s(m	PROPN
ejpam-6202	632	11	,	,	PUNCT
ejpam-6202	632	12	k	k	NOUN
ejpam-6202	632	13	)	)	PUNCT
ejpam-6202	632	14	(	(	PUNCT
ejpam-6202	632	15	n	n	X
ejpam-6202	632	16	m	m	VERB
ejpam-6202	632	17	)	)	PUNCT
ejpam-6202	632	18	gw	gw	PROPN
ejpam-6202	632	19	n−m(x	n−m(x	PROPN
ejpam-6202	632	20	)	)	PUNCT
ejpam-6202	632	21	}	}	PUNCT
ejpam-6202	632	22	tn	tn	PROPN
ejpam-6202	632	23	n	n	NOUN
ejpam-6202	632	24	!	!	PUNCT
ejpam-6202	632	25	)	)	PUNCT
ejpam-6202	633	1	=	=	PUNCT
ejpam-6202	634	1	∞∑	∞∑	NUM
ejpam-6202	634	2	n=0	n=0	NUM
ejpam-6202	634	3	n∑	n∑	DET
ejpam-6202	634	4	j=0	j=0	PROPN
ejpam-6202	634	5	j∑	j∑	PROPN
ejpam-6202	634	6	m	m	PROPN
ejpam-6202	634	7	=	=	PROPN
ejpam-6202	634	8	k	k	PROPN
ejpam-6202	634	9	s(m	s(m	PROPN
ejpam-6202	634	10	,	,	PUNCT
ejpam-6202	634	11	k	k	NOUN
ejpam-6202	634	12	)	)	PUNCT
ejpam-6202	634	13	(	(	PUNCT
ejpam-6202	634	14	j	j	PROPN
ejpam-6202	634	15	m	m	VERB
ejpam-6202	634	16	)	)	PUNCT
ejpam-6202	634	17	gw	gw	PROPN
ejpam-6202	634	18	j−m(x	j−m(x	PROPN
ejpam-6202	634	19	)	)	PUNCT
ejpam-6202	634	20	tj	tj	PROPN
ejpam-6202	634	21	j	j	PROPN
ejpam-6202	634	22	!	!	PUNCT
ejpam-6202	634	23	(	(	PUNCT
ejpam-6202	634	24	−1)n−jrn−j	−1)n−jrn−j	ADV
ejpam-6202	634	25	tn−j	tn−j	NOUN
ejpam-6202	634	26	(	(	PUNCT
ejpam-6202	634	27	n−	n−	NOUN
ejpam-6202	634	28	j	j	NOUN
ejpam-6202	634	29	)	)	PUNCT
ejpam-6202	634	30	!	!	PUNCT
ejpam-6202	635	1	=	=	PUNCT
ejpam-6202	636	1	∞∑	∞∑	DET
ejpam-6202	636	2	n=0	n=0	NUM
ejpam-6202	636	3	n∑	n∑	DET
ejpam-6202	636	4	j=0	j=0	PROPN
ejpam-6202	636	5	j∑	j∑	PROPN
ejpam-6202	636	6	m	m	PROPN
ejpam-6202	636	7	=	=	PROPN
ejpam-6202	636	8	k	k	PROPN
ejpam-6202	636	9	s(m	s(m	PROPN
ejpam-6202	636	10	,	,	PUNCT
ejpam-6202	636	11	k	k	NOUN
ejpam-6202	636	12	)	)	PUNCT
ejpam-6202	636	13	(	(	PUNCT
ejpam-6202	636	14	j	j	PROPN
ejpam-6202	636	15	m	m	VERB
ejpam-6202	636	16	)	)	PUNCT
ejpam-6202	636	17	gw	gw	PROPN
ejpam-6202	636	18	j−m(x	j−m(x	PROPN
ejpam-6202	636	19	)	)	PUNCT
ejpam-6202	636	20	tj−j+n	tj−j+n	NOUN
ejpam-6202	636	21	(	(	PUNCT
ejpam-6202	636	22	n−	n−	NOUN
ejpam-6202	636	23	j)!j	j)!j	PROPN
ejpam-6202	636	24	!	!	PUNCT
ejpam-6202	637	1	(	(	PUNCT
ejpam-6202	637	2	−1)n−jrn−j	−1)n−jrn−j	ADV
ejpam-6202	637	3	=	=	VERB
ejpam-6202	638	1	∞∑	∞∑	NUM
ejpam-6202	638	2	n=0	n=0	NUM
ejpam-6202	638	3			PUNCT
ejpam-6202	638	4	n∑	n∑	PROPN
ejpam-6202	638	5	m=0	m=0	PROPN
ejpam-6202	638	6	n∑	n∑	PROPN
ejpam-6202	638	7	j	j	PROPN
ejpam-6202	639	1	=	=	PROPN
ejpam-6202	639	2	m	m	PROPN
ejpam-6202	639	3	s(m	s(m	PROPN
ejpam-6202	639	4	,	,	PUNCT
ejpam-6202	639	5	k	k	NOUN
ejpam-6202	639	6	)	)	PUNCT
ejpam-6202	639	7	(	(	PUNCT
ejpam-6202	639	8	j	j	PROPN
ejpam-6202	639	9	m	m	VERB
ejpam-6202	639	10	)	)	PUNCT
ejpam-6202	639	11	gw	gw	PROPN
ejpam-6202	639	12	j−m(x	j−m(x	PROPN
ejpam-6202	639	13	)	)	PUNCT
ejpam-6202	639	14	1	1	NUM
ejpam-6202	639	15	(	(	PUNCT
ejpam-6202	639	16	n−	n−	NOUN
ejpam-6202	639	17	j)!j	j)!j	PROPN
ejpam-6202	639	18	!	!	PUNCT
ejpam-6202	640	1	(	(	PUNCT
ejpam-6202	640	2	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	640	3			ADV
ejpam-6202	640	4	tn	tn	NOUN
ejpam-6202	641	1	=	=	PUNCT
ejpam-6202	641	2	∞∑	∞∑	NUM
ejpam-6202	641	3	n=0	n=0	NUM
ejpam-6202	641	4			PUNCT
ejpam-6202	641	5	n∑	n∑	PROPN
ejpam-6202	641	6	m=0	m=0	PROPN
ejpam-6202	641	7	n∑	n∑	PROPN
ejpam-6202	641	8	j	j	PROPN
ejpam-6202	642	1	=	=	PROPN
ejpam-6202	642	2	m	m	PROPN
ejpam-6202	642	3	s(m	s(m	PROPN
ejpam-6202	642	4	,	,	PUNCT
ejpam-6202	642	5	k	k	NOUN
ejpam-6202	642	6	)	)	PUNCT
ejpam-6202	642	7	(	(	PUNCT
ejpam-6202	642	8	j	j	PROPN
ejpam-6202	642	9	m	m	VERB
ejpam-6202	642	10	)	)	PUNCT
ejpam-6202	642	11	gw	gw	PROPN
ejpam-6202	642	12	j−m(x	j−m(x	PROPN
ejpam-6202	642	13	)	)	PUNCT
ejpam-6202	642	14	(	(	PUNCT
ejpam-6202	642	15	n	n	X
ejpam-6202	642	16	j	j	NOUN
ejpam-6202	642	17	)	)	PUNCT
ejpam-6202	642	18	(	(	PUNCT
ejpam-6202	642	19	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	642	20			PROPN
ejpam-6202	642	21	tn	tn	PROPN
ejpam-6202	642	22	n	n	CCONJ
ejpam-6202	642	23	!	!	PROPN
ejpam-6202	642	24	22	22	NUM
ejpam-6202	642	25	of	of	ADP
ejpam-6202	642	26	26	26	NUM
ejpam-6202	642	27	comparing	compare	VERB
ejpam-6202	642	28	the	the	DET
ejpam-6202	642	29	coefficients	coefficient	NOUN
ejpam-6202	642	30	of	of	ADP
ejpam-6202	642	31	tn	tn	NOUN
ejpam-6202	642	32	n	n	CCONJ
ejpam-6202	642	33	!	!	PUNCT
ejpam-6202	642	34	,	,	PUNCT
ejpam-6202	642	35	sg1w	sg1w	PROPN
ejpam-6202	642	36	n	n	PROPN
ejpam-6202	642	37	(	(	PUNCT
ejpam-6202	642	38	x	x	X
ejpam-6202	642	39	;	;	PUNCT
ejpam-6202	642	40	k	k	X
ejpam-6202	642	41	,	,	PUNCT
ejpam-6202	642	42	r	r	NOUN
ejpam-6202	642	43	)	)	PUNCT
ejpam-6202	642	44	=	=	SYM
ejpam-6202	643	1	n∑	n∑	PROPN
ejpam-6202	643	2	m=0	m=0	PROPN
ejpam-6202	643	3	n∑	n∑	PROPN
ejpam-6202	643	4	j	j	PROPN
ejpam-6202	643	5	=	=	PROPN
ejpam-6202	643	6	m	m	PROPN
ejpam-6202	643	7	s(m	s(m	PROPN
ejpam-6202	643	8	,	,	PUNCT
ejpam-6202	643	9	k	k	NOUN
ejpam-6202	643	10	)	)	PUNCT
ejpam-6202	643	11	(	(	PUNCT
ejpam-6202	643	12	j	j	PROPN
ejpam-6202	643	13	m	m	VERB
ejpam-6202	643	14	)	)	PUNCT
ejpam-6202	643	15	gw	gw	PROPN
ejpam-6202	643	16	j−m(x	j−m(x	PROPN
ejpam-6202	643	17	)	)	PUNCT
ejpam-6202	643	18	(	(	PUNCT
ejpam-6202	643	19	n	n	X
ejpam-6202	643	20	j	j	NOUN
ejpam-6202	643	21	)	)	PUNCT
ejpam-6202	643	22	(	(	PUNCT
ejpam-6202	643	23	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	643	24	using	use	VERB
ejpam-6202	643	25	the	the	DET
ejpam-6202	643	26	schlömilch	schlömilch	NOUN
ejpam-6202	643	27	formula	formula	NOUN
ejpam-6202	643	28	for	for	ADP
ejpam-6202	643	29	the	the	DET
ejpam-6202	643	30	stirling	stirling	NOUN
ejpam-6202	643	31	numbers	number	NOUN
ejpam-6202	643	32	of	of	ADP
ejpam-6202	643	33	the	the	DET
ejpam-6202	643	34	first	first	ADJ
ejpam-6202	643	35	kind	kind	NOUN
ejpam-6202	643	36	,	,	PUNCT
ejpam-6202	643	37	s(n	s(n	PROPN
ejpam-6202	643	38	,	,	PUNCT
ejpam-6202	643	39	k	k	NOUN
ejpam-6202	643	40	)	)	PUNCT
ejpam-6202	643	41	=	=	PUNCT
ejpam-6202	644	1	n−k∑	n−k∑	NOUN
ejpam-6202	644	2	r=0	r=0	VERB
ejpam-6202	644	3	r∑	r∑	PRON
ejpam-6202	644	4	j	j	X
ejpam-6202	645	1	=	=	NOUN
ejpam-6202	645	2	i	i	PROPN
ejpam-6202	645	3	(	(	PUNCT
ejpam-6202	645	4	−1)j+r	−1)j+r	NOUN
ejpam-6202	645	5	(	(	PUNCT
ejpam-6202	645	6	r	r	NOUN
ejpam-6202	645	7	j	j	PROPN
ejpam-6202	645	8	)	)	PUNCT
ejpam-6202	645	9	(	(	PUNCT
ejpam-6202	645	10	n−	n−	NOUN
ejpam-6202	645	11	1	1	NUM
ejpam-6202	645	12	+	+	CCONJ
ejpam-6202	645	13	r	r	NOUN
ejpam-6202	645	14	n−	n−	NOUN
ejpam-6202	645	15	k	k	NOUN
ejpam-6202	645	16	+	+	CCONJ
ejpam-6202	645	17	r	r	NOUN
ejpam-6202	645	18	)	)	PUNCT
ejpam-6202	645	19	(	(	PUNCT
ejpam-6202	645	20	2n−	2n−	NUM
ejpam-6202	645	21	k	k	NOUN
ejpam-6202	645	22	n−	n−	NOUN
ejpam-6202	645	23	k	k	NOUN
ejpam-6202	646	1	+	+	CCONJ
ejpam-6202	646	2	r	r	NOUN
ejpam-6202	646	3	)	)	PUNCT
ejpam-6202	646	4	(	(	PUNCT
ejpam-6202	646	5	r	r	NOUN
ejpam-6202	646	6	−	−	PROPN
ejpam-6202	646	7	j)n−k+r	j)n−k+r	PROPN
ejpam-6202	646	8	r	r	NOUN
ejpam-6202	646	9	!	!	PUNCT
ejpam-6202	647	1	then	then	ADV
ejpam-6202	647	2	the	the	DET
ejpam-6202	647	3	schlömilch	schlömilch	ADJ
ejpam-6202	647	4	formula	formula	NOUN
ejpam-6202	647	5	for	for	ADP
ejpam-6202	647	6	the	the	DET
ejpam-6202	647	7	r	r	NOUN
ejpam-6202	647	8	-	-	PUNCT
ejpam-6202	647	9	stirling	stirling	NOUN
ejpam-6202	647	10	genocchi	genocchi	PROPN
ejpam-6202	647	11	number	number	NOUN
ejpam-6202	647	12	of	of	ADP
ejpam-6202	647	13	the	the	DET
ejpam-6202	647	14	first	first	ADJ
ejpam-6202	647	15	kind	kind	NOUN
ejpam-6202	647	16	is	be	AUX
ejpam-6202	647	17	given	give	VERB
ejpam-6202	647	18	by	by	ADP
ejpam-6202	647	19	sg1w	sg1w	PROPN
ejpam-6202	647	20	n	n	CCONJ
ejpam-6202	647	21	(	(	PUNCT
ejpam-6202	647	22	x	x	X
ejpam-6202	647	23	;	;	PUNCT
ejpam-6202	647	24	k	k	X
ejpam-6202	647	25	,	,	PUNCT
ejpam-6202	647	26	r	r	NOUN
ejpam-6202	647	27	)	)	PUNCT
ejpam-6202	647	28	=	=	SYM
ejpam-6202	647	29	n∑	n∑	PROPN
ejpam-6202	647	30	m=0	m=0	PROPN
ejpam-6202	647	31	n∑	n∑	PROPN
ejpam-6202	647	32	j	j	PROPN
ejpam-6202	648	1	=	=	NOUN
ejpam-6202	648	2	m	m	PROPN
ejpam-6202	648	3	(	(	PUNCT
ejpam-6202	648	4	j	j	PROPN
ejpam-6202	648	5	m	m	VERB
ejpam-6202	648	6	)	)	PUNCT
ejpam-6202	648	7	gw	gw	PROPN
ejpam-6202	648	8	j−m(x	j−m(x	PROPN
ejpam-6202	648	9	)	)	PUNCT
ejpam-6202	648	10	(	(	PUNCT
ejpam-6202	648	11	n	n	X
ejpam-6202	648	12	j	j	NOUN
ejpam-6202	648	13	)	)	PUNCT
ejpam-6202	648	14	(	(	PUNCT
ejpam-6202	648	15	−1)n−jrn−j	−1)n−jrn−j	ADV
ejpam-6202	648	16	m−k∑	m−k∑	X
ejpam-6202	649	1	f=0	f=0	X
ejpam-6202	649	2	f∑	f∑	PROPN
ejpam-6202	650	1	d	d	X
ejpam-6202	651	1	=	=	X
ejpam-6202	651	2	i	i	PROPN
ejpam-6202	651	3	(	(	PUNCT
ejpam-6202	651	4	−1)d+f	−1)d+f	X
ejpam-6202	651	5	(	(	PUNCT
ejpam-6202	651	6	f	f	NOUN
ejpam-6202	651	7	d	d	PROPN
ejpam-6202	651	8	)	)	PUNCT
ejpam-6202	651	9	(	(	PUNCT
ejpam-6202	651	10	m−	m−	PROPN
ejpam-6202	651	11	1	1	NUM
ejpam-6202	651	12	+	+	CCONJ
ejpam-6202	651	13	f	f	PROPN
ejpam-6202	651	14	m−	m−	PROPN
ejpam-6202	651	15	k	k	PROPN
ejpam-6202	652	1	+	+	CCONJ
ejpam-6202	652	2	f	f	NOUN
ejpam-6202	652	3	)	)	PUNCT
ejpam-6202	653	1	(	(	PUNCT
ejpam-6202	653	2	2m−	2m−	NUM
ejpam-6202	653	3	k	k	NOUN
ejpam-6202	653	4	m−	m−	PROPN
ejpam-6202	653	5	k	k	PROPN
ejpam-6202	654	1	+	+	CCONJ
ejpam-6202	654	2	f	f	PROPN
ejpam-6202	654	3	)	)	PUNCT
ejpam-6202	655	1	(	(	PUNCT
ejpam-6202	655	2	f	f	X
ejpam-6202	655	3	−	−	PROPN
ejpam-6202	655	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	655	5	f	f	X
ejpam-6202	655	6	!	!	PUNCT
ejpam-6202	656	1	=	=	PUNCT
ejpam-6202	657	1	n∑	n∑	PROPN
ejpam-6202	657	2	m=0	m=0	PROPN
ejpam-6202	657	3	n∑	n∑	PROPN
ejpam-6202	657	4	j	j	PROPN
ejpam-6202	658	1	=	=	NOUN
ejpam-6202	658	2	m	m	VERB
ejpam-6202	658	3	m−k∑	m−k∑	X
ejpam-6202	659	1	f=0	f=0	X
ejpam-6202	659	2	f∑	f∑	PROPN
ejpam-6202	660	1	d	d	X
ejpam-6202	661	1	=	=	X
ejpam-6202	661	2	i	i	PROPN
ejpam-6202	661	3	(	(	PUNCT
ejpam-6202	661	4	j	j	PROPN
ejpam-6202	661	5	m	m	VERB
ejpam-6202	661	6	)	)	PUNCT
ejpam-6202	661	7	gw	gw	PROPN
ejpam-6202	661	8	j−m(x	j−m(x	PROPN
ejpam-6202	661	9	)	)	PUNCT
ejpam-6202	661	10	(	(	PUNCT
ejpam-6202	661	11	n	n	X
ejpam-6202	661	12	j	j	NOUN
ejpam-6202	661	13	)	)	PUNCT
ejpam-6202	661	14	(	(	PUNCT
ejpam-6202	661	15	−1)n−jrn−j	−1)n−jrn−j	X
ejpam-6202	661	16	(	(	PUNCT
ejpam-6202	661	17	−1)d+f	−1)d+f	NUM
ejpam-6202	661	18	(	(	PUNCT
ejpam-6202	661	19	f	f	NOUN
ejpam-6202	661	20	d	d	PROPN
ejpam-6202	661	21	)	)	PUNCT
ejpam-6202	661	22	(	(	PUNCT
ejpam-6202	661	23	m−	m−	PROPN
ejpam-6202	661	24	1	1	NUM
ejpam-6202	661	25	+	+	CCONJ
ejpam-6202	661	26	f	f	PROPN
ejpam-6202	661	27	m−	m−	PROPN
ejpam-6202	661	28	k	k	PROPN
ejpam-6202	662	1	+	+	CCONJ
ejpam-6202	662	2	f	f	NOUN
ejpam-6202	662	3	)	)	PUNCT
ejpam-6202	663	1	(	(	PUNCT
ejpam-6202	663	2	2m−	2m−	NUM
ejpam-6202	663	3	k	k	NOUN
ejpam-6202	663	4	m−	m−	PROPN
ejpam-6202	663	5	k	k	PROPN
ejpam-6202	664	1	+	+	CCONJ
ejpam-6202	664	2	f	f	PROPN
ejpam-6202	664	3	)	)	PUNCT
ejpam-6202	665	1	(	(	PUNCT
ejpam-6202	665	2	f	f	X
ejpam-6202	665	3	−	−	PROPN
ejpam-6202	665	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	665	5	f	f	X
ejpam-6202	665	6	!	!	PUNCT
ejpam-6202	666	1	=	=	PUNCT
ejpam-6202	667	1	n∑	n∑	PROPN
ejpam-6202	667	2	m=0	m=0	PROPN
ejpam-6202	667	3	n∑	n∑	PROPN
ejpam-6202	667	4	j	j	PROPN
ejpam-6202	668	1	=	=	NOUN
ejpam-6202	668	2	m	m	VERB
ejpam-6202	668	3	m−k∑	m−k∑	X
ejpam-6202	669	1	f=0	f=0	X
ejpam-6202	669	2	f∑	f∑	PROPN
ejpam-6202	670	1	d	d	X
ejpam-6202	671	1	=	=	X
ejpam-6202	671	2	i	i	PROPN
ejpam-6202	671	3	(	(	PUNCT
ejpam-6202	671	4	−1)n−j+d+fgw	−1)n−j+d+fgw	PROPN
ejpam-6202	671	5	j−m(x	j−m(x	PROPN
ejpam-6202	671	6	)	)	PUNCT
ejpam-6202	671	7	(	(	PUNCT
ejpam-6202	671	8	j	j	NOUN
ejpam-6202	671	9	m	m	VERB
ejpam-6202	671	10	)	)	PUNCT
ejpam-6202	671	11	(	(	PUNCT
ejpam-6202	671	12	n	n	X
ejpam-6202	671	13	j	j	NOUN
ejpam-6202	671	14	)	)	PUNCT
ejpam-6202	671	15	(	(	PUNCT
ejpam-6202	671	16	f	f	PROPN
ejpam-6202	671	17	d	d	PROPN
ejpam-6202	671	18	)	)	PUNCT
ejpam-6202	671	19	(	(	PUNCT
ejpam-6202	671	20	m−	m−	PROPN
ejpam-6202	671	21	1	1	NUM
ejpam-6202	671	22	+	+	CCONJ
ejpam-6202	671	23	f	f	PROPN
ejpam-6202	671	24	m−	m−	PROPN
ejpam-6202	671	25	k	k	PROPN
ejpam-6202	672	1	+	+	CCONJ
ejpam-6202	672	2	f	f	NOUN
ejpam-6202	672	3	)	)	PUNCT
ejpam-6202	673	1	(	(	PUNCT
ejpam-6202	673	2	2m−	2m−	NUM
ejpam-6202	673	3	k	k	NOUN
ejpam-6202	673	4	m−	m−	PROPN
ejpam-6202	673	5	k	k	PROPN
ejpam-6202	674	1	+	+	CCONJ
ejpam-6202	674	2	f	f	PROPN
ejpam-6202	674	3	)	)	PUNCT
ejpam-6202	675	1	(	(	PUNCT
ejpam-6202	675	2	f	f	X
ejpam-6202	675	3	−	−	PROPN
ejpam-6202	675	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	675	5	f	f	X
ejpam-6202	675	6	!	!	PUNCT
ejpam-6202	676	1	rn−j	rn−j	PROPN
ejpam-6202	676	2	theorem	theorem	VERB
ejpam-6202	676	3	3.4	3.4	NUM
ejpam-6202	676	4	.	.	PUNCT
ejpam-6202	677	1	the	the	DET
ejpam-6202	677	2	formula	formula	NOUN
ejpam-6202	677	3	for	for	ADP
ejpam-6202	677	4	the	the	DET
ejpam-6202	677	5	second	second	ADJ
ejpam-6202	677	6	kind	kind	NOUN
ejpam-6202	677	7	of	of	ADP
ejpam-6202	677	8	r	r	NOUN
ejpam-6202	677	9	-	-	PUNCT
ejpam-6202	677	10	stirling	stirling	NOUN
ejpam-6202	677	11	genocchi	genocchi	PROPN
ejpam-6202	677	12	polynomials	polynomial	NOUN
ejpam-6202	677	13	of	of	ADP
ejpam-6202	677	14	higher	high	ADJ
ejpam-6202	677	15	order	order	NOUN
ejpam-6202	677	16	is	be	AUX
ejpam-6202	677	17	explicitly	explicitly	ADV
ejpam-6202	677	18	defined	define	VERB
ejpam-6202	677	19	by	by	ADP
ejpam-6202	677	20	the	the	DET
ejpam-6202	677	21	following	follow	VERB
ejpam-6202	677	22	formula	formula	NOUN
ejpam-6202	677	23	:	:	PUNCT
ejpam-6202	677	24	sg2w	sg2w	PROPN
ejpam-6202	677	25	n	n	CCONJ
ejpam-6202	677	26	(	(	PUNCT
ejpam-6202	677	27	x	x	X
ejpam-6202	677	28	;	;	PUNCT
ejpam-6202	677	29	k	k	X
ejpam-6202	677	30	,	,	PUNCT
ejpam-6202	677	31	r	r	NOUN
ejpam-6202	677	32	)	)	PUNCT
ejpam-6202	677	33	=	=	SYM
ejpam-6202	677	34	n∑	n∑	PROPN
ejpam-6202	677	35	m=0	m=0	PROPN
ejpam-6202	677	36	{	{	PUNCT
ejpam-6202	678	1	m+	m+	NOUN
ejpam-6202	678	2	r	r	NOUN
ejpam-6202	678	3	k	k	PROPN
ejpam-6202	679	1	+	+	CCONJ
ejpam-6202	679	2	r	r	NOUN
ejpam-6202	679	3	}	}	PUNCT
ejpam-6202	679	4	r	r	NOUN
ejpam-6202	679	5	(	(	PUNCT
ejpam-6202	679	6	n	n	NOUN
ejpam-6202	679	7	m	m	VERB
ejpam-6202	679	8	)	)	PUNCT
ejpam-6202	679	9	gw	gw	PROPN
ejpam-6202	679	10	n−m(x	n−m(x	NOUN
ejpam-6202	679	11	)	)	PUNCT
ejpam-6202	679	12	proof	proof	NOUN
ejpam-6202	679	13	.	.	PUNCT
ejpam-6202	680	1	the	the	DET
ejpam-6202	680	2	exponential	exponential	ADJ
ejpam-6202	680	3	generating	generating	NOUN
ejpam-6202	680	4	function	function	NOUN
ejpam-6202	680	5	in	in	ADP
ejpam-6202	680	6	(	(	PUNCT
ejpam-6202	680	7	14	14	NUM
ejpam-6202	680	8	)	)	PUNCT
ejpam-6202	680	9	can	can	AUX
ejpam-6202	680	10	be	be	AUX
ejpam-6202	680	11	written	write	VERB
ejpam-6202	680	12	as	as	ADP
ejpam-6202	680	13	n∑	n∑	PROPN
ejpam-6202	680	14	n≥k	n≥k	PROPN
ejpam-6202	680	15	k!sg2w	k!sg2w	PROPN
ejpam-6202	680	16	n	n	CCONJ
ejpam-6202	680	17	(	(	PUNCT
ejpam-6202	680	18	x	x	X
ejpam-6202	680	19	;	;	PUNCT
ejpam-6202	680	20	k	k	X
ejpam-6202	680	21	,	,	PUNCT
ejpam-6202	680	22	r	r	NOUN
ejpam-6202	680	23	)	)	PUNCT
ejpam-6202	680	24	tn	tn	NOUN
ejpam-6202	680	25	n	n	NOUN
ejpam-6202	680	26	!	!	PUNCT
ejpam-6202	681	1	=	=	PUNCT
ejpam-6202	681	2	(	(	PUNCT
ejpam-6202	681	3	2	2	NUM
ejpam-6202	681	4	t	t	NOUN
ejpam-6202	681	5	et	et	NOUN
ejpam-6202	681	6	+	+	CCONJ
ejpam-6202	681	7	1	1	X
ejpam-6202	681	8	)	)	PUNCT
ejpam-6202	681	9	w	w	NOUN
ejpam-6202	681	10	extert	extert	PROPN
ejpam-6202	681	11	k∑	k∑	PROPN
ejpam-6202	681	12	i=0	i=0	PROPN
ejpam-6202	681	13	(	(	PUNCT
ejpam-6202	681	14	k	k	NOUN
ejpam-6202	681	15	i	i	PROPN
ejpam-6202	681	16	)	)	PUNCT
ejpam-6202	681	17	(	(	PUNCT
ejpam-6202	681	18	et)k−i(−1)i	et)k−i(−1)i	X
ejpam-6202	681	19	23	23	NUM
ejpam-6202	681	20	of	of	ADP
ejpam-6202	681	21	26	26	NUM
ejpam-6202	681	22	=	=	SYM
ejpam-6202	681	23	(	(	PUNCT
ejpam-6202	681	24	2	2	NUM
ejpam-6202	681	25	t	t	NOUN
ejpam-6202	681	26	et	et	NOUN
ejpam-6202	681	27	+	+	CCONJ
ejpam-6202	681	28	1	1	X
ejpam-6202	681	29	)	)	PUNCT
ejpam-6202	681	30	w	w	PROPN
ejpam-6202	681	31	ext	ext	NOUN
ejpam-6202	681	32	k∑	k∑	PROPN
ejpam-6202	682	1	i=0	i=0	PROPN
ejpam-6202	682	2	(	(	PUNCT
ejpam-6202	682	3	k	k	NOUN
ejpam-6202	682	4	i	i	PROPN
ejpam-6202	682	5	)	)	PUNCT
ejpam-6202	682	6	ert(et)k−i(−1)i	ert(et)k−i(−1)i	PROPN
ejpam-6202	682	7	=	=	PUNCT
ejpam-6202	682	8	(	(	PUNCT
ejpam-6202	682	9	2	2	NUM
ejpam-6202	682	10	t	t	NOUN
ejpam-6202	682	11	et	et	NOUN
ejpam-6202	682	12	+	+	CCONJ
ejpam-6202	682	13	1	1	X
ejpam-6202	682	14	)	)	PUNCT
ejpam-6202	682	15	w	w	PROPN
ejpam-6202	682	16	ext	ext	NOUN
ejpam-6202	682	17	k∑	k∑	PROPN
ejpam-6202	683	1	i=0	i=0	PROPN
ejpam-6202	683	2	(	(	PUNCT
ejpam-6202	683	3	k	k	NOUN
ejpam-6202	683	4	i	i	PROPN
ejpam-6202	683	5	)	)	PUNCT
ejpam-6202	683	6	ert+(k−i)t(−1)i	ert+(k−i)t(−1)i	X
ejpam-6202	684	1	=	=	SYM
ejpam-6202	684	2	k∑	k∑	PROPN
ejpam-6202	684	3	i=0	i=0	PROPN
ejpam-6202	684	4	(	(	PUNCT
ejpam-6202	684	5	k	k	NOUN
ejpam-6202	684	6	i	i	PROPN
ejpam-6202	684	7	)	)	PUNCT
ejpam-6202	684	8	ert(et)k−i(−1)i	ert(et)k−i(−1)i	VERB
ejpam-6202	684	9	∞∑	∞∑	PRON
ejpam-6202	684	10	n=0	n=0	PUNCT
ejpam-6202	684	11	gw	gw	PROPN
ejpam-6202	684	12	n	n	PROPN
ejpam-6202	684	13	(	(	PUNCT
ejpam-6202	684	14	x	x	NOUN
ejpam-6202	684	15	)	)	PUNCT
ejpam-6202	684	16	tn	tn	PROPN
ejpam-6202	684	17	n	n	NOUN
ejpam-6202	684	18	!	!	PUNCT
ejpam-6202	685	1	=	=	PUNCT
ejpam-6202	686	1			PROPN
ejpam-6202	686	2	k∑	k∑	PROPN
ejpam-6202	686	3	i=0	i=0	PROPN
ejpam-6202	686	4	(	(	PUNCT
ejpam-6202	686	5	k	k	NOUN
ejpam-6202	686	6	i	i	PROPN
ejpam-6202	686	7	)	)	PUNCT
ejpam-6202	686	8	∑	∑	PROPN
ejpam-6202	686	9	n≥0	n≥0	ADP
ejpam-6202	686	10	[	[	X
ejpam-6202	686	11	(	(	PUNCT
ejpam-6202	686	12	(	(	PUNCT
ejpam-6202	686	13	k	k	NOUN
ejpam-6202	686	14	−	−	PROPN
ejpam-6202	686	15	i	i	PROPN
ejpam-6202	686	16	)	)	PUNCT
ejpam-6202	686	17	+	+	NUM
ejpam-6202	686	18	r)t]n	r)t]n	NOUN
ejpam-6202	686	19	n	n	CCONJ
ejpam-6202	686	20	!	!	PUNCT
ejpam-6202	687	1	(	(	PUNCT
ejpam-6202	687	2	−1)i	−1)i	X
ejpam-6202	687	3			PROPN
ejpam-6202	687	4	(	(	PUNCT
ejpam-6202	687	5	∞∑	∞∑	PROPN
ejpam-6202	687	6	n=0	n=0	NUM
ejpam-6202	687	7	gw	gw	PROPN
ejpam-6202	687	8	n	n	PROPN
ejpam-6202	687	9	(	(	PUNCT
ejpam-6202	687	10	x	x	NOUN
ejpam-6202	687	11	)	)	PUNCT
ejpam-6202	687	12	tn	tn	PROPN
ejpam-6202	687	13	n	n	NOUN
ejpam-6202	687	14	!	!	PUNCT
ejpam-6202	687	15	)	)	PUNCT
ejpam-6202	688	1	=	=	PUNCT
ejpam-6202	689	1			PROPN
ejpam-6202	689	2	∞∑	∞∑	NUM
ejpam-6202	689	3	n≥0	n≥0	PROPN
ejpam-6202	689	4	{	{	PUNCT
ejpam-6202	689	5	k∑	k∑	NOUN
ejpam-6202	689	6	i=0	i=0	PROPN
ejpam-6202	689	7	(	(	PUNCT
ejpam-6202	689	8	−1)i	−1)i	X
ejpam-6202	689	9	(	(	PUNCT
ejpam-6202	689	10	k	k	X
ejpam-6202	689	11	i	i	PROPN
ejpam-6202	689	12	)	)	PUNCT
ejpam-6202	689	13	(	(	PUNCT
ejpam-6202	689	14	(	(	PUNCT
ejpam-6202	689	15	k	k	X
ejpam-6202	689	16	−	−	PROPN
ejpam-6202	689	17	i	i	PROPN
ejpam-6202	689	18	)	)	PUNCT
ejpam-6202	689	19	+	+	PUNCT
ejpam-6202	689	20	r)n	r)n	X
ejpam-6202	689	21	}	}	PUNCT
ejpam-6202	689	22	tn	tn	PROPN
ejpam-6202	689	23	n	n	NOUN
ejpam-6202	689	24	!	!	PUNCT
ejpam-6202	690	1			PROPN
ejpam-6202	690	2	(	(	PUNCT
ejpam-6202	690	3	∞∑	∞∑	PROPN
ejpam-6202	690	4	n=0	n=0	NUM
ejpam-6202	690	5	gw	gw	PROPN
ejpam-6202	690	6	n	n	PROPN
ejpam-6202	690	7	(	(	PUNCT
ejpam-6202	690	8	x	x	NOUN
ejpam-6202	690	9	)	)	PUNCT
ejpam-6202	690	10	tn	tn	PROPN
ejpam-6202	690	11	n	n	NOUN
ejpam-6202	690	12	!	!	PUNCT
ejpam-6202	690	13	)	)	PUNCT
ejpam-6202	691	1	=	=	PUNCT
ejpam-6202	692	1			PROPN
ejpam-6202	692	2	∞∑	∞∑	NUM
ejpam-6202	692	3	n≥0	n≥0	PROPN
ejpam-6202	692	4	k	k	NOUN
ejpam-6202	692	5	!	!	PUNCT
ejpam-6202	692	6	{	{	PUNCT
ejpam-6202	693	1	n+	n+	ADP
ejpam-6202	693	2	r	r	NOUN
ejpam-6202	693	3	k	k	NOUN
ejpam-6202	694	1	+	+	CCONJ
ejpam-6202	694	2	r	r	NOUN
ejpam-6202	694	3	}	}	PUNCT
ejpam-6202	694	4	r	r	NOUN
ejpam-6202	694	5	tn	tn	NOUN
ejpam-6202	694	6	n	n	ADV
ejpam-6202	694	7	!	!	PUNCT
ejpam-6202	695	1			PROPN
ejpam-6202	695	2	(	(	PUNCT
ejpam-6202	695	3	∞∑	∞∑	PROPN
ejpam-6202	695	4	n=0	n=0	NUM
ejpam-6202	695	5	gw	gw	PROPN
ejpam-6202	695	6	n	n	PROPN
ejpam-6202	695	7	(	(	PUNCT
ejpam-6202	695	8	x	x	NOUN
ejpam-6202	695	9	)	)	PUNCT
ejpam-6202	695	10	tn	tn	PROPN
ejpam-6202	695	11	n	n	NOUN
ejpam-6202	695	12	!	!	PUNCT
ejpam-6202	695	13	)	)	PUNCT
ejpam-6202	696	1	=	=	PUNCT
ejpam-6202	697	1	∞∑	∞∑	NUM
ejpam-6202	697	2	n=0	n=0	NUM
ejpam-6202	697	3	n∑	n∑	NOUN
ejpam-6202	697	4	m=0	m=0	PROPN
ejpam-6202	697	5	k	k	PROPN
ejpam-6202	697	6	!	!	PUNCT
ejpam-6202	697	7	{	{	PUNCT
ejpam-6202	698	1	m+	m+	NOUN
ejpam-6202	699	1	r	r	NOUN
ejpam-6202	699	2	k	k	PROPN
ejpam-6202	700	1	+	+	CCONJ
ejpam-6202	700	2	r	r	NOUN
ejpam-6202	700	3	}	}	PUNCT
ejpam-6202	700	4	r	r	NOUN
ejpam-6202	700	5	tm	tm	NOUN
ejpam-6202	700	6	m	m	PROPN
ejpam-6202	700	7	!	!	PUNCT
ejpam-6202	701	1	gw	gw	PROPN
ejpam-6202	701	2	n−m(x	n−m(x	PROPN
ejpam-6202	701	3	)	)	PUNCT
ejpam-6202	702	1	tn−m	tn−m	PROPN
ejpam-6202	702	2	(	(	PUNCT
ejpam-6202	702	3	n−m	n−m	PROPN
ejpam-6202	702	4	)	)	PUNCT
ejpam-6202	702	5	!	!	PUNCT
ejpam-6202	703	1	=	=	PUNCT
ejpam-6202	704	1	∞∑	∞∑	PRON
ejpam-6202	704	2	n=0	n=0	PRON
ejpam-6202	704	3	{	{	PUNCT
ejpam-6202	704	4	n∑	n∑	NOUN
ejpam-6202	704	5	m=0	m=0	PROPN
ejpam-6202	704	6	k	k	PROPN
ejpam-6202	704	7	!	!	PUNCT
ejpam-6202	704	8	{	{	PUNCT
ejpam-6202	705	1	m+	m+	NOUN
ejpam-6202	706	1	r	r	NOUN
ejpam-6202	706	2	k	k	PROPN
ejpam-6202	707	1	+	+	CCONJ
ejpam-6202	707	2	r	r	NOUN
ejpam-6202	707	3	}	}	PUNCT
ejpam-6202	707	4	r	r	NOUN
ejpam-6202	707	5	1	1	NUM
ejpam-6202	707	6	(	(	PUNCT
ejpam-6202	707	7	n−m)!m	n−m)!m	PROPN
ejpam-6202	707	8	!	!	PUNCT
ejpam-6202	708	1	gw	gw	PROPN
ejpam-6202	708	2	n−m(x	n−m(x	PROPN
ejpam-6202	708	3	)	)	PUNCT
ejpam-6202	708	4	}	}	PUNCT
ejpam-6202	709	1	tn	tn	NOUN
ejpam-6202	710	1	=	=	SYM
ejpam-6202	710	2	∞∑	∞∑	NUM
ejpam-6202	710	3	n=0	n=0	PRON
ejpam-6202	710	4	{	{	PUNCT
ejpam-6202	710	5	n∑	n∑	NOUN
ejpam-6202	710	6	m=0	m=0	PROPN
ejpam-6202	710	7	k	k	PROPN
ejpam-6202	710	8	!	!	PUNCT
ejpam-6202	710	9	{	{	PUNCT
ejpam-6202	711	1	m+	m+	NOUN
ejpam-6202	712	1	r	r	NOUN
ejpam-6202	712	2	k	k	PROPN
ejpam-6202	713	1	+	+	CCONJ
ejpam-6202	713	2	r	r	NOUN
ejpam-6202	713	3	}	}	PUNCT
ejpam-6202	713	4	r	r	NOUN
ejpam-6202	713	5	(	(	PUNCT
ejpam-6202	713	6	n	n	NOUN
ejpam-6202	713	7	m	m	VERB
ejpam-6202	713	8	)	)	PUNCT
ejpam-6202	713	9	gw	gw	PROPN
ejpam-6202	713	10	n−m(x	n−m(x	PROPN
ejpam-6202	713	11	)	)	PUNCT
ejpam-6202	713	12	}	}	PUNCT
ejpam-6202	713	13	tn	tn	PROPN
ejpam-6202	713	14	n	n	CCONJ
ejpam-6202	713	15	!	!	PUNCT
ejpam-6202	714	1	comparing	compare	VERB
ejpam-6202	714	2	the	the	DET
ejpam-6202	714	3	coefficients	coefficient	NOUN
ejpam-6202	714	4	of	of	ADP
ejpam-6202	714	5	tn	tn	NOUN
ejpam-6202	714	6	n	n	ADP
ejpam-6202	714	7	!	!	PROPN
ejpam-6202	714	8	completes	complete	VERB
ejpam-6202	714	9	the	the	DET
ejpam-6202	714	10	proof	proof	NOUN
ejpam-6202	714	11	of	of	ADP
ejpam-6202	714	12	the	the	DET
ejpam-6202	714	13	theorem	theorem	NOUN
ejpam-6202	714	14	.	.	PUNCT
ejpam-6202	715	1	when	when	SCONJ
ejpam-6202	715	2	x	x	X
ejpam-6202	715	3	=	=	SYM
ejpam-6202	715	4	0	0	NUM
ejpam-6202	715	5	in	in	ADP
ejpam-6202	715	6	the	the	DET
ejpam-6202	715	7	genocchi	genocchi	PROPN
ejpam-6202	715	8	polynomials	polynomial	NOUN
ejpam-6202	715	9	of	of	ADP
ejpam-6202	715	10	higher	high	ADJ
ejpam-6202	715	11	order	order	NOUN
ejpam-6202	715	12	,	,	PUNCT
ejpam-6202	715	13	we	we	PRON
ejpam-6202	715	14	have	have	VERB
ejpam-6202	715	15	the	the	DET
ejpam-6202	715	16	following	follow	VERB
ejpam-6202	715	17	corollaries	corollary	NOUN
ejpam-6202	715	18	.	.	PUNCT
ejpam-6202	716	1	corollary	corollary	ADJ
ejpam-6202	716	2	3.5	3.5	NUM
ejpam-6202	716	3	.	.	PUNCT
ejpam-6202	717	1	convolution	convolution	NOUN
ejpam-6202	717	2	formula	formula	NOUN
ejpam-6202	717	3	of	of	ADP
ejpam-6202	717	4	the	the	DET
ejpam-6202	717	5	r	r	NOUN
ejpam-6202	717	6	-	-	PUNCT
ejpam-6202	717	7	stirling	stirling	NOUN
ejpam-6202	717	8	numbers	number	NOUN
ejpam-6202	717	9	and	and	CCONJ
ejpam-6202	717	10	genocchi	genocchi	PROPN
ejpam-6202	717	11	numbers	number	NOUN
ejpam-6202	717	12	of	of	ADP
ejpam-6202	717	13	higher	high	ADJ
ejpam-6202	717	14	order	order	NOUN
ejpam-6202	717	15	are	be	AUX
ejpam-6202	717	16	given	give	VERB
ejpam-6202	717	17	as	as	SCONJ
ejpam-6202	717	18	follows	follow	VERB
ejpam-6202	717	19	:	:	PUNCT
ejpam-6202	717	20	sg1w	sg1w	PROPN
ejpam-6202	717	21	n	n	CCONJ
ejpam-6202	717	22	(	(	PUNCT
ejpam-6202	717	23	k	k	X
ejpam-6202	717	24	;	;	PUNCT
ejpam-6202	717	25	r	r	X
ejpam-6202	717	26	)	)	PUNCT
ejpam-6202	717	27	=	=	SYM
ejpam-6202	717	28	n∑	n∑	PROPN
ejpam-6202	717	29	j	j	PROPN
ejpam-6202	718	1	=	=	PROPN
ejpam-6202	718	2	k	k	PROPN
ejpam-6202	718	3	̂[j	̂[j	PROPN
ejpam-6202	719	1	+	+	CCONJ
ejpam-6202	720	1	r	r	X
ejpam-6202	720	2	k	k	NOUN
ejpam-6202	721	1	+	+	CCONJ
ejpam-6202	721	2	r	r	NOUN
ejpam-6202	721	3	]	]	X
ejpam-6202	721	4	r	r	NOUN
ejpam-6202	721	5	(	(	PUNCT
ejpam-6202	721	6	n	n	X
ejpam-6202	721	7	j	j	PROPN
ejpam-6202	721	8	)	)	PUNCT
ejpam-6202	722	1	gw	gw	PROPN
ejpam-6202	722	2	n−j	n−j	ADV
ejpam-6202	722	3	sg2w	sg2w	PROPN
ejpam-6202	722	4	n	n	CCONJ
ejpam-6202	722	5	(	(	PUNCT
ejpam-6202	722	6	k	k	X
ejpam-6202	722	7	;	;	PUNCT
ejpam-6202	722	8	r	r	X
ejpam-6202	722	9	)	)	PUNCT
ejpam-6202	722	10	=	=	SYM
ejpam-6202	722	11	n∑	n∑	PROPN
ejpam-6202	722	12	j	j	PROPN
ejpam-6202	723	1	=	=	PROPN
ejpam-6202	723	2	k	k	PROPN
ejpam-6202	723	3	{	{	PUNCT
ejpam-6202	723	4	j	j	PROPN
ejpam-6202	723	5	+	+	CCONJ
ejpam-6202	723	6	r	r	NOUN
ejpam-6202	723	7	k	k	NOUN
ejpam-6202	723	8	+	+	CCONJ
ejpam-6202	723	9	r	r	NOUN
ejpam-6202	723	10	}	}	PUNCT
ejpam-6202	723	11	r	r	NOUN
ejpam-6202	723	12	(	(	PUNCT
ejpam-6202	723	13	n	n	X
ejpam-6202	723	14	j	j	PROPN
ejpam-6202	723	15	)	)	PUNCT
ejpam-6202	723	16	gw	gw	ADP
ejpam-6202	723	17	n−j	n−j	ADV
ejpam-6202	723	18	where	where	SCONJ
ejpam-6202	723	19	n	n	PRON
ejpam-6202	723	20	≥	≥	NOUN
ejpam-6202	723	21	k.	k.	PROPN
ejpam-6202	723	22	proof	proof	PROPN
ejpam-6202	723	23	.	.	PUNCT
ejpam-6202	724	1	setting	set	VERB
ejpam-6202	724	2	x	x	PUNCT
ejpam-6202	724	3	=	=	SYM
ejpam-6202	724	4	0	0	NUM
ejpam-6202	724	5	of	of	ADP
ejpam-6202	724	6	theorem	theorem	NOUN
ejpam-6202	724	7	9	9	NUM
ejpam-6202	724	8	,	,	PUNCT
ejpam-6202	724	9	the	the	DET
ejpam-6202	724	10	proof	proof	NOUN
ejpam-6202	724	11	of	of	ADP
ejpam-6202	724	12	this	this	DET
ejpam-6202	724	13	theorem	theorem	NOUN
ejpam-6202	724	14	follows	follow	VERB
ejpam-6202	724	15	immediately	immediately	ADV
ejpam-6202	724	16	.	.	PUNCT
ejpam-6202	725	1	24	24	NUM
ejpam-6202	725	2	of	of	ADP
ejpam-6202	725	3	26	26	NUM
ejpam-6202	725	4	corollary	corollary	ADJ
ejpam-6202	725	5	3.6	3.6	NUM
ejpam-6202	725	6	.	.	PUNCT
ejpam-6202	726	1	the	the	DET
ejpam-6202	726	2	horizontal	horizontal	ADJ
ejpam-6202	726	3	generating	generate	VERB
ejpam-6202	726	4	function	function	NOUN
ejpam-6202	726	5	for	for	ADP
ejpam-6202	726	6	both	both	DET
ejpam-6202	726	7	kinds	kind	NOUN
ejpam-6202	726	8	of	of	ADP
ejpam-6202	726	9	r	r	NOUN
ejpam-6202	726	10	-	-	PUNCT
ejpam-6202	726	11	stirling	stirling	NOUN
ejpam-6202	726	12	genocchi	genocchi	PROPN
ejpam-6202	726	13	numbers	number	NOUN
ejpam-6202	726	14	of	of	ADP
ejpam-6202	726	15	higher	high	ADJ
ejpam-6202	726	16	order	order	NOUN
ejpam-6202	726	17	are	be	AUX
ejpam-6202	726	18	given	give	VERB
ejpam-6202	726	19	as	as	SCONJ
ejpam-6202	726	20	follows	follow	VERB
ejpam-6202	726	21	:	:	PUNCT
ejpam-6202	727	1	gw	gw	PROPN
ejpam-6202	727	2	n	n	PROPN
ejpam-6202	727	3	(	(	PUNCT
ejpam-6202	727	4	z	z	NOUN
ejpam-6202	727	5	−	−	NOUN
ejpam-6202	728	1	r	r	NOUN
ejpam-6202	728	2	)	)	PUNCT
ejpam-6202	728	3	=	=	SYM
ejpam-6202	728	4	n∑	n∑	NOUN
ejpam-6202	728	5	k=0	k=0	PROPN
ejpam-6202	728	6	sg1w	sg1w	PROPN
ejpam-6202	728	7	n	n	CCONJ
ejpam-6202	728	8	(	(	PUNCT
ejpam-6202	728	9	k	k	X
ejpam-6202	728	10	,	,	PUNCT
ejpam-6202	728	11	r)zk	r)zk	PROPN
ejpam-6202	728	12	gw	gw	PROPN
ejpam-6202	728	13	n	n	PROPN
ejpam-6202	728	14	(	(	PUNCT
ejpam-6202	728	15	z	z	NOUN
ejpam-6202	728	16	+	+	CCONJ
ejpam-6202	728	17	r	r	NOUN
ejpam-6202	728	18	)	)	PUNCT
ejpam-6202	728	19	=	=	SYM
ejpam-6202	728	20	n∑	n∑	PROPN
ejpam-6202	728	21	k=0	k=0	PROPN
ejpam-6202	728	22	sg2w	sg2w	PROPN
ejpam-6202	728	23	n	n	CCONJ
ejpam-6202	728	24	(	(	PUNCT
ejpam-6202	728	25	k	k	X
ejpam-6202	728	26	,	,	PUNCT
ejpam-6202	728	27	r)zk	r)zk	PROPN
ejpam-6202	728	28	proof	proof	NOUN
ejpam-6202	728	29	.	.	PUNCT
ejpam-6202	729	1	setting	set	VERB
ejpam-6202	729	2	x	x	PUNCT
ejpam-6202	729	3	=	=	SYM
ejpam-6202	729	4	0	0	NUM
ejpam-6202	729	5	of	of	ADP
ejpam-6202	729	6	theorem	theorem	NOUN
ejpam-6202	729	7	10	10	NUM
ejpam-6202	729	8	,	,	PUNCT
ejpam-6202	729	9	the	the	DET
ejpam-6202	729	10	proof	proof	NOUN
ejpam-6202	729	11	of	of	ADP
ejpam-6202	729	12	this	this	DET
ejpam-6202	729	13	theorem	theorem	NOUN
ejpam-6202	729	14	follows	follow	VERB
ejpam-6202	729	15	immediately	immediately	ADV
ejpam-6202	729	16	.	.	PUNCT
ejpam-6202	730	1	corollary	corollary	ADJ
ejpam-6202	730	2	3.7	3.7	NUM
ejpam-6202	730	3	.	.	PUNCT
ejpam-6202	731	1	the	the	DET
ejpam-6202	731	2	formula	formula	NOUN
ejpam-6202	731	3	for	for	ADP
ejpam-6202	731	4	the	the	DET
ejpam-6202	731	5	first	first	ADJ
ejpam-6202	731	6	kind	kind	NOUN
ejpam-6202	731	7	of	of	ADP
ejpam-6202	731	8	r	r	NOUN
ejpam-6202	731	9	-	-	PUNCT
ejpam-6202	731	10	stirling	stirling	NOUN
ejpam-6202	731	11	genocchi	genocchi	PROPN
ejpam-6202	731	12	numbers	number	NOUN
ejpam-6202	731	13	of	of	ADP
ejpam-6202	731	14	higher	high	ADJ
ejpam-6202	731	15	order	order	NOUN
ejpam-6202	731	16	is	be	AUX
ejpam-6202	731	17	explicitly	explicitly	ADV
ejpam-6202	731	18	stated	state	VERB
ejpam-6202	731	19	as	as	SCONJ
ejpam-6202	731	20	follows	follow	VERB
ejpam-6202	731	21	:	:	PUNCT
ejpam-6202	731	22	sg1w	sg1w	PROPN
ejpam-6202	731	23	n	n	CCONJ
ejpam-6202	731	24	(	(	PUNCT
ejpam-6202	731	25	k	k	X
ejpam-6202	731	26	;	;	PUNCT
ejpam-6202	731	27	r	r	X
ejpam-6202	731	28	)	)	PUNCT
ejpam-6202	731	29	=	=	SYM
ejpam-6202	731	30	n∑	n∑	PROPN
ejpam-6202	731	31	m=0	m=0	PROPN
ejpam-6202	731	32	n∑	n∑	PROPN
ejpam-6202	731	33	j	j	PROPN
ejpam-6202	732	1	=	=	NOUN
ejpam-6202	732	2	m	m	VERB
ejpam-6202	732	3	m−k∑	m−k∑	X
ejpam-6202	733	1	f=0	f=0	X
ejpam-6202	733	2	f∑	f∑	PROPN
ejpam-6202	734	1	d	d	X
ejpam-6202	735	1	=	=	X
ejpam-6202	735	2	i	i	PROPN
ejpam-6202	735	3	(	(	PUNCT
ejpam-6202	735	4	−1)n−j+d+fgw	−1)n−j+d+fgw	VERB
ejpam-6202	735	5	j−m	j−m	PROPN
ejpam-6202	735	6	(	(	PUNCT
ejpam-6202	735	7	j	j	PROPN
ejpam-6202	735	8	m	m	VERB
ejpam-6202	735	9	)	)	PUNCT
ejpam-6202	735	10	(	(	PUNCT
ejpam-6202	735	11	n	n	X
ejpam-6202	735	12	j	j	NOUN
ejpam-6202	735	13	)	)	PUNCT
ejpam-6202	735	14	(	(	PUNCT
ejpam-6202	735	15	f	f	PROPN
ejpam-6202	735	16	d	d	PROPN
ejpam-6202	735	17	)	)	PUNCT
ejpam-6202	735	18	(	(	PUNCT
ejpam-6202	735	19	m−	m−	PROPN
ejpam-6202	735	20	1	1	NUM
ejpam-6202	735	21	+	+	CCONJ
ejpam-6202	735	22	f	f	PROPN
ejpam-6202	735	23	m−	m−	PROPN
ejpam-6202	735	24	k	k	PROPN
ejpam-6202	736	1	+	+	CCONJ
ejpam-6202	736	2	f	f	NOUN
ejpam-6202	736	3	)	)	PUNCT
ejpam-6202	737	1	(	(	PUNCT
ejpam-6202	737	2	2m−	2m−	NUM
ejpam-6202	737	3	k	k	NOUN
ejpam-6202	737	4	m−	m−	PROPN
ejpam-6202	737	5	k	k	PROPN
ejpam-6202	738	1	+	+	CCONJ
ejpam-6202	738	2	f	f	PROPN
ejpam-6202	738	3	)	)	PUNCT
ejpam-6202	739	1	(	(	PUNCT
ejpam-6202	739	2	f	f	X
ejpam-6202	739	3	−	−	PROPN
ejpam-6202	739	4	d)m−k+f	d)m−k+f	PROPN
ejpam-6202	739	5	f	f	X
ejpam-6202	739	6	!	!	PUNCT
ejpam-6202	740	1	rn−j	rn−j	NOUN
ejpam-6202	740	2	proof	proof	NOUN
ejpam-6202	740	3	.	.	PUNCT
ejpam-6202	741	1	setting	set	VERB
ejpam-6202	741	2	x	x	PUNCT
ejpam-6202	741	3	=	=	SYM
ejpam-6202	741	4	0	0	NUM
ejpam-6202	741	5	of	of	ADP
ejpam-6202	741	6	theorem	theorem	NOUN
ejpam-6202	741	7	11	11	NUM
ejpam-6202	741	8	,	,	PUNCT
ejpam-6202	741	9	the	the	DET
ejpam-6202	741	10	proof	proof	NOUN
ejpam-6202	741	11	of	of	ADP
ejpam-6202	741	12	this	this	DET
ejpam-6202	741	13	theorem	theorem	NOUN
ejpam-6202	741	14	follows	follow	VERB
ejpam-6202	741	15	immediately	immediately	ADV
ejpam-6202	741	16	.	.	PUNCT
ejpam-6202	742	1	corollary	corollary	ADJ
ejpam-6202	742	2	3.8	3.8	NUM
ejpam-6202	742	3	.	.	PUNCT
ejpam-6202	743	1	the	the	DET
ejpam-6202	743	2	formula	formula	NOUN
ejpam-6202	743	3	for	for	ADP
ejpam-6202	743	4	the	the	DET
ejpam-6202	743	5	second	second	ADJ
ejpam-6202	743	6	kind	kind	NOUN
ejpam-6202	743	7	of	of	ADP
ejpam-6202	743	8	r	r	NOUN
ejpam-6202	743	9	-	-	PUNCT
ejpam-6202	743	10	stirling	stirling	NOUN
ejpam-6202	743	11	genocchi	genocchi	PROPN
ejpam-6202	743	12	numbers	number	NOUN
ejpam-6202	743	13	of	of	ADP
ejpam-6202	743	14	higher	high	ADJ
ejpam-6202	743	15	order	order	NOUN
ejpam-6202	743	16	is	be	AUX
ejpam-6202	743	17	explicitly	explicitly	ADV
ejpam-6202	743	18	defined	define	VERB
ejpam-6202	743	19	by	by	ADP
ejpam-6202	743	20	the	the	DET
ejpam-6202	743	21	following	follow	VERB
ejpam-6202	743	22	formula	formula	NOUN
ejpam-6202	743	23	:	:	PUNCT
ejpam-6202	744	1	sg2w	sg2w	PROPN
ejpam-6202	744	2	n	n	CCONJ
ejpam-6202	744	3	(	(	PUNCT
ejpam-6202	744	4	k	k	X
ejpam-6202	744	5	;	;	PUNCT
ejpam-6202	744	6	r	r	X
ejpam-6202	744	7	)	)	PUNCT
ejpam-6202	744	8	=	=	SYM
ejpam-6202	744	9	n∑	n∑	PROPN
ejpam-6202	744	10	m=0	m=0	PROPN
ejpam-6202	744	11	{	{	PUNCT
ejpam-6202	744	12	m+	m+	NOUN
ejpam-6202	744	13	r	r	NOUN
ejpam-6202	744	14	k	k	PROPN
ejpam-6202	744	15	+	+	CCONJ
ejpam-6202	744	16	r	r	NOUN
ejpam-6202	744	17	}	}	PUNCT
ejpam-6202	744	18	r	r	NOUN
ejpam-6202	744	19	(	(	PUNCT
ejpam-6202	744	20	n	n	NOUN
ejpam-6202	744	21	m	m	VERB
ejpam-6202	744	22	)	)	PUNCT
ejpam-6202	744	23	gw	gw	ADP
ejpam-6202	744	24	n−m	n−m	VERB
ejpam-6202	744	25	proof	proof	NOUN
ejpam-6202	744	26	.	.	PUNCT
ejpam-6202	745	1	setting	set	VERB
ejpam-6202	745	2	x	x	PUNCT
ejpam-6202	745	3	=	=	SYM
ejpam-6202	745	4	0	0	NUM
ejpam-6202	745	5	of	of	ADP
ejpam-6202	745	6	theorem	theorem	NOUN
ejpam-6202	745	7	12	12	NUM
ejpam-6202	745	8	,	,	PUNCT
ejpam-6202	745	9	the	the	DET
ejpam-6202	745	10	proof	proof	NOUN
ejpam-6202	745	11	of	of	ADP
ejpam-6202	745	12	this	this	DET
ejpam-6202	745	13	theorem	theorem	NOUN
ejpam-6202	745	14	follows	follow	VERB
ejpam-6202	745	15	immediately	immediately	ADV
ejpam-6202	745	16	.	.	PUNCT
ejpam-6202	746	1	4	4	X
ejpam-6202	746	2	.	.	X
ejpam-6202	746	3	conclusion	conclusion	NOUN
ejpam-6202	746	4	and	and	CCONJ
ejpam-6202	746	5	recommendation	recommendation	NOUN
ejpam-6202	746	6	in	in	ADP
ejpam-6202	746	7	this	this	DET
ejpam-6202	746	8	research	research	NOUN
ejpam-6202	746	9	,	,	PUNCT
ejpam-6202	746	10	we	we	PRON
ejpam-6202	746	11	introduced	introduce	VERB
ejpam-6202	746	12	the	the	DET
ejpam-6202	746	13	novel	novel	ADJ
ejpam-6202	746	14	concept	concept	NOUN
ejpam-6202	746	15	of	of	ADP
ejpam-6202	746	16	r	r	NOUN
ejpam-6202	746	17	-	-	PUNCT
ejpam-6202	746	18	stirling	stirling	NOUN
ejpam-6202	746	19	genocchi	genocchi	PROPN
ejpam-6202	746	20	numbers	number	NOUN
ejpam-6202	746	21	,	,	PUNCT
ejpam-6202	746	22	expanding	expand	VERB
ejpam-6202	746	23	the	the	DET
ejpam-6202	746	24	field	field	NOUN
ejpam-6202	746	25	’s	’s	PART
ejpam-6202	746	26	understanding	understanding	NOUN
ejpam-6202	746	27	of	of	ADP
ejpam-6202	746	28	combinatorial	combinatorial	ADJ
ejpam-6202	746	29	number	number	NOUN
ejpam-6202	746	30	theory	theory	NOUN
ejpam-6202	746	31	by	by	ADP
ejpam-6202	746	32	drawing	draw	VERB
ejpam-6202	746	33	connections	connection	NOUN
ejpam-6202	746	34	between	between	ADP
ejpam-6202	746	35	r	r	NOUN
ejpam-6202	746	36	-	-	PUNCT
ejpam-6202	746	37	stirling	stirling	NOUN
ejpam-6202	746	38	and	and	CCONJ
ejpam-6202	746	39	genocchi	genocchi	PROPN
ejpam-6202	746	40	numbers	number	NOUN
ejpam-6202	746	41	.	.	PUNCT
ejpam-6202	747	1	we	we	PRON
ejpam-6202	747	2	derived	derive	VERB
ejpam-6202	747	3	significant	significant	ADJ
ejpam-6202	747	4	results	result	NOUN
ejpam-6202	747	5	that	that	PRON
ejpam-6202	747	6	include	include	VERB
ejpam-6202	747	7	a	a	DET
ejpam-6202	747	8	convolution	convolution	NOUN
ejpam-6202	747	9	formula	formula	NOUN
ejpam-6202	747	10	,	,	PUNCT
ejpam-6202	747	11	which	which	PRON
ejpam-6202	747	12	establishes	establish	VERB
ejpam-6202	747	13	structural	structural	ADJ
ejpam-6202	747	14	relations	relation	NOUN
ejpam-6202	747	15	among	among	ADP
ejpam-6202	747	16	these	these	DET
ejpam-6202	747	17	numbers	number	NOUN
ejpam-6202	747	18	,	,	PUNCT
ejpam-6202	747	19	as	as	ADV
ejpam-6202	747	20	well	well	ADV
ejpam-6202	747	21	as	as	ADP
ejpam-6202	747	22	a	a	DET
ejpam-6202	747	23	horizontal	horizontal	ADJ
ejpam-6202	747	24	generating	generating	NOUN
ejpam-6202	747	25	function	function	NOUN
ejpam-6202	747	26	,	,	PUNCT
ejpam-6202	747	27	which	which	PRON
ejpam-6202	747	28	provides	provide	VERB
ejpam-6202	747	29	insight	insight	NOUN
ejpam-6202	747	30	into	into	ADP
ejpam-6202	747	31	the	the	DET
ejpam-6202	747	32	sequence	sequence	NOUN
ejpam-6202	747	33	’s	’s	PART
ejpam-6202	747	34	behavior	behavior	NOUN
ejpam-6202	747	35	and	and	CCONJ
ejpam-6202	747	36	recursive	recursive	ADJ
ejpam-6202	747	37	properties	property	NOUN
ejpam-6202	747	38	.	.	PUNCT
ejpam-6202	748	1	additionally	additionally	ADV
ejpam-6202	748	2	,	,	PUNCT
ejpam-6202	748	3	we	we	PRON
ejpam-6202	748	4	formulated	formulate	VERB
ejpam-6202	748	5	explicit	explicit	ADJ
ejpam-6202	748	6	expressions	expression	NOUN
ejpam-6202	748	7	for	for	ADP
ejpam-6202	748	8	both	both	CCONJ
ejpam-6202	748	9	the	the	DET
ejpam-6202	748	10	first	first	ADJ
ejpam-6202	748	11	and	and	CCONJ
ejpam-6202	748	12	second	second	ADJ
ejpam-6202	748	13	kinds	kind	NOUN
ejpam-6202	748	14	of	of	ADP
ejpam-6202	748	15	r	r	NOUN
ejpam-6202	748	16	-	-	PUNCT
ejpam-6202	748	17	stirling	stirling	NOUN
ejpam-6202	748	18	genocchi	genocchi	PROPN
ejpam-6202	748	19	numbers	number	NOUN
ejpam-6202	748	20	,	,	PUNCT
ejpam-6202	748	21	offering	offer	VERB
ejpam-6202	748	22	concrete	concrete	ADJ
ejpam-6202	748	23	tools	tool	NOUN
ejpam-6202	748	24	for	for	ADP
ejpam-6202	748	25	calculating	calculate	VERB
ejpam-6202	748	26	these	these	DET
ejpam-6202	748	27	values	value	NOUN
ejpam-6202	748	28	directly	directly	ADV
ejpam-6202	748	29	.	.	PUNCT
ejpam-6202	749	1	the	the	DET
ejpam-6202	749	2	study	study	NOUN
ejpam-6202	749	3	was	be	AUX
ejpam-6202	749	4	also	also	ADV
ejpam-6202	749	5	extended	extend	VERB
ejpam-6202	749	6	to	to	PART
ejpam-6202	749	7	encompass	encompass	VERB
ejpam-6202	749	8	genocchi	genocchi	NOUN
ejpam-6202	749	9	polynomials	polynomial	NOUN
ejpam-6202	749	10	and	and	CCONJ
ejpam-6202	749	11	higher	high	ADJ
ejpam-6202	749	12	-	-	PUNCT
ejpam-6202	749	13	order	order	NOUN
ejpam-6202	749	14	genocchi	genocchi	NOUN
ejpam-6202	749	15	polynomials	polynomial	NOUN
ejpam-6202	749	16	,	,	PUNCT
ejpam-6202	749	17	broadening	broaden	VERB
ejpam-6202	749	18	the	the	DET
ejpam-6202	749	19	scope	scope	NOUN
ejpam-6202	749	20	of	of	ADP
ejpam-6202	749	21	applicability	applicability	NOUN
ejpam-6202	749	22	.	.	PUNCT
ejpam-6202	750	1	these	these	DET
ejpam-6202	750	2	findings	finding	NOUN
ejpam-6202	750	3	contribute	contribute	VERB
ejpam-6202	750	4	to	to	ADP
ejpam-6202	750	5	the	the	DET
ejpam-6202	750	6	theoretical	theoretical	ADJ
ejpam-6202	750	7	framework	framework	NOUN
ejpam-6202	750	8	and	and	CCONJ
ejpam-6202	750	9	may	may	AUX
ejpam-6202	750	10	open	open	VERB
ejpam-6202	750	11	up	up	ADP
ejpam-6202	750	12	avenues	avenue	NOUN
ejpam-6202	750	13	for	for	ADP
ejpam-6202	750	14	further	further	ADJ
ejpam-6202	750	15	exploration	exploration	NOUN
ejpam-6202	750	16	into	into	ADP
ejpam-6202	750	17	generalized	generalized	ADJ
ejpam-6202	750	18	stirling	stirling	NOUN
ejpam-6202	750	19	and	and	CCONJ
ejpam-6202	750	20	genocchi	genocchi	PROPN
ejpam-6202	750	21	number	number	NOUN
ejpam-6202	750	22	applications	application	NOUN
ejpam-6202	750	23	,	,	PUNCT
ejpam-6202	750	24	particularly	particularly	ADV
ejpam-6202	750	25	in	in	ADP
ejpam-6202	750	26	areas	area	NOUN
ejpam-6202	750	27	involving	involve	VERB
ejpam-6202	750	28	combinatorial	combinatorial	ADJ
ejpam-6202	750	29	identities	identity	NOUN
ejpam-6202	750	30	,	,	PUNCT
ejpam-6202	750	31	partition	partition	NOUN
ejpam-6202	750	32	theory	theory	NOUN
ejpam-6202	750	33	,	,	PUNCT
ejpam-6202	750	34	and	and	CCONJ
ejpam-6202	750	35	potentially	potentially	ADV
ejpam-6202	750	36	in	in	ADP
ejpam-6202	750	37	solving	solve	VERB
ejpam-6202	750	38	25	25	NUM
ejpam-6202	750	39	of	of	ADP
ejpam-6202	750	40	26	26	NUM
ejpam-6202	750	41	specific	specific	ADJ
ejpam-6202	750	42	recurrence	recurrence	NOUN
ejpam-6202	750	43	relations	relation	NOUN
ejpam-6202	750	44	.	.	PUNCT
ejpam-6202	751	1	furthermore	furthermore	ADV
ejpam-6202	751	2	,	,	PUNCT
ejpam-6202	751	3	the	the	DET
ejpam-6202	751	4	results	result	NOUN
ejpam-6202	751	5	of	of	ADP
ejpam-6202	751	6	this	this	DET
ejpam-6202	751	7	study	study	NOUN
ejpam-6202	751	8	,	,	PUNCT
ejpam-6202	751	9	particularly	particularly	ADV
ejpam-6202	751	10	the	the	DET
ejpam-6202	751	11	use	use	NOUN
ejpam-6202	751	12	of	of	ADP
ejpam-6202	751	13	exponential	exponential	ADJ
ejpam-6202	751	14	generating	generating	NOUN
ejpam-6202	751	15	functions	function	NOUN
ejpam-6202	751	16	,	,	PUNCT
ejpam-6202	751	17	convolution	convolution	NOUN
ejpam-6202	751	18	identities	identity	NOUN
ejpam-6202	751	19	,	,	PUNCT
ejpam-6202	751	20	and	and	CCONJ
ejpam-6202	751	21	explicit	explicit	ADJ
ejpam-6202	751	22	formulas	formula	NOUN
ejpam-6202	751	23	parallel	parallel	VERB
ejpam-6202	751	24	the	the	DET
ejpam-6202	751	25	methods	method	NOUN
ejpam-6202	751	26	employed	employ	VERB
ejpam-6202	751	27	in	in	ADP
ejpam-6202	751	28	recent	recent	ADJ
ejpam-6202	751	29	work	work	NOUN
ejpam-6202	751	30	on	on	ADP
ejpam-6202	751	31	degenerate	degenerate	ADJ
ejpam-6202	751	32	r	r	NOUN
ejpam-6202	751	33	-	-	PUNCT
ejpam-6202	751	34	whitney	whitney	NOUN
ejpam-6202	751	35	numbers	number	NOUN
ejpam-6202	751	36	and	and	CCONJ
ejpam-6202	751	37	polynomials	polynomial	NOUN
ejpam-6202	751	38	in	in	ADP
ejpam-6202	751	39	[	[	X
ejpam-6202	751	40	10	10	NUM
ejpam-6202	751	41	]	]	PUNCT
ejpam-6202	751	42	.	.	PUNCT
ejpam-6202	752	1	this	this	DET
ejpam-6202	752	2	alignment	alignment	NOUN
ejpam-6202	752	3	suggests	suggest	VERB
ejpam-6202	752	4	that	that	SCONJ
ejpam-6202	752	5	the	the	DET
ejpam-6202	752	6	framework	framework	NOUN
ejpam-6202	752	7	developed	develop	VERB
ejpam-6202	752	8	here	here	ADV
ejpam-6202	752	9	can	can	AUX
ejpam-6202	752	10	be	be	AUX
ejpam-6202	752	11	naturally	naturally	ADV
ejpam-6202	752	12	extended	extend	VERB
ejpam-6202	752	13	to	to	PART
ejpam-6202	752	14	define	define	VERB
ejpam-6202	752	15	and	and	CCONJ
ejpam-6202	752	16	investigate	investigate	VERB
ejpam-6202	752	17	r	r	NOUN
ejpam-6202	752	18	-	-	PUNCT
ejpam-6202	752	19	whitney	whitney	NOUN
ejpam-6202	752	20	genocchi	genocchi	PROPN
ejpam-6202	752	21	numbers	number	NOUN
ejpam-6202	752	22	,	,	PUNCT
ejpam-6202	752	23	potentially	potentially	ADV
ejpam-6202	752	24	including	include	VERB
ejpam-6202	752	25	degenerate	degenerate	ADJ
ejpam-6202	752	26	versions	version	NOUN
ejpam-6202	752	27	.	.	PUNCT
ejpam-6202	753	1	acknowledgements	acknowledgement	NOUN
ejpam-6202	753	2	the	the	DET
ejpam-6202	753	3	authors	author	NOUN
ejpam-6202	753	4	sincerely	sincerely	ADV
ejpam-6202	753	5	thank	thank	VERB
ejpam-6202	753	6	the	the	DET
ejpam-6202	753	7	referees	referee	NOUN
ejpam-6202	753	8	for	for	ADP
ejpam-6202	753	9	their	their	PRON
ejpam-6202	753	10	thorough	thorough	ADJ
ejpam-6202	753	11	and	and	CCONJ
ejpam-6202	753	12	insightful	insightful	ADJ
ejpam-6202	753	13	review	review	NOUN
ejpam-6202	753	14	of	of	ADP
ejpam-6202	753	15	the	the	DET
ejpam-6202	753	16	manuscript	manuscript	NOUN
ejpam-6202	753	17	.	.	PUNCT
ejpam-6202	754	1	their	their	PRON
ejpam-6202	754	2	valuable	valuable	ADJ
ejpam-6202	754	3	feedback	feedback	NOUN
ejpam-6202	754	4	and	and	CCONJ
ejpam-6202	754	5	constructive	constructive	ADJ
ejpam-6202	754	6	suggestions	suggestion	NOUN
ejpam-6202	754	7	greatly	greatly	ADV
ejpam-6202	754	8	helped	help	VERB
ejpam-6202	754	9	improve	improve	VERB
ejpam-6202	754	10	the	the	DET
ejpam-6202	754	11	clarity	clarity	NOUN
ejpam-6202	754	12	and	and	CCONJ
ejpam-6202	754	13	overall	overall	ADJ
ejpam-6202	754	14	quality	quality	NOUN
ejpam-6202	754	15	of	of	ADP
ejpam-6202	754	16	the	the	DET
ejpam-6202	754	17	paper	paper	NOUN
ejpam-6202	754	18	.	.	PUNCT
ejpam-6202	755	1	the	the	DET
ejpam-6202	755	2	authors	author	NOUN
ejpam-6202	755	3	are	be	AUX
ejpam-6202	755	4	also	also	ADV
ejpam-6202	755	5	grateful	grateful	ADJ
ejpam-6202	755	6	to	to	PART
ejpam-6202	755	7	cebu	cebu	VERB
ejpam-6202	755	8	normal	normal	ADJ
ejpam-6202	755	9	university	university	NOUN
ejpam-6202	755	10	for	for	ADP
ejpam-6202	755	11	providing	provide	VERB
ejpam-6202	755	12	financial	financial	ADJ
ejpam-6202	755	13	support	support	NOUN
ejpam-6202	755	14	for	for	ADP
ejpam-6202	755	15	this	this	DET
ejpam-6202	755	16	research	research	NOUN
ejpam-6202	755	17	project	project	NOUN
ejpam-6202	755	18	.	.	PUNCT
ejpam-6202	756	1	references	reference	NOUN
ejpam-6202	756	2	[	[	X
ejpam-6202	756	3	1	1	NUM
ejpam-6202	756	4	]	]	X
ejpam-6202	756	5	james	james	PROPN
ejpam-6202	756	6	stirling	stirling	PROPN
ejpam-6202	756	7	.	.	PUNCT
ejpam-6202	757	1	methodus	methodus	PROPN
ejpam-6202	757	2	differentialis	differentialis	PROPN
ejpam-6202	757	3	,	,	PUNCT
ejpam-6202	757	4	sive	sive	ADJ
ejpam-6202	757	5	tractatus	tractatus	X
ejpam-6202	757	6	de	de	ADP
ejpam-6202	757	7	summatione	summatione	NOUN
ejpam-6202	757	8	et	et	NOUN
ejpam-6202	757	9	interpolatione	interpolatione	ADJ
ejpam-6202	757	10	serierum	serierum	PROPN
ejpam-6202	757	11	infinitorum	infinitorum	PROPN
ejpam-6202	757	12	.	.	PUNCT
ejpam-6202	758	1	1730	1730	NUM
ejpam-6202	758	2	.	.	PUNCT
ejpam-6202	759	1	[	[	X
ejpam-6202	759	2	2	2	NUM
ejpam-6202	759	3	]	]	PUNCT
ejpam-6202	759	4	andrei	andrei	PROPN
ejpam-6202	759	5	z.	z.	PROPN
ejpam-6202	759	6	broder	broder	PROPN
ejpam-6202	759	7	.	.	PUNCT
ejpam-6202	760	1	the	the	DET
ejpam-6202	760	2	r	r	NOUN
ejpam-6202	760	3	-	-	PUNCT
ejpam-6202	760	4	stirling	stirling	NOUN
ejpam-6202	760	5	numbers	number	NOUN
ejpam-6202	760	6	.	.	PUNCT
ejpam-6202	761	1	discrete	discrete	ADJ
ejpam-6202	761	2	mathematics	mathematic	NOUN
ejpam-6202	761	3	,	,	PUNCT
ejpam-6202	761	4	49(3):241–259	49(3):241–259	PROPN
ejpam-6202	761	5	,	,	PUNCT
ejpam-6202	761	6	1984	1984	NUM
ejpam-6202	761	7	.	.	PUNCT
ejpam-6202	762	1	[	[	X
ejpam-6202	762	2	3	3	X
ejpam-6202	762	3	]	]	X
ejpam-6202	762	4	roberto	roberto	PROPN
ejpam-6202	762	5	b.	b.	PROPN
ejpam-6202	762	6	corcino	corcino	PROPN
ejpam-6202	762	7	,	,	PUNCT
ejpam-6202	762	8	vernard	vernard	NOUN
ejpam-6202	762	9	dechosa	dechosa	PROPN
ejpam-6202	762	10	,	,	PUNCT
ejpam-6202	762	11	romeo	romeo	PROPN
ejpam-6202	762	12	coronel	coronel	PROPN
ejpam-6202	762	13	,	,	PUNCT
ejpam-6202	762	14	and	and	CCONJ
ejpam-6202	762	15	vienna	vienna	PROPN
ejpam-6202	762	16	mae	mae	PROPN
ejpam-6202	762	17	deveraturda	deveraturda	PROPN
ejpam-6202	762	18	.	.	PUNCT
ejpam-6202	763	1	the	the	DET
ejpam-6202	763	2	sm	sm	PROPN
ejpam-6202	763	3	r	r	PROPN
ejpam-6202	763	4	-	-	PUNCT
ejpam-6202	763	5	stirling	stirling	NOUN
ejpam-6202	763	6	numbers	number	NOUN
ejpam-6202	763	7	:	:	PUNCT
ejpam-6202	763	8	an	an	DET
ejpam-6202	763	9	algebraic	algebraic	ADJ
ejpam-6202	763	10	approach	approach	NOUN
ejpam-6202	763	11	.	.	PUNCT
ejpam-6202	764	1	cnu	cnu	PROPN
ejpam-6202	764	2	journal	journal	PROPN
ejpam-6202	764	3	of	of	ADP
ejpam-6202	764	4	higher	high	ADJ
ejpam-6202	764	5	education	education	NOUN
ejpam-6202	764	6	,	,	PUNCT
ejpam-6202	764	7	17:1–14	17:1–14	NUM
ejpam-6202	764	8	,	,	PUNCT
ejpam-6202	764	9	2023	2023	NUM
ejpam-6202	764	10	.	.	PUNCT
ejpam-6202	765	1	[	[	X
ejpam-6202	765	2	4	4	X
ejpam-6202	765	3	]	]	X
ejpam-6202	765	4	serkan	serkan	ADJ
ejpam-6202	765	5	araci	araci	NOUN
ejpam-6202	765	6	,	,	PUNCT
ejpam-6202	765	7	erdogan	erdogan	PROPN
ejpam-6202	765	8	sen	sen	PROPN
ejpam-6202	765	9	,	,	PUNCT
ejpam-6202	765	10	and	and	CCONJ
ejpam-6202	765	11	mehmet	mehmet	PROPN
ejpam-6202	765	12	acikgoz	acikgoz	PROPN
ejpam-6202	765	13	.	.	PUNCT
ejpam-6202	766	1	theorems	theorem	NOUN
ejpam-6202	766	2	on	on	ADP
ejpam-6202	766	3	genocchi	genocchi	PROPN
ejpam-6202	766	4	polynomials	polynomial	NOUN
ejpam-6202	766	5	of	of	ADP
ejpam-6202	766	6	higher	high	ADJ
ejpam-6202	766	7	order	order	NOUN
ejpam-6202	766	8	arising	arise	VERB
ejpam-6202	766	9	from	from	ADP
ejpam-6202	766	10	genocchi	genocchi	PROPN
ejpam-6202	766	11	basis	basis	NOUN
ejpam-6202	766	12	.	.	PUNCT
ejpam-6202	767	1	taiwanese	taiwanese	ADJ
ejpam-6202	767	2	journal	journal	NOUN
ejpam-6202	767	3	of	of	ADP
ejpam-6202	767	4	mathematics	mathematics	PROPN
ejpam-6202	767	5	,	,	PUNCT
ejpam-6202	767	6	18(2):473–482	18(2):473–482	PROPN
ejpam-6202	767	7	,	,	PUNCT
ejpam-6202	767	8	2014	2014	NUM
ejpam-6202	767	9	.	.	PUNCT
ejpam-6202	768	1	[	[	X
ejpam-6202	768	2	5	5	NUM
ejpam-6202	768	3	]	]	PUNCT
ejpam-6202	768	4	taekyun	taekyun	NOUN
ejpam-6202	768	5	kim	kim	PROPN
ejpam-6202	768	6	,	,	PUNCT
ejpam-6202	768	7	seog	seog	NOUN
ejpam-6202	768	8	-	-	PUNCT
ejpam-6202	768	9	hoon	hoon	NOUN
ejpam-6202	768	10	rim	rim	NOUN
ejpam-6202	768	11	,	,	PUNCT
ejpam-6202	768	12	dmitry	dmitry	PROPN
ejpam-6202	768	13	v.	v.	PROPN
ejpam-6202	768	14	dolgy	dolgy	PROPN
ejpam-6202	768	15	,	,	PUNCT
ejpam-6202	768	16	and	and	CCONJ
ejpam-6202	768	17	sang	sing	VERB
ejpam-6202	768	18	-	-	PUNCT
ejpam-6202	768	19	hun	hun	PROPN
ejpam-6202	768	20	lee	lee	PROPN
ejpam-6202	768	21	.	.	PUNCT
ejpam-6202	769	1	some	some	DET
ejpam-6202	769	2	identities	identity	NOUN
ejpam-6202	769	3	of	of	ADP
ejpam-6202	769	4	genocchi	genocchi	PROPN
ejpam-6202	769	5	polynomials	polynomial	NOUN
ejpam-6202	769	6	arising	arise	VERB
ejpam-6202	769	7	from	from	ADP
ejpam-6202	769	8	genocchi	genocchi	PROPN
ejpam-6202	769	9	basis	basis	NOUN
ejpam-6202	769	10	.	.	PUNCT
ejpam-6202	770	1	journal	journal	PROPN
ejpam-6202	770	2	of	of	ADP
ejpam-6202	770	3	inequalities	inequality	NOUN
ejpam-6202	770	4	and	and	CCONJ
ejpam-6202	770	5	applications	application	NOUN
ejpam-6202	770	6	,	,	PUNCT
ejpam-6202	770	7	2013:143	2013:143	NOUN
ejpam-6202	770	8	,	,	PUNCT
ejpam-6202	770	9	2013	2013	NUM
ejpam-6202	770	10	.	.	PUNCT
ejpam-6202	771	1	[	[	X
ejpam-6202	771	2	6	6	NUM
ejpam-6202	771	3	]	]	PUNCT
ejpam-6202	771	4	taekyun	taekyun	VERB
ejpam-6202	771	5	kim	kim	PROPN
ejpam-6202	771	6	.	.	PUNCT
ejpam-6202	772	1	some	some	DET
ejpam-6202	772	2	identities	identity	NOUN
ejpam-6202	772	3	for	for	ADP
ejpam-6202	772	4	the	the	DET
ejpam-6202	772	5	bernoulli	bernoulli	NOUN
ejpam-6202	772	6	,	,	PUNCT
ejpam-6202	772	7	the	the	DET
ejpam-6202	772	8	euler	euler	NOUN
ejpam-6202	772	9	and	and	CCONJ
ejpam-6202	772	10	the	the	DET
ejpam-6202	772	11	genocchi	genocchi	PROPN
ejpam-6202	772	12	numbers	number	NOUN
ejpam-6202	772	13	and	and	CCONJ
ejpam-6202	772	14	polynomials	polynomial	NOUN
ejpam-6202	772	15	.	.	PUNCT
ejpam-6202	773	1	advanced	advanced	ADJ
ejpam-6202	773	2	studies	study	NOUN
ejpam-6202	773	3	in	in	ADP
ejpam-6202	773	4	contemporary	contemporary	ADJ
ejpam-6202	773	5	mathematics	mathematic	NOUN
ejpam-6202	773	6	,	,	PUNCT
ejpam-6202	773	7	20(1):23–28	20(1):23–28	NUM
ejpam-6202	773	8	,	,	PUNCT
ejpam-6202	773	9	2010	2010	NUM
ejpam-6202	773	10	.	.	PUNCT
ejpam-6202	774	1	[	[	X
ejpam-6202	774	2	7	7	X
ejpam-6202	774	3	]	]	X
ejpam-6202	774	4	roberto	roberto	PROPN
ejpam-6202	774	5	b.	b.	PROPN
ejpam-6202	774	6	corcino	corcino	PROPN
ejpam-6202	774	7	and	and	CCONJ
ejpam-6202	774	8	cristina	cristina	PROPN
ejpam-6202	774	9	b.	b.	PROPN
ejpam-6202	774	10	corcino	corcino	PROPN
ejpam-6202	774	11	.	.	PUNCT
ejpam-6202	774	12	degenerate	degenerate	ADJ
ejpam-6202	774	13	apostol	apostol	NOUN
ejpam-6202	774	14	-	-	PUNCT
ejpam-6202	774	15	frobenius	frobenius	NOUN
ejpam-6202	774	16	-	-	PUNCT
ejpam-6202	774	17	type	type	NOUN
ejpam-6202	774	18	poly	poly	ADJ
ejpam-6202	774	19	-	-	PUNCT
ejpam-6202	774	20	genocchi	genocchi	NOUN
ejpam-6202	774	21	polynomials	polynomial	NOUN
ejpam-6202	774	22	of	of	ADP
ejpam-6202	774	23	higher	high	ADJ
ejpam-6202	774	24	order	order	NOUN
ejpam-6202	774	25	with	with	ADP
ejpam-6202	774	26	parameters	parameter	NOUN
ejpam-6202	774	27	a	a	PRON
ejpam-6202	774	28	and	and	CCONJ
ejpam-6202	774	29	b.	b.	PROPN
ejpam-6202	774	30	european	european	PROPN
ejpam-6202	774	31	journal	journal	PROPN
ejpam-6202	774	32	of	of	ADP
ejpam-6202	774	33	pure	pure	ADJ
ejpam-6202	774	34	and	and	CCONJ
ejpam-6202	774	35	applied	applied	ADJ
ejpam-6202	774	36	mathematics	mathematic	NOUN
ejpam-6202	774	37	,	,	PUNCT
ejpam-6202	774	38	16(2):687–712	16(2):687–712	NOUN
ejpam-6202	774	39	,	,	PUNCT
ejpam-6202	774	40	2023	2023	NUM
ejpam-6202	774	41	.	.	PUNCT
ejpam-6202	775	1	[	[	X
ejpam-6202	775	2	8	8	NUM
ejpam-6202	775	3	]	]	X
ejpam-6202	775	4	cristina	cristina	PROPN
ejpam-6202	775	5	b.	b.	PROPN
ejpam-6202	775	6	corcino	corcino	PROPN
ejpam-6202	775	7	and	and	CCONJ
ejpam-6202	775	8	roberto	roberto	PROPN
ejpam-6202	775	9	b.	b.	PROPN
ejpam-6202	775	10	corcino	corcino	PROPN
ejpam-6202	775	11	.	.	PUNCT
ejpam-6202	776	1	asymptotic	asymptotic	ADJ
ejpam-6202	776	2	approximations	approximation	NOUN
ejpam-6202	776	3	for	for	ADP
ejpam-6202	776	4	generalized	generalized	ADJ
ejpam-6202	776	5	apostol	apostol	NOUN
ejpam-6202	776	6	-	-	PUNCT
ejpam-6202	776	7	bernoulli	bernoulli	NOUN
ejpam-6202	776	8	,	,	PUNCT
ejpam-6202	776	9	apostol	apostol	NOUN
ejpam-6202	776	10	-	-	PUNCT
ejpam-6202	776	11	euler	euler	NOUN
ejpam-6202	776	12	and	and	CCONJ
ejpam-6202	776	13	apostol	apostol	NOUN
ejpam-6202	776	14	-	-	PUNCT
ejpam-6202	776	15	genocchi	genocchi	PROPN
ejpam-6202	776	16	polynomials	polynomial	NOUN
ejpam-6202	776	17	in	in	ADP
ejpam-6202	776	18	terms	term	NOUN
ejpam-6202	776	19	of	of	ADP
ejpam-6202	776	20	hyperbolic	hyperbolic	ADJ
ejpam-6202	776	21	functions	function	NOUN
ejpam-6202	776	22	.	.	PUNCT
ejpam-6202	777	1	european	european	ADJ
ejpam-6202	777	2	journal	journal	PROPN
ejpam-6202	777	3	of	of	ADP
ejpam-6202	777	4	pure	pure	ADJ
ejpam-6202	777	5	and	and	CCONJ
ejpam-6202	777	6	applied	applied	ADJ
ejpam-6202	777	7	mathematics	mathematic	NOUN
ejpam-6202	777	8	,	,	PUNCT
ejpam-6202	777	9	16(2):791	16(2):791	NUM
ejpam-6202	777	10	–	–	PUNCT
ejpam-6202	777	11	805	805	NUM
ejpam-6202	777	12	,	,	PUNCT
ejpam-6202	777	13	2023	2023	NUM
ejpam-6202	777	14	.	.	PUNCT
ejpam-6202	778	1	[	[	X
ejpam-6202	778	2	9	9	NUM
ejpam-6202	778	3	]	]	PUNCT
ejpam-6202	778	4	roberto	roberto	PROPN
ejpam-6202	778	5	b.	b.	PROPN
ejpam-6202	778	6	corcino	corcino	PROPN
ejpam-6202	778	7	and	and	CCONJ
ejpam-6202	778	8	cristina	cristina	PROPN
ejpam-6202	778	9	b.	b.	PROPN
ejpam-6202	778	10	corcino	corcino	PROPN
ejpam-6202	778	11	.	.	PUNCT
ejpam-6202	779	1	higher	high	ADJ
ejpam-6202	779	2	order	order	NOUN
ejpam-6202	779	3	bivariate	bivariate	ADJ
ejpam-6202	779	4	bell	bell	NOUN
ejpam-6202	779	5	-	-	PUNCT
ejpam-6202	779	6	based	base	VERB
ejpam-6202	779	7	apostol	apostol	NOUN
ejpam-6202	779	8	-	-	PUNCT
ejpam-6202	779	9	frobenius	frobenius	NOUN
ejpam-6202	779	10	-	-	PUNCT
ejpam-6202	779	11	type	type	NOUN
ejpam-6202	779	12	poly	poly	ADJ
ejpam-6202	779	13	-	-	PUNCT
ejpam-6202	779	14	genocchi	genocchi	NOUN
ejpam-6202	779	15	polynomials	polynomial	NOUN
ejpam-6202	779	16	with	with	ADP
ejpam-6202	779	17	parameters	parameter	NOUN
ejpam-6202	779	18	a	a	DET
ejpam-6202	779	19	and	and	CCONJ
ejpam-6202	779	20	b.	b.	PROPN
ejpam-6202	779	21	european	european	PROPN
ejpam-6202	779	22	journal	journal	PROPN
ejpam-6202	779	23	of	of	ADP
ejpam-6202	779	24	pure	pure	ADJ
ejpam-6202	779	25	and	and	CCONJ
ejpam-6202	779	26	applied	applied	ADJ
ejpam-6202	779	27	mathematics	mathematic	NOUN
ejpam-6202	779	28	,	,	PUNCT
ejpam-6202	779	29	17(3):1471–1489	17(3):1471–1489	NUM
ejpam-6202	779	30	,	,	PUNCT
ejpam-6202	779	31	2024	2024	NUM
ejpam-6202	779	32	.	.	PUNCT
ejpam-6202	780	1	[	[	X
ejpam-6202	780	2	10	10	NUM
ejpam-6202	780	3	]	]	PUNCT
ejpam-6202	780	4	taekyun	taekyun	VERB
ejpam-6202	780	5	kim	kim	PROPN
ejpam-6202	780	6	and	and	CCONJ
ejpam-6202	780	7	dae	dae	VERB
ejpam-6202	780	8	san	san	PROPN
ejpam-6202	780	9	kim	kim	PROPN
ejpam-6202	780	10	.	.	PUNCT
ejpam-6202	781	1	degenerate	degenerate	ADJ
ejpam-6202	781	2	r	r	NOUN
ejpam-6202	781	3	-	-	PUNCT
ejpam-6202	781	4	whitney	whitney	NOUN
ejpam-6202	781	5	numbers	number	NOUN
ejpam-6202	781	6	and	and	CCONJ
ejpam-6202	781	7	degener26	degener26	NOUN
ejpam-6202	781	8	of	of	ADP
ejpam-6202	781	9	26	26	NUM
ejpam-6202	781	10	ate	eat	VERB
ejpam-6202	781	11	r	r	NOUN
ejpam-6202	781	12	-	-	PUNCT
ejpam-6202	781	13	dowling	dowle	VERB
ejpam-6202	781	14	polynomials	polynomial	NOUN
ejpam-6202	781	15	via	via	ADP
ejpam-6202	781	16	boson	boson	NOUN
ejpam-6202	781	17	operators	operator	NOUN
ejpam-6202	781	18	.	.	PUNCT
ejpam-6202	782	1	advances	advance	NOUN
ejpam-6202	782	2	in	in	ADP
ejpam-6202	782	3	applied	apply	VERB
ejpam-6202	782	4	mathematics	mathematic	NOUN
ejpam-6202	782	5	,	,	PUNCT
ejpam-6202	782	6	140:102394	140:102394	NUM
ejpam-6202	782	7	,	,	PUNCT
ejpam-6202	782	8	2022	2022	NUM
ejpam-6202	782	9	.	.	PUNCT