id	sid	tid	token	lemma	pos
ejpam-3424	1	1	european	european	PROPN
ejpam-3424	1	2	journal	journal	PROPN
ejpam-3424	1	3	of	of	ADP
ejpam-3424	1	4	pure	pure	ADJ
ejpam-3424	1	5	and	and	CCONJ
ejpam-3424	1	6	applied	apply	VERB
ejpam-3424	1	7	mathematics	mathematic	NOUN
ejpam-3424	1	8	vol	vol	NOUN
ejpam-3424	1	9	.	.	PROPN
ejpam-3424	2	1	12	12	NUM
ejpam-3424	2	2	,	,	PUNCT
ejpam-3424	2	3	no	no	INTJ
ejpam-3424	2	4	.	.	NOUN
ejpam-3424	2	5	3	3	NUM
ejpam-3424	2	6	,	,	PUNCT
ejpam-3424	2	7	2019	2019	NUM
ejpam-3424	2	8	,	,	PUNCT
ejpam-3424	2	9	1069	1069	NUM
ejpam-3424	2	10	-	-	SYM
ejpam-3424	2	11	1081	1081	NUM
ejpam-3424	2	12	issn	issn	PROPN
ejpam-3424	2	13	1307	1307	NUM
ejpam-3424	2	14	-	-	SYM
ejpam-3424	2	15	5543	5543	NUM
ejpam-3424	2	16	–	–	PUNCT
ejpam-3424	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3424	2	18	published	publish	VERB
ejpam-3424	2	19	by	by	ADP
ejpam-3424	2	20	new	new	PROPN
ejpam-3424	2	21	york	york	PROPN
ejpam-3424	2	22	business	business	NOUN
ejpam-3424	2	23	global	global	VERB
ejpam-3424	2	24	some	some	DET
ejpam-3424	2	25	theorems	theorem	NOUN
ejpam-3424	2	26	on	on	ADP
ejpam-3424	2	27	tauber	tauber	PROPN
ejpam-3424	2	28	’s	’s	PART
ejpam-3424	2	29	generalized	generalized	ADJ
ejpam-3424	2	30	stirling	stirling	PROPN
ejpam-3424	2	31	,	,	PUNCT
ejpam-3424	2	32	lah	lah	PROPN
ejpam-3424	2	33	,	,	PUNCT
ejpam-3424	2	34	and	and	CCONJ
ejpam-3424	2	35	bell	bell	NOUN
ejpam-3424	2	36	numbers	number	NOUN
ejpam-3424	2	37	roberto	roberto	PROPN
ejpam-3424	2	38	b.	b.	PROPN
ejpam-3424	2	39	corcino1,∗	corcino1,∗	PROPN
ejpam-3424	2	40	,	,	PUNCT
ejpam-3424	2	41	cristina	cristina	PROPN
ejpam-3424	2	42	b.	b.	PROPN
ejpam-3424	2	43	corcino2	corcino2	PROPN
ejpam-3424	2	44	,	,	PUNCT
ejpam-3424	2	45	gladys	gladys	PROPN
ejpam-3424	2	46	jane	jane	PROPN
ejpam-3424	2	47	s.	s.	PROPN
ejpam-3424	2	48	rama2	rama2	PROPN
ejpam-3424	2	49	1	1	NUM
ejpam-3424	2	50	research	research	NOUN
ejpam-3424	2	51	institute	institute	NOUN
ejpam-3424	2	52	for	for	ADP
ejpam-3424	2	53	computational	computational	ADJ
ejpam-3424	2	54	mathematics	mathematic	NOUN
ejpam-3424	2	55	and	and	CCONJ
ejpam-3424	2	56	physics	physics	NOUN
ejpam-3424	2	57	,	,	PUNCT
ejpam-3424	2	58	cebu	cebu	NOUN
ejpam-3424	2	59	normal	normal	ADJ
ejpam-3424	2	60	university	university	NOUN
ejpam-3424	2	61	,	,	PUNCT
ejpam-3424	2	62	6000	6000	NUM
ejpam-3424	2	63	cebu	cebu	NOUN
ejpam-3424	2	64	city	city	NOUN
ejpam-3424	2	65	,	,	PUNCT
ejpam-3424	2	66	philippines	philippines	PROPN
ejpam-3424	2	67	2	2	NUM
ejpam-3424	2	68	department	department	NOUN
ejpam-3424	2	69	of	of	ADP
ejpam-3424	2	70	mathematics	mathematic	NOUN
ejpam-3424	2	71	,	,	PUNCT
ejpam-3424	2	72	cebu	cebu	NOUN
ejpam-3424	2	73	normal	normal	ADJ
ejpam-3424	2	74	university	university	NOUN
ejpam-3424	2	75	,	,	PUNCT
ejpam-3424	2	76	6000	6000	NUM
ejpam-3424	2	77	cebu	cebu	NOUN
ejpam-3424	2	78	city	city	NOUN
ejpam-3424	2	79	,	,	PUNCT
ejpam-3424	2	80	philippines	philippine	NOUN
ejpam-3424	2	81	abstract	abstract	ADJ
ejpam-3424	2	82	.	.	PUNCT
ejpam-3424	3	1	in	in	ADP
ejpam-3424	3	2	this	this	DET
ejpam-3424	3	3	paper	paper	NOUN
ejpam-3424	3	4	,	,	PUNCT
ejpam-3424	3	5	the	the	DET
ejpam-3424	3	6	authors	author	NOUN
ejpam-3424	3	7	obtain	obtain	VERB
ejpam-3424	3	8	some	some	DET
ejpam-3424	3	9	properties	property	NOUN
ejpam-3424	3	10	for	for	ADP
ejpam-3424	3	11	tauber	tauber	PROPN
ejpam-3424	3	12	’s	’s	PART
ejpam-3424	3	13	generalized	generalized	ADJ
ejpam-3424	3	14	stirling	stirling	NOUN
ejpam-3424	3	15	and	and	CCONJ
ejpam-3424	3	16	lah	lah	NOUN
ejpam-3424	3	17	numbers	number	NOUN
ejpam-3424	3	18	,	,	PUNCT
ejpam-3424	3	19	including	include	VERB
ejpam-3424	3	20	other	other	ADJ
ejpam-3424	3	21	forms	form	NOUN
ejpam-3424	3	22	of	of	ADP
ejpam-3424	3	23	recurrence	recurrence	NOUN
ejpam-3424	3	24	relations	relation	NOUN
ejpam-3424	3	25	,	,	PUNCT
ejpam-3424	3	26	orthogonality	orthogonality	NOUN
ejpam-3424	3	27	and	and	CCONJ
ejpam-3424	3	28	inverse	inverse	NOUN
ejpam-3424	3	29	relations	relation	NOUN
ejpam-3424	3	30	,	,	PUNCT
ejpam-3424	3	31	rational	rational	ADJ
ejpam-3424	3	32	generating	generating	NOUN
ejpam-3424	3	33	function	function	NOUN
ejpam-3424	3	34	and	and	CCONJ
ejpam-3424	3	35	explicit	explicit	ADJ
ejpam-3424	3	36	formula	formula	NOUN
ejpam-3424	3	37	in	in	ADP
ejpam-3424	3	38	symmetric	symmetric	ADJ
ejpam-3424	3	39	function	function	NOUN
ejpam-3424	3	40	form	form	NOUN
ejpam-3424	3	41	.	.	PUNCT
ejpam-3424	4	1	moreover	moreover	ADV
ejpam-3424	4	2	,	,	PUNCT
ejpam-3424	4	3	the	the	DET
ejpam-3424	4	4	authors	author	NOUN
ejpam-3424	4	5	derive	derive	VERB
ejpam-3424	4	6	a	a	DET
ejpam-3424	4	7	new	new	ADJ
ejpam-3424	4	8	explicit	explicit	ADJ
ejpam-3424	4	9	formula	formula	NOUN
ejpam-3424	4	10	,	,	PUNCT
ejpam-3424	4	11	which	which	PRON
ejpam-3424	4	12	is	be	AUX
ejpam-3424	4	13	analogous	analogous	ADJ
ejpam-3424	4	14	to	to	ADP
ejpam-3424	4	15	the	the	DET
ejpam-3424	4	16	qi	qi	NOUN
ejpam-3424	4	17	formula	formula	NOUN
ejpam-3424	4	18	.	.	PUNCT
ejpam-3424	5	1	2010	2010	NUM
ejpam-3424	5	2	mathematics	mathematic	NOUN
ejpam-3424	5	3	subject	subject	NOUN
ejpam-3424	5	4	classifications	classification	NOUN
ejpam-3424	5	5	:	:	PUNCT
ejpam-3424	5	6	05a15	05a15	NUM
ejpam-3424	5	7	,	,	PUNCT
ejpam-3424	5	8	11b65	11b65	NUM
ejpam-3424	5	9	,	,	PUNCT
ejpam-3424	5	10	11b73	11b73	NUM
ejpam-3424	5	11	key	key	ADJ
ejpam-3424	5	12	words	word	NOUN
ejpam-3424	5	13	and	and	CCONJ
ejpam-3424	5	14	phrases	phrase	NOUN
ejpam-3424	5	15	:	:	PUNCT
ejpam-3424	5	16	stirling	stirling	NOUN
ejpam-3424	5	17	numbers	number	NOUN
ejpam-3424	5	18	,	,	PUNCT
ejpam-3424	5	19	whitney	whitney	NOUN
ejpam-3424	5	20	numbers	number	NOUN
ejpam-3424	5	21	,	,	PUNCT
ejpam-3424	5	22	dowling	dowling	NOUN
ejpam-3424	5	23	numbers	number	NOUN
ejpam-3424	5	24	,	,	PUNCT
ejpam-3424	5	25	generating	generate	VERB
ejpam-3424	5	26	function	function	NOUN
ejpam-3424	5	27	,	,	PUNCT
ejpam-3424	5	28	recurrence	recurrence	NOUN
ejpam-3424	5	29	relation	relation	NOUN
ejpam-3424	5	30	1	1	NUM
ejpam-3424	5	31	.	.	PUNCT
ejpam-3424	6	1	introduction	introduction	NOUN
ejpam-3424	6	2	the	the	DET
ejpam-3424	6	3	nth	nth	PROPN
ejpam-3424	6	4	bell	bell	NOUN
ejpam-3424	6	5	numbers	number	NOUN
ejpam-3424	6	6	,	,	PUNCT
ejpam-3424	6	7	denoted	denote	VERB
ejpam-3424	6	8	by	by	ADP
ejpam-3424	6	9	bn	bn	PROPN
ejpam-3424	6	10	,	,	PUNCT
ejpam-3424	6	11	are	be	AUX
ejpam-3424	6	12	known	know	VERB
ejpam-3424	6	13	by	by	ADP
ejpam-3424	6	14	their	their	PRON
ejpam-3424	6	15	combinatorial	combinatorial	ADJ
ejpam-3424	6	16	interpretation	interpretation	NOUN
ejpam-3424	6	17	as	as	ADP
ejpam-3424	6	18	the	the	DET
ejpam-3424	6	19	number	number	NOUN
ejpam-3424	6	20	of	of	ADP
ejpam-3424	6	21	ways	way	NOUN
ejpam-3424	6	22	to	to	PART
ejpam-3424	6	23	partition	partition	VERB
ejpam-3424	6	24	an	an	DET
ejpam-3424	6	25	n	n	ADV
ejpam-3424	6	26	-	-	PUNCT
ejpam-3424	6	27	set	set	NOUN
ejpam-3424	6	28	.	.	PUNCT
ejpam-3424	7	1	this	this	DET
ejpam-3424	7	2	interpretation	interpretation	NOUN
ejpam-3424	7	3	is	be	AUX
ejpam-3424	7	4	based	base	VERB
ejpam-3424	7	5	on	on	ADP
ejpam-3424	7	6	the	the	DET
ejpam-3424	7	7	definition	definition	NOUN
ejpam-3424	7	8	of	of	ADP
ejpam-3424	7	9	bell	bell	NOUN
ejpam-3424	7	10	numbers	number	NOUN
ejpam-3424	7	11	as	as	ADP
ejpam-3424	7	12	the	the	DET
ejpam-3424	7	13	sum	sum	NOUN
ejpam-3424	7	14	of	of	ADP
ejpam-3424	7	15	the	the	DET
ejpam-3424	7	16	classical	classical	ADJ
ejpam-3424	7	17	stirling	stirling	NOUN
ejpam-3424	7	18	numbers	number	NOUN
ejpam-3424	7	19	of	of	ADP
ejpam-3424	7	20	the	the	DET
ejpam-3424	7	21	second	second	ADJ
ejpam-3424	7	22	kind	kind	NOUN
ejpam-3424	7	23	[	[	X
ejpam-3424	7	24	2	2	NUM
ejpam-3424	7	25	]	]	PUNCT
ejpam-3424	7	26	.	.	PUNCT
ejpam-3424	8	1	that	that	PRON
ejpam-3424	8	2	is	be	AUX
ejpam-3424	8	3	,	,	PUNCT
ejpam-3424	8	4	bn	bn	PROPN
ejpam-3424	8	5	=	=	SYM
ejpam-3424	8	6	n∑	n∑	PROPN
ejpam-3424	8	7	k=0	k=0	PROPN
ejpam-3424	8	8	{	{	PUNCT
ejpam-3424	8	9	n	n	NOUN
ejpam-3424	8	10	k	k	NOUN
ejpam-3424	8	11	}	}	PUNCT
ejpam-3424	8	12	(	(	PUNCT
ejpam-3424	8	13	1	1	X
ejpam-3424	8	14	)	)	PUNCT
ejpam-3424	8	15	where	where	SCONJ
ejpam-3424	8	16	{	{	PUNCT
ejpam-3424	8	17	n	n	X
ejpam-3424	8	18	k	k	NOUN
ejpam-3424	8	19	}	}	PUNCT
ejpam-3424	8	20	denotes	denote	VERB
ejpam-3424	8	21	the	the	DET
ejpam-3424	8	22	stirling	stirling	NOUN
ejpam-3424	8	23	numbers	number	NOUN
ejpam-3424	8	24	of	of	ADP
ejpam-3424	8	25	the	the	DET
ejpam-3424	8	26	second	second	ADJ
ejpam-3424	8	27	kind	kind	NOUN
ejpam-3424	8	28	(	(	PUNCT
ejpam-3424	8	29	the	the	DET
ejpam-3424	8	30	karamata	karamata	ADJ
ejpam-3424	8	31	-	-	PUNCT
ejpam-3424	8	32	knuth	knuth	NOUN
ejpam-3424	8	33	notation	notation	NOUN
ejpam-3424	8	34	)	)	PUNCT
ejpam-3424	8	35	,	,	PUNCT
ejpam-3424	8	36	which	which	PRON
ejpam-3424	8	37	can	can	AUX
ejpam-3424	8	38	be	be	AUX
ejpam-3424	8	39	interpreted	interpret	VERB
ejpam-3424	8	40	as	as	ADP
ejpam-3424	8	41	the	the	DET
ejpam-3424	8	42	number	number	NOUN
ejpam-3424	8	43	of	of	ADP
ejpam-3424	8	44	ways	way	NOUN
ejpam-3424	8	45	to	to	PART
ejpam-3424	8	46	partition	partition	VERB
ejpam-3424	8	47	an	an	DET
ejpam-3424	8	48	n	n	ADV
ejpam-3424	8	49	-	-	PUNCT
ejpam-3424	8	50	set	set	NOUN
ejpam-3424	8	51	into	into	ADP
ejpam-3424	8	52	k	k	PROPN
ejpam-3424	8	53	nonempty	nonempty	PROPN
ejpam-3424	8	54	subsets	subset	NOUN
ejpam-3424	8	55	.	.	PUNCT
ejpam-3424	9	1	the	the	DET
ejpam-3424	9	2	bell	bell	PROPN
ejpam-3424	9	3	numbers	number	NOUN
ejpam-3424	9	4	were	be	AUX
ejpam-3424	9	5	expressed	express	VERB
ejpam-3424	9	6	by	by	ADP
ejpam-3424	9	7	spivey	spivey	PROPN
ejpam-3424	9	8	[	[	X
ejpam-3424	9	9	5	5	NUM
ejpam-3424	9	10	]	]	PUNCT
ejpam-3424	9	11	as	as	ADP
ejpam-3424	9	12	bm+n	bm+n	PROPN
ejpam-3424	9	13	=	=	PROPN
ejpam-3424	9	14	n∑	n∑	PROPN
ejpam-3424	9	15	k=0	k=0	PROPN
ejpam-3424	9	16	m∑	m∑	CCONJ
ejpam-3424	9	17	j=0	j=0	PROPN
ejpam-3424	9	18	jn−k	jn−k	PROPN
ejpam-3424	9	19	{	{	PUNCT
ejpam-3424	9	20	m	m	PROPN
ejpam-3424	9	21	j	j	NOUN
ejpam-3424	9	22	}	}	PUNCT
ejpam-3424	9	23	(	(	PUNCT
ejpam-3424	9	24	n	n	X
ejpam-3424	9	25	k	k	PROPN
ejpam-3424	9	26	)	)	PUNCT
ejpam-3424	9	27	bk	bk	PROPN
ejpam-3424	9	28	.	.	PUNCT
ejpam-3424	10	1	(	(	PUNCT
ejpam-3424	10	2	2	2	X
ejpam-3424	10	3	)	)	PUNCT
ejpam-3424	10	4	∗corresponding	∗corresponde	VERB
ejpam-3424	10	5	author	author	NOUN
ejpam-3424	10	6	.	.	PUNCT
ejpam-3424	11	1	doi	doi	NOUN
ejpam-3424	11	2	:	:	PUNCT
ejpam-3424	11	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3424	https://doi.org/10.29020/nybg.ejpam.v12i3.3424	NUM
ejpam-3424	11	4	email	email	NOUN
ejpam-3424	11	5	addresses	address	NOUN
ejpam-3424	11	6	:	:	PUNCT
ejpam-3424	11	7	rcorcino@yahoo.com	rcorcino@yahoo.com	X
ejpam-3424	11	8	(	(	PUNCT
ejpam-3424	11	9	r.	r.	PROPN
ejpam-3424	11	10	corcino	corcino	PROPN
ejpam-3424	11	11	)	)	PUNCT
ejpam-3424	11	12	,	,	PUNCT
ejpam-3424	11	13	cristinacorcino@yahoo.com	cristinacorcino@yahoo.com	PROPN
ejpam-3424	11	14	(	(	PUNCT
ejpam-3424	11	15	c.	c.	PROPN
ejpam-3424	11	16	corcino	corcino	PROPN
ejpam-3424	11	17	)	)	PUNCT
ejpam-3424	11	18	,	,	PUNCT
ejpam-3424	11	19	gjsrama@yahoo.com	gjsrama@yahoo.com	X
ejpam-3424	11	20	(	(	PUNCT
ejpam-3424	11	21	g.	g.	PROPN
ejpam-3424	11	22	rama	rama	PROPN
ejpam-3424	11	23	)	)	PUNCT
ejpam-3424	11	24	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3424	12	1	1069	1069	NUM
ejpam-3424	13	1	c	c	NOUN
ejpam-3424	13	2	©	©	PROPN
ejpam-3424	13	3	2019	2019	NUM
ejpam-3424	13	4	ejpam	ejpam	NOUN
ejpam-3424	13	5	all	all	DET
ejpam-3424	13	6	rights	right	NOUN
ejpam-3424	13	7	reserved	reserve	VERB
ejpam-3424	13	8	.	.	PUNCT
ejpam-3424	14	1	r.	r.	PROPN
ejpam-3424	14	2	corcino	corcino	PROPN
ejpam-3424	14	3	,	,	PUNCT
ejpam-3424	14	4	c.	c.	PROPN
ejpam-3424	14	5	corcino	corcino	PROPN
ejpam-3424	14	6	,	,	PUNCT
ejpam-3424	14	7	g.	g.	PROPN
ejpam-3424	14	8	rama	rama	PROPN
ejpam-3424	14	9	/	/	SYM
ejpam-3424	14	10	eur	eur	PROPN
ejpam-3424	14	11	.	.	PUNCT
ejpam-3424	15	1	j.	j.	PROPN
ejpam-3424	15	2	pure	pure	PROPN
ejpam-3424	15	3	appl	appl	PROPN
ejpam-3424	15	4	.	.	PROPN
ejpam-3424	15	5	math	math	PROPN
ejpam-3424	15	6	,	,	PUNCT
ejpam-3424	15	7	12	12	NUM
ejpam-3424	15	8	(	(	PUNCT
ejpam-3424	15	9	3	3	NUM
ejpam-3424	15	10	)	)	PUNCT
ejpam-3424	15	11	(	(	PUNCT
ejpam-3424	15	12	2019	2019	NUM
ejpam-3424	15	13	)	)	PUNCT
ejpam-3424	15	14	,	,	PUNCT
ejpam-3424	15	15	1069	1069	NUM
ejpam-3424	15	16	-	-	SYM
ejpam-3424	15	17	1081	1081	NUM
ejpam-3424	15	18	1070	1070	NUM
ejpam-3424	15	19	the	the	DET
ejpam-3424	15	20	above	above	ADJ
ejpam-3424	15	21	formula	formula	NOUN
ejpam-3424	15	22	was	be	AUX
ejpam-3424	15	23	proven	prove	VERB
ejpam-3424	15	24	combinatorially	combinatorially	ADV
ejpam-3424	15	25	by	by	ADP
ejpam-3424	15	26	considering	consider	VERB
ejpam-3424	15	27	another	another	DET
ejpam-3424	15	28	way	way	NOUN
ejpam-3424	15	29	of	of	ADP
ejpam-3424	15	30	counting	count	VERB
ejpam-3424	15	31	the	the	DET
ejpam-3424	15	32	number	number	NOUN
ejpam-3424	15	33	of	of	ADP
ejpam-3424	15	34	ways	way	NOUN
ejpam-3424	15	35	to	to	PART
ejpam-3424	15	36	partition	partition	VERB
ejpam-3424	15	37	the	the	DET
ejpam-3424	15	38	set	set	NOUN
ejpam-3424	15	39	with	with	ADP
ejpam-3424	15	40	m+	m+	NOUN
ejpam-3424	15	41	n	n	DET
ejpam-3424	15	42	objects	object	NOUN
ejpam-3424	15	43	.	.	PUNCT
ejpam-3424	16	1	recently	recently	ADV
ejpam-3424	16	2	,	,	PUNCT
ejpam-3424	16	3	feng	feng	PROPN
ejpam-3424	16	4	qi	qi	PROPN
ejpam-3424	16	5	[	[	X
ejpam-3424	16	6	4	4	NUM
ejpam-3424	16	7	]	]	PUNCT
ejpam-3424	16	8	established	establish	VERB
ejpam-3424	16	9	a	a	DET
ejpam-3424	16	10	new	new	ADJ
ejpam-3424	16	11	explicit	explicit	ADJ
ejpam-3424	16	12	formula	formula	NOUN
ejpam-3424	16	13	for	for	ADP
ejpam-3424	16	14	bell	bell	NOUN
ejpam-3424	16	15	numbers	number	NOUN
ejpam-3424	16	16	,	,	PUNCT
ejpam-3424	16	17	which	which	PRON
ejpam-3424	16	18	is	be	AUX
ejpam-3424	16	19	expressed	express	VERB
ejpam-3424	16	20	in	in	ADP
ejpam-3424	16	21	terms	term	NOUN
ejpam-3424	16	22	of	of	ADP
ejpam-3424	16	23	stirling	stirling	NOUN
ejpam-3424	16	24	numbers	number	NOUN
ejpam-3424	16	25	of	of	ADP
ejpam-3424	16	26	the	the	DET
ejpam-3424	16	27	second	second	ADJ
ejpam-3424	16	28	kind	kind	NOUN
ejpam-3424	16	29	{	{	PUNCT
ejpam-3424	16	30	n	n	NOUN
ejpam-3424	16	31	k	k	NOUN
ejpam-3424	16	32	}	}	PUNCT
ejpam-3424	16	33	and	and	CCONJ
ejpam-3424	16	34	lah	lah	NOUN
ejpam-3424	16	35	numbers	number	NOUN
ejpam-3424	16	36	l(n	l(n	PROPN
ejpam-3424	16	37	,	,	PUNCT
ejpam-3424	16	38	k	k	NOUN
ejpam-3424	16	39	)	)	PUNCT
ejpam-3424	16	40	.	.	PUNCT
ejpam-3424	17	1	the	the	DET
ejpam-3424	17	2	formula	formula	NOUN
ejpam-3424	17	3	is	be	AUX
ejpam-3424	17	4	given	give	VERB
ejpam-3424	17	5	by	by	ADP
ejpam-3424	17	6	bn	bn	PROPN
ejpam-3424	17	7	=	=	SYM
ejpam-3424	17	8	n∑	n∑	NOUN
ejpam-3424	17	9	k=1	k=1	PROPN
ejpam-3424	18	1	(	(	PUNCT
ejpam-3424	18	2	−1)n−k	−1)n−k	PROPN
ejpam-3424	18	3	[	[	PUNCT
ejpam-3424	18	4	k∑	k∑	NOUN
ejpam-3424	18	5	l=1	l=1	NOUN
ejpam-3424	18	6	l(k	l(k	PROPN
ejpam-3424	18	7	,	,	PUNCT
ejpam-3424	18	8	l	l	NOUN
ejpam-3424	18	9	)	)	PUNCT
ejpam-3424	18	10	]	]	PUNCT
ejpam-3424	18	11	{	{	PUNCT
ejpam-3424	18	12	n	n	X
ejpam-3424	18	13	k	k	NOUN
ejpam-3424	18	14	}	}	PUNCT
ejpam-3424	18	15	(	(	PUNCT
ejpam-3424	18	16	3	3	X
ejpam-3424	18	17	)	)	PUNCT
ejpam-3424	18	18	which	which	PRON
ejpam-3424	18	19	may	may	AUX
ejpam-3424	18	20	be	be	AUX
ejpam-3424	18	21	referred	refer	VERB
ejpam-3424	18	22	to	to	ADP
ejpam-3424	18	23	as	as	ADP
ejpam-3424	18	24	the	the	DET
ejpam-3424	18	25	qi	qi	NOUN
ejpam-3424	18	26	formula	formula	NOUN
ejpam-3424	18	27	for	for	ADP
ejpam-3424	18	28	bell	bell	NOUN
ejpam-3424	18	29	numbers	number	NOUN
ejpam-3424	18	30	.	.	PUNCT
ejpam-3424	19	1	the	the	DET
ejpam-3424	19	2	formula	formula	NOUN
ejpam-3424	19	3	has	have	AUX
ejpam-3424	19	4	been	be	AUX
ejpam-3424	19	5	derived	derive	VERB
ejpam-3424	19	6	in	in	ADP
ejpam-3424	19	7	two	two	NUM
ejpam-3424	19	8	ways	way	NOUN
ejpam-3424	19	9	:	:	PUNCT
ejpam-3424	19	10	•	•	ADP
ejpam-3424	19	11	using	use	VERB
ejpam-3424	19	12	faa	faa	PROPN
ejpam-3424	19	13	di	di	PROPN
ejpam-3424	19	14	bruno	bruno	PROPN
ejpam-3424	19	15	’s	’s	PART
ejpam-3424	19	16	formula	formula	NOUN
ejpam-3424	19	17	and	and	CCONJ
ejpam-3424	19	18	the	the	DET
ejpam-3424	19	19	formula	formula	NOUN
ejpam-3424	19	20	for	for	ADP
ejpam-3424	19	21	the	the	DET
ejpam-3424	19	22	n	n	ADV
ejpam-3424	19	23	-	-	PUNCT
ejpam-3424	19	24	th	th	X
ejpam-3424	19	25	derivative	derivative	NOUN
ejpam-3424	19	26	of	of	ADP
ejpam-3424	19	27	e	e	PROPN
ejpam-3424	19	28	1	1	NUM
ejpam-3424	19	29	x	x	SYM
ejpam-3424	19	30	containing	contain	VERB
ejpam-3424	19	31	lah	lah	NOUN
ejpam-3424	19	32	numbers	number	NOUN
ejpam-3424	19	33	[	[	X
ejpam-3424	19	34	3	3	NUM
ejpam-3424	19	35	,	,	PUNCT
ejpam-3424	19	36	9	9	NUM
ejpam-3424	19	37	]	]	PUNCT
ejpam-3424	19	38	;	;	PUNCT
ejpam-3424	19	39	•	•	ADP
ejpam-3424	19	40	using	use	VERB
ejpam-3424	19	41	the	the	DET
ejpam-3424	19	42	inverse	inverse	NOUN
ejpam-3424	19	43	relation	relation	NOUN
ejpam-3424	19	44	for	for	ADP
ejpam-3424	19	45	the	the	DET
ejpam-3424	19	46	classical	classical	ADJ
ejpam-3424	19	47	stirling	stirling	NOUN
ejpam-3424	19	48	numbers	number	NOUN
ejpam-3424	19	49	of	of	ADP
ejpam-3424	19	50	the	the	DET
ejpam-3424	19	51	first	first	ADJ
ejpam-3424	19	52	and	and	CCONJ
ejpam-3424	19	53	second	second	ADJ
ejpam-3424	19	54	kind	kind	NOUN
ejpam-3424	19	55	.	.	PUNCT
ejpam-3424	20	1	these	these	DET
ejpam-3424	20	2	methods	method	NOUN
ejpam-3424	20	3	have	have	AUX
ejpam-3424	20	4	been	be	AUX
ejpam-3424	20	5	applied	apply	VERB
ejpam-3424	20	6	to	to	PART
ejpam-3424	20	7	obtain	obtain	VERB
ejpam-3424	20	8	new	new	ADJ
ejpam-3424	20	9	explicit	explicit	ADJ
ejpam-3424	20	10	formula	formula	NOUN
ejpam-3424	20	11	for	for	ADP
ejpam-3424	20	12	different	different	ADJ
ejpam-3424	20	13	generalizations	generalization	NOUN
ejpam-3424	20	14	of	of	ADP
ejpam-3424	20	15	stirling	stirling	NOUN
ejpam-3424	20	16	numbers	number	NOUN
ejpam-3424	20	17	.	.	PUNCT
ejpam-3424	21	1	certain	certain	ADJ
ejpam-3424	21	2	generalization	generalization	NOUN
ejpam-3424	21	3	of	of	ADP
ejpam-3424	21	4	stirling	stirling	NOUN
ejpam-3424	21	5	numbers	number	NOUN
ejpam-3424	21	6	was	be	AUX
ejpam-3424	21	7	introduced	introduce	VERB
ejpam-3424	21	8	by	by	ADP
ejpam-3424	21	9	s.	s.	PROPN
ejpam-3424	21	10	tauber	tauber	PROPN
ejpam-3424	22	1	[	[	X
ejpam-3424	22	2	6–8	6–8	X
ejpam-3424	22	3	]	]	X
ejpam-3424	22	4	as	as	ADP
ejpam-3424	22	5	the	the	DET
ejpam-3424	22	6	coefficients	coefficient	NOUN
ejpam-3424	22	7	cmk	cmk	NOUN
ejpam-3424	22	8	,	,	PUNCT
ejpam-3424	22	9	n	n	PROPN
ejpam-3424	22	10	and	and	CCONJ
ejpam-3424	22	11	dm	dm	PROPN
ejpam-3424	22	12	k	k	PROPN
ejpam-3424	22	13	,	,	PUNCT
ejpam-3424	22	14	n	n	PROPN
ejpam-3424	22	15	of	of	ADP
ejpam-3424	22	16	the	the	DET
ejpam-3424	22	17	following	follow	VERB
ejpam-3424	22	18	expansions	expansion	NOUN
ejpam-3424	22	19	of	of	ADP
ejpam-3424	22	20	the	the	DET
ejpam-3424	22	21	given	give	VERB
ejpam-3424	22	22	two	two	NUM
ejpam-3424	22	23	sequences	sequence	NOUN
ejpam-3424	22	24	of	of	ADP
ejpam-3424	22	25	polynomials	polynomial	NOUN
ejpam-3424	22	26	q1(x	q1(x	NOUN
ejpam-3424	22	27	,	,	PUNCT
ejpam-3424	22	28	n	n	CCONJ
ejpam-3424	22	29	)	)	PUNCT
ejpam-3424	22	30	and	and	CCONJ
ejpam-3424	22	31	q2(x	q2(x	PROPN
ejpam-3424	22	32	,	,	PUNCT
ejpam-3424	22	33	n	n	CCONJ
ejpam-3424	22	34	)	)	PUNCT
ejpam-3424	22	35	for	for	ADP
ejpam-3424	22	36	n	n	NOUN
ejpam-3424	22	37	=	=	SYM
ejpam-3424	22	38	0	0	NUM
ejpam-3424	22	39	,	,	PUNCT
ejpam-3424	22	40	1	1	NUM
ejpam-3424	22	41	,	,	PUNCT
ejpam-3424	22	42	2	2	NUM
ejpam-3424	22	43	,	,	PUNCT
ejpam-3424	22	44	.	.	PUNCT
ejpam-3424	22	45	.	.	PUNCT
ejpam-3424	23	1	.	.	PUNCT
ejpam-3424	23	2	,	,	PUNCT
ejpam-3424	24	1	qk(x	qk(x	X
ejpam-3424	24	2	,	,	PUNCT
ejpam-3424	24	3	n	n	CCONJ
ejpam-3424	24	4	)	)	PUNCT
ejpam-3424	24	5	=	=	SYM
ejpam-3424	24	6	n∑	n∑	PROPN
ejpam-3424	24	7	m=0	m=0	PROPN
ejpam-3424	24	8	cmk	cmk	PROPN
ejpam-3424	24	9	,	,	PUNCT
ejpam-3424	24	10	nx	nx	PROPN
ejpam-3424	24	11	m	m	PROPN
ejpam-3424	24	12	(	(	PUNCT
ejpam-3424	24	13	4	4	NUM
ejpam-3424	24	14	)	)	PUNCT
ejpam-3424	24	15	xn	xn	PUNCT
ejpam-3424	25	1	=	=	SYM
ejpam-3424	25	2	n∑	n∑	PROPN
ejpam-3424	25	3	m=0	m=0	PROPN
ejpam-3424	25	4	dm	dm	NUM
ejpam-3424	25	5	k	k	PROPN
ejpam-3424	25	6	,	,	PUNCT
ejpam-3424	25	7	nqk(x	nqk(x	PROPN
ejpam-3424	25	8	,	,	PUNCT
ejpam-3424	25	9	m	m	NOUN
ejpam-3424	25	10	)	)	PUNCT
ejpam-3424	25	11	(	(	PUNCT
ejpam-3424	25	12	5	5	NUM
ejpam-3424	25	13	)	)	PUNCT
ejpam-3424	25	14	for	for	ADP
ejpam-3424	25	15	k=1	k=1	PROPN
ejpam-3424	25	16	,	,	PUNCT
ejpam-3424	25	17	2	2	NUM
ejpam-3424	25	18	.	.	PUNCT
ejpam-3424	25	19	also	also	ADV
ejpam-3424	25	20	,	,	PUNCT
ejpam-3424	25	21	these	these	DET
ejpam-3424	25	22	numbers	number	NOUN
ejpam-3424	25	23	are	be	AUX
ejpam-3424	25	24	equal	equal	ADJ
ejpam-3424	25	25	to	to	ADP
ejpam-3424	25	26	zero	zero	NUM
ejpam-3424	25	27	if	if	SCONJ
ejpam-3424	25	28	n	n	CCONJ
ejpam-3424	25	29	<	<	X
ejpam-3424	25	30	m	m	PROPN
ejpam-3424	25	31	,	,	PUNCT
ejpam-3424	25	32	m	m	VERB
ejpam-3424	25	33	<	<	X
ejpam-3424	25	34	0	0	NUM
ejpam-3424	25	35	,	,	PUNCT
ejpam-3424	25	36	n	n	X
ejpam-3424	25	37	<	<	X
ejpam-3424	25	38	0	0	NUM
ejpam-3424	25	39	.	.	PUNCT
ejpam-3424	26	1	these	these	DET
ejpam-3424	26	2	generalized	generalize	VERB
ejpam-3424	26	3	stirling	stirling	NOUN
ejpam-3424	26	4	numbers	number	NOUN
ejpam-3424	26	5	of	of	ADP
ejpam-3424	26	6	the	the	DET
ejpam-3424	26	7	first	first	ADJ
ejpam-3424	26	8	and	and	CCONJ
ejpam-3424	26	9	second	second	ADJ
ejpam-3424	26	10	kind	kind	NOUN
ejpam-3424	26	11	on	on	ADP
ejpam-3424	26	12	qpolynomials	qpolynomial	NOUN
ejpam-3424	26	13	satisfy	satisfy	VERB
ejpam-3424	26	14	the	the	DET
ejpam-3424	26	15	following	follow	VERB
ejpam-3424	26	16	triangular	triangular	NOUN
ejpam-3424	26	17	recurrence	recurrence	NOUN
ejpam-3424	26	18	relations	relation	NOUN
ejpam-3424	26	19	in	in	ADP
ejpam-3424	26	20	[	[	X
ejpam-3424	26	21	8	8	NUM
ejpam-3424	26	22	]	]	PUNCT
ejpam-3424	26	23	,	,	PUNCT
ejpam-3424	26	24	cmn	cmn	VERB
ejpam-3424	26	25	=	=	PUNCT
ejpam-3424	26	26	m(n)cmn−1	m(n)cmn−1	X
ejpam-3424	27	1	+	+	NOUN
ejpam-3424	27	2	n(n)cm−1	n(n)cm−1	ADJ
ejpam-3424	27	3	n−1	n−1	PROPN
ejpam-3424	27	4	(	(	PUNCT
ejpam-3424	27	5	6	6	NUM
ejpam-3424	27	6	)	)	PUNCT
ejpam-3424	27	7	dm	dm	NOUN
ejpam-3424	27	8	n	n	NOUN
ejpam-3424	27	9	=	=	SYM
ejpam-3424	27	10	−m(m+	−m(m+	ADP
ejpam-3424	27	11	1	1	X
ejpam-3424	27	12	)	)	PUNCT
ejpam-3424	27	13	n(m+	n(m+	NOUN
ejpam-3424	27	14	1	1	NUM
ejpam-3424	27	15	)	)	PUNCT
ejpam-3424	27	16	dm	dm	NOUN
ejpam-3424	27	17	n−1	n−1	PROPN
ejpam-3424	28	1	+	+	CCONJ
ejpam-3424	28	2	1	1	NUM
ejpam-3424	28	3	n(m+	n(m+	NUM
ejpam-3424	28	4	1	1	NUM
ejpam-3424	28	5	)	)	PUNCT
ejpam-3424	28	6	dm−1	dm−1	NOUN
ejpam-3424	28	7	n−1	n−1	PROPN
ejpam-3424	28	8	,	,	PUNCT
ejpam-3424	28	9	(	(	PUNCT
ejpam-3424	28	10	7	7	X
ejpam-3424	28	11	)	)	PUNCT
ejpam-3424	29	1	where	where	SCONJ
ejpam-3424	29	2	m	m	VERB
ejpam-3424	29	3	and	and	CCONJ
ejpam-3424	29	4	n	n	PRON
ejpam-3424	29	5	are	be	AUX
ejpam-3424	29	6	two	two	NUM
ejpam-3424	29	7	functions	function	NOUN
ejpam-3424	29	8	of	of	ADP
ejpam-3424	29	9	the	the	DET
ejpam-3424	29	10	variable	variable	NOUN
ejpam-3424	29	11	n	n	CCONJ
ejpam-3424	29	12	,	,	PUNCT
ejpam-3424	29	13	such	such	ADJ
ejpam-3424	29	14	that	that	DET
ejpam-3424	29	15	m(0	m(0	NOUN
ejpam-3424	29	16	)	)	PUNCT
ejpam-3424	29	17	6=	6=	ADP
ejpam-3424	29	18	0	0	NUM
ejpam-3424	29	19	and	and	CCONJ
ejpam-3424	29	20	for	for	ADP
ejpam-3424	29	21	n	n	PRON
ejpam-3424	29	22	a	a	DET
ejpam-3424	29	23	positive	positive	ADJ
ejpam-3424	29	24	integer	integer	NOUN
ejpam-3424	29	25	or	or	CCONJ
ejpam-3424	29	26	zero	zero	NUM
ejpam-3424	29	27	n(0	n(0	PROPN
ejpam-3424	29	28	)	)	PUNCT
ejpam-3424	29	29	6=	6=	ADP
ejpam-3424	29	30	0	0	X
ejpam-3424	29	31	.	.	PUNCT
ejpam-3424	30	1	in	in	ADP
ejpam-3424	30	2	the	the	DET
ejpam-3424	30	3	paper	paper	NOUN
ejpam-3424	30	4	[	[	X
ejpam-3424	30	5	6	6	NUM
ejpam-3424	30	6	]	]	PUNCT
ejpam-3424	30	7	of	of	ADP
ejpam-3424	30	8	tauber	tauber	PROPN
ejpam-3424	30	9	,	,	PUNCT
ejpam-3424	30	10	a	a	DET
ejpam-3424	30	11	generalization	generalization	NOUN
ejpam-3424	30	12	of	of	ADP
ejpam-3424	30	13	lah	lah	PROPN
ejpam-3424	30	14	numbers	number	NOUN
ejpam-3424	30	15	lmk	lmk	PROPN
ejpam-3424	30	16	,	,	PUNCT
ejpam-3424	30	17	h	h	NOUN
ejpam-3424	30	18	,	,	PUNCT
ejpam-3424	30	19	n	n	PRON
ejpam-3424	30	20	was	be	AUX
ejpam-3424	30	21	introduced	introduce	VERB
ejpam-3424	30	22	as	as	ADP
ejpam-3424	30	23	the	the	DET
ejpam-3424	30	24	coefficient	coefficient	NOUN
ejpam-3424	30	25	of	of	ADP
ejpam-3424	30	26	the	the	DET
ejpam-3424	30	27	following	follow	VERB
ejpam-3424	30	28	relation	relation	NOUN
ejpam-3424	30	29	,	,	PUNCT
ejpam-3424	30	30	qk(x	qk(x	NOUN
ejpam-3424	30	31	,	,	PUNCT
ejpam-3424	30	32	n	n	CCONJ
ejpam-3424	30	33	)	)	PUNCT
ejpam-3424	30	34	=	=	SYM
ejpam-3424	30	35	n∑	n∑	PROPN
ejpam-3424	30	36	m=0	m=0	PROPN
ejpam-3424	30	37	lmk	lmk	PROPN
ejpam-3424	30	38	,	,	PUNCT
ejpam-3424	30	39	h	h	NOUN
ejpam-3424	30	40	,	,	PUNCT
ejpam-3424	30	41	nqh(x	nqh(x	PROPN
ejpam-3424	30	42	,	,	PUNCT
ejpam-3424	30	43	m	m	NOUN
ejpam-3424	30	44	)	)	PUNCT
ejpam-3424	30	45	(	(	PUNCT
ejpam-3424	30	46	8)	8)	PROPN
ejpam-3424	30	47	r.	r.	PROPN
ejpam-3424	30	48	corcino	corcino	PROPN
ejpam-3424	30	49	,	,	PUNCT
ejpam-3424	30	50	c.	c.	PROPN
ejpam-3424	30	51	corcino	corcino	PROPN
ejpam-3424	30	52	,	,	PUNCT
ejpam-3424	30	53	g.	g.	PROPN
ejpam-3424	30	54	rama	rama	PROPN
ejpam-3424	30	55	/	/	SYM
ejpam-3424	30	56	eur	eur	PROPN
ejpam-3424	30	57	.	.	PUNCT
ejpam-3424	31	1	j.	j.	PROPN
ejpam-3424	31	2	pure	pure	PROPN
ejpam-3424	31	3	appl	appl	PROPN
ejpam-3424	31	4	.	.	PROPN
ejpam-3424	31	5	math	math	PROPN
ejpam-3424	31	6	,	,	PUNCT
ejpam-3424	31	7	12	12	NUM
ejpam-3424	31	8	(	(	PUNCT
ejpam-3424	31	9	3	3	NUM
ejpam-3424	31	10	)	)	PUNCT
ejpam-3424	31	11	(	(	PUNCT
ejpam-3424	31	12	2019	2019	NUM
ejpam-3424	31	13	)	)	PUNCT
ejpam-3424	31	14	,	,	PUNCT
ejpam-3424	31	15	1069	1069	NUM
ejpam-3424	31	16	-	-	SYM
ejpam-3424	31	17	1081	1081	NUM
ejpam-3424	31	18	1071	1071	NUM
ejpam-3424	31	19	for	for	ADP
ejpam-3424	31	20	two	two	NUM
ejpam-3424	31	21	sequences	sequence	NOUN
ejpam-3424	31	22	of	of	ADP
ejpam-3424	31	23	polynomials	polynomial	NOUN
ejpam-3424	31	24	qk	qk	NOUN
ejpam-3424	31	25	and	and	CCONJ
ejpam-3424	31	26	qh	qh	VERB
ejpam-3424	31	27	where	where	SCONJ
ejpam-3424	31	28	k	k	PROPN
ejpam-3424	31	29	6=	6=	PROPN
ejpam-3424	31	30	h	h	PROPN
ejpam-3424	31	31	,	,	PUNCT
ejpam-3424	31	32	and	and	CCONJ
ejpam-3424	31	33	k	k	NOUN
ejpam-3424	31	34	,	,	PUNCT
ejpam-3424	31	35	h	h	NOUN
ejpam-3424	31	36	∈	∈	PROPN
ejpam-3424	31	37	{	{	PUNCT
ejpam-3424	31	38	1	1	NUM
ejpam-3424	31	39	,	,	PUNCT
ejpam-3424	31	40	2	2	NUM
ejpam-3424	31	41	}	}	PUNCT
ejpam-3424	31	42	.	.	PUNCT
ejpam-3424	32	1	these	these	DET
ejpam-3424	32	2	numbers	number	NOUN
ejpam-3424	32	3	satisfy	satisfy	VERB
ejpam-3424	32	4	the	the	DET
ejpam-3424	32	5	following	follow	VERB
ejpam-3424	32	6	triangular	triangular	NOUN
ejpam-3424	32	7	recurrence	recurrence	NOUN
ejpam-3424	32	8	relation	relation	PROPN
ejpam-3424	32	9	,	,	PUNCT
ejpam-3424	32	10	lmk	lmk	PROPN
ejpam-3424	32	11	,	,	PUNCT
ejpam-3424	32	12	h	h	NOUN
ejpam-3424	32	13	,	,	PUNCT
ejpam-3424	32	14	n	n	NOUN
ejpam-3424	32	15	=	=	PUNCT
ejpam-3424	32	16	[	[	PUNCT
ejpam-3424	32	17	mk(n)−	mk(n)−	NOUN
ejpam-3424	32	18	nk(n)mh(m+	nk(n)mh(m+	NOUN
ejpam-3424	32	19	1	1	NUM
ejpam-3424	32	20	)	)	PUNCT
ejpam-3424	32	21	nh(m+	nh(m+	NUM
ejpam-3424	32	22	1	1	NUM
ejpam-3424	32	23	)	)	PUNCT
ejpam-3424	32	24	]	]	PUNCT
ejpam-3424	33	1	lmk	lmk	PROPN
ejpam-3424	33	2	,	,	PUNCT
ejpam-3424	33	3	h	h	NOUN
ejpam-3424	33	4	,	,	PUNCT
ejpam-3424	33	5	n−1	n−1	PROPN
ejpam-3424	33	6	+	+	NUM
ejpam-3424	33	7	nk(n	nk(n	NOUN
ejpam-3424	33	8	)	)	PUNCT
ejpam-3424	33	9	nh(m	nh(m	NUM
ejpam-3424	33	10	)	)	PUNCT
ejpam-3424	33	11	lm−1	lm−1	PROPN
ejpam-3424	33	12	k	k	PROPN
ejpam-3424	33	13	,	,	PUNCT
ejpam-3424	33	14	h	h	NOUN
ejpam-3424	33	15	,	,	PUNCT
ejpam-3424	33	16	n−1	n−1	PROPN
ejpam-3424	33	17	,	,	PUNCT
ejpam-3424	33	18	(	(	PUNCT
ejpam-3424	33	19	9	9	NUM
ejpam-3424	33	20	)	)	PUNCT
ejpam-3424	33	21	where	where	SCONJ
ejpam-3424	33	22	mk(n	mk(n	X
ejpam-3424	33	23	)	)	PUNCT
ejpam-3424	33	24	and	and	CCONJ
ejpam-3424	33	25	nk(n	nk(n	PRON
ejpam-3424	33	26	)	)	PUNCT
ejpam-3424	33	27	are	be	AUX
ejpam-3424	33	28	the	the	DET
ejpam-3424	33	29	subscripted	subscripte	VERB
ejpam-3424	33	30	version	version	NOUN
ejpam-3424	33	31	of	of	ADP
ejpam-3424	33	32	the	the	DET
ejpam-3424	33	33	functions	function	NOUN
ejpam-3424	33	34	m(n	m(n	NOUN
ejpam-3424	33	35	)	)	PUNCT
ejpam-3424	33	36	and	and	CCONJ
ejpam-3424	33	37	n(n	n(n	NUM
ejpam-3424	33	38	)	)	PUNCT
ejpam-3424	33	39	that	that	PRON
ejpam-3424	33	40	correspond	correspond	VERB
ejpam-3424	33	41	to	to	ADP
ejpam-3424	33	42	qk(x	qk(x	NOUN
ejpam-3424	33	43	,	,	PUNCT
ejpam-3424	33	44	n	n	CCONJ
ejpam-3424	33	45	)	)	PUNCT
ejpam-3424	33	46	.	.	PUNCT
ejpam-3424	34	1	furthermore	furthermore	ADV
ejpam-3424	34	2	,	,	PUNCT
ejpam-3424	34	3	the	the	DET
ejpam-3424	34	4	generalized	generalize	VERB
ejpam-3424	34	5	lah	lah	PROPN
ejpam-3424	34	6	numbers	number	NOUN
ejpam-3424	34	7	lmk	lmk	PROPN
ejpam-3424	34	8	,	,	PUNCT
ejpam-3424	34	9	h	h	NOUN
ejpam-3424	34	10	,	,	PUNCT
ejpam-3424	34	11	n	n	PRON
ejpam-3424	34	12	have	have	AUX
ejpam-3424	34	13	been	be	AUX
ejpam-3424	34	14	expressed	express	VERB
ejpam-3424	34	15	in	in	ADP
ejpam-3424	34	16	terms	term	NOUN
ejpam-3424	34	17	of	of	ADP
ejpam-3424	34	18	generalized	generalized	ADJ
ejpam-3424	34	19	stirling	stirling	NOUN
ejpam-3424	34	20	numbers	number	NOUN
ejpam-3424	34	21	of	of	ADP
ejpam-3424	34	22	the	the	DET
ejpam-3424	34	23	first	first	ADJ
ejpam-3424	34	24	kind	kind	NOUN
ejpam-3424	34	25	and	and	CCONJ
ejpam-3424	34	26	the	the	DET
ejpam-3424	34	27	second	second	ADJ
ejpam-3424	34	28	kind	kind	NOUN
ejpam-3424	34	29	as	as	SCONJ
ejpam-3424	34	30	follows	follow	VERB
ejpam-3424	34	31	lmk	lmk	PROPN
ejpam-3424	34	32	,	,	PUNCT
ejpam-3424	34	33	h	h	NOUN
ejpam-3424	34	34	,	,	PUNCT
ejpam-3424	34	35	n	n	PROPN
ejpam-3424	34	36	=	=	SYM
ejpam-3424	34	37	n∑	n∑	PROPN
ejpam-3424	34	38	s	s	PROPN
ejpam-3424	34	39	=	=	NOUN
ejpam-3424	34	40	m	m	NOUN
ejpam-3424	34	41	csk	csk	PROPN
ejpam-3424	34	42	,	,	PUNCT
ejpam-3424	34	43	nd	nd	NOUN
ejpam-3424	34	44	m	m	NOUN
ejpam-3424	34	45	h	h	NOUN
ejpam-3424	34	46	,	,	PUNCT
ejpam-3424	34	47	s.	s.	PROPN
ejpam-3424	34	48	(	(	PUNCT
ejpam-3424	34	49	10	10	NUM
ejpam-3424	34	50	)	)	PUNCT
ejpam-3424	34	51	the	the	DET
ejpam-3424	34	52	generalized	generalized	ADJ
ejpam-3424	34	53	bell	bell	NOUN
ejpam-3424	34	54	numbers	number	NOUN
ejpam-3424	34	55	,	,	PUNCT
ejpam-3424	34	56	denoted	denote	VERB
ejpam-3424	34	57	by	by	ADP
ejpam-3424	34	58	bh	bh	PROPN
ejpam-3424	34	59	,	,	PUNCT
ejpam-3424	34	60	n	n	CCONJ
ejpam-3424	34	61	,	,	PUNCT
ejpam-3424	34	62	may	may	AUX
ejpam-3424	34	63	be	be	AUX
ejpam-3424	34	64	defined	define	VERB
ejpam-3424	34	65	as	as	ADP
ejpam-3424	34	66	the	the	DET
ejpam-3424	34	67	sum	sum	NOUN
ejpam-3424	34	68	of	of	ADP
ejpam-3424	34	69	the	the	DET
ejpam-3424	34	70	generalized	generalized	ADJ
ejpam-3424	34	71	stirling	stirling	NOUN
ejpam-3424	34	72	numbers	number	NOUN
ejpam-3424	34	73	of	of	ADP
ejpam-3424	34	74	the	the	DET
ejpam-3424	34	75	second	second	ADJ
ejpam-3424	34	76	kind	kind	NOUN
ejpam-3424	34	77	dm	dm	NOUN
ejpam-3424	34	78	h	h	NOUN
ejpam-3424	34	79	,	,	PUNCT
ejpam-3424	34	80	n	n	CCONJ
ejpam-3424	34	81	,	,	PUNCT
ejpam-3424	34	82	bh	bh	NOUN
ejpam-3424	34	83	,	,	PUNCT
ejpam-3424	34	84	n	n	PROPN
ejpam-3424	34	85	=	=	SYM
ejpam-3424	34	86	n∑	n∑	PROPN
ejpam-3424	34	87	m=0	m=0	PROPN
ejpam-3424	34	88	dm	dm	NUM
ejpam-3424	34	89	h	h	NOUN
ejpam-3424	34	90	,	,	PUNCT
ejpam-3424	34	91	n.	n.	PROPN
ejpam-3424	34	92	(	(	PUNCT
ejpam-3424	34	93	11	11	NUM
ejpam-3424	34	94	)	)	PUNCT
ejpam-3424	34	95	the	the	DET
ejpam-3424	34	96	lah	lah	PROPN
ejpam-3424	34	97	numbers	number	NOUN
ejpam-3424	34	98	can	can	AUX
ejpam-3424	34	99	be	be	AUX
ejpam-3424	34	100	defined	define	VERB
ejpam-3424	34	101	as	as	ADP
ejpam-3424	34	102	the	the	DET
ejpam-3424	34	103	coefficients	coefficient	NOUN
ejpam-3424	34	104	of	of	ADP
ejpam-3424	34	105	the	the	DET
ejpam-3424	34	106	following	follow	VERB
ejpam-3424	34	107	relations	relation	NOUN
ejpam-3424	34	108	:	:	PUNCT
ejpam-3424	34	109	(	(	PUNCT
ejpam-3424	34	110	−x)n	−x)n	NOUN
ejpam-3424	34	111	=	=	SYM
ejpam-3424	34	112	n∑	n∑	PROPN
ejpam-3424	34	113	k=0	k=0	PROPN
ejpam-3424	34	114	ln	ln	PROPN
ejpam-3424	34	115	,	,	PUNCT
ejpam-3424	34	116	k(x)k	k(x)k	PROPN
ejpam-3424	34	117	(	(	PUNCT
ejpam-3424	34	118	12	12	NUM
ejpam-3424	34	119	)	)	PUNCT
ejpam-3424	34	120	(	(	PUNCT
ejpam-3424	34	121	x)n	x)n	PUNCT
ejpam-3424	35	1	=	=	PUNCT
ejpam-3424	35	2	n∑	n∑	PROPN
ejpam-3424	35	3	k=0	k=0	PROPN
ejpam-3424	35	4	ln	ln	PROPN
ejpam-3424	35	5	,	,	PUNCT
ejpam-3424	35	6	k(−x)k	k(−x)k	NOUN
ejpam-3424	35	7	(	(	PUNCT
ejpam-3424	35	8	13	13	NUM
ejpam-3424	35	9	)	)	PUNCT
ejpam-3424	35	10	where	where	SCONJ
ejpam-3424	35	11	(	(	PUNCT
ejpam-3424	35	12	x)n	x)n	X
ejpam-3424	35	13	is	be	AUX
ejpam-3424	35	14	the	the	DET
ejpam-3424	35	15	falling	fall	VERB
ejpam-3424	35	16	factorial	factorial	NOUN
ejpam-3424	35	17	,	,	PUNCT
ejpam-3424	35	18	defined	define	VERB
ejpam-3424	35	19	by	by	ADP
ejpam-3424	35	20	(	(	PUNCT
ejpam-3424	35	21	x)n	x)n	PUNCT
ejpam-3424	35	22	=	=	PRON
ejpam-3424	35	23	{	{	PUNCT
ejpam-3424	35	24	x(x−	x(x−	PROPN
ejpam-3424	35	25	1	1	NUM
ejpam-3424	35	26	)	)	PUNCT
ejpam-3424	35	27	.	.	PUNCT
ejpam-3424	35	28	.	.	PUNCT
ejpam-3424	35	29	.	.	PUNCT
ejpam-3424	36	1	(	(	PUNCT
ejpam-3424	36	2	x−	x−	PROPN
ejpam-3424	36	3	n+	n+	PROPN
ejpam-3424	36	4	1	1	NUM
ejpam-3424	36	5	)	)	PUNCT
ejpam-3424	36	6	,	,	PUNCT
ejpam-3424	36	7	n	n	PRON
ejpam-3424	36	8	≥	≥	NUM
ejpam-3424	36	9	1	1	NUM
ejpam-3424	36	10	1	1	NUM
ejpam-3424	36	11	,	,	PUNCT
ejpam-3424	36	12	n	n	NOUN
ejpam-3424	36	13	=	=	SYM
ejpam-3424	36	14	0	0	NUM
ejpam-3424	36	15	.	.	PUNCT
ejpam-3424	37	1	also	also	ADV
ejpam-3424	37	2	,	,	PUNCT
ejpam-3424	37	3	(	(	PUNCT
ejpam-3424	37	4	−x)n	−x)n	NOUN
ejpam-3424	37	5	=	=	SYM
ejpam-3424	37	6	(	(	PUNCT
ejpam-3424	37	7	−1)n(x)(x+	−1)n(x)(x+	ADP
ejpam-3424	37	8	1	1	NUM
ejpam-3424	37	9	)	)	PUNCT
ejpam-3424	37	10	.	.	PUNCT
ejpam-3424	37	11	.	.	PUNCT
ejpam-3424	37	12	.	.	PUNCT
ejpam-3424	38	1	(	(	PUNCT
ejpam-3424	38	2	x+	x+	X
ejpam-3424	38	3	n−	n−	NOUN
ejpam-3424	38	4	1	1	NUM
ejpam-3424	38	5	)	)	PUNCT
ejpam-3424	38	6	=	=	PRON
ejpam-3424	38	7	(	(	PUNCT
ejpam-3424	38	8	−1)nx(n	−1)nx(n	NOUN
ejpam-3424	38	9	)	)	PUNCT
ejpam-3424	38	10	where	where	SCONJ
ejpam-3424	38	11	x(n	x(n	NOUN
ejpam-3424	38	12	)	)	PUNCT
ejpam-3424	38	13	is	be	AUX
ejpam-3424	38	14	the	the	DET
ejpam-3424	38	15	rising	rise	VERB
ejpam-3424	38	16	factorial	factorial	NOUN
ejpam-3424	38	17	,	,	PUNCT
ejpam-3424	38	18	defined	define	VERB
ejpam-3424	38	19	by	by	ADP
ejpam-3424	38	20	(	(	PUNCT
ejpam-3424	38	21	x)(n	x)(n	PROPN
ejpam-3424	38	22	)	)	PUNCT
ejpam-3424	38	23	=	=	PRON
ejpam-3424	38	24	{	{	PUNCT
ejpam-3424	38	25	x(x+	x(x+	PROPN
ejpam-3424	38	26	1	1	NUM
ejpam-3424	38	27	)	)	PUNCT
ejpam-3424	38	28	.	.	PUNCT
ejpam-3424	38	29	.	.	PUNCT
ejpam-3424	38	30	.	.	PUNCT
ejpam-3424	39	1	(	(	PUNCT
ejpam-3424	39	2	x+	x+	X
ejpam-3424	39	3	n−	n−	NOUN
ejpam-3424	39	4	1	1	NUM
ejpam-3424	39	5	)	)	PUNCT
ejpam-3424	39	6	,	,	PUNCT
ejpam-3424	39	7	n	n	PRON
ejpam-3424	39	8	≥	≥	NUM
ejpam-3424	39	9	1	1	NUM
ejpam-3424	39	10	1	1	NUM
ejpam-3424	39	11	,	,	PUNCT
ejpam-3424	39	12	n	n	NOUN
ejpam-3424	39	13	=	=	SYM
ejpam-3424	39	14	0	0	NUM
ejpam-3424	39	15	.	.	PUNCT
ejpam-3424	40	1	given	give	VERB
ejpam-3424	40	2	polynomial	polynomial	ADJ
ejpam-3424	40	3	qk(x	qk(x	NOUN
ejpam-3424	40	4	,	,	PUNCT
ejpam-3424	40	5	n	n	CCONJ
ejpam-3424	40	6	)	)	PUNCT
ejpam-3424	40	7	=	=	SYM
ejpam-3424	40	8	(	(	PUNCT
ejpam-3424	40	9	(	(	PUNCT
ejpam-3424	40	10	−1)k−1x)n	−1)k−1x)n	PROPN
ejpam-3424	40	11	,	,	PUNCT
ejpam-3424	40	12	tauber	tauber	PROPN
ejpam-3424	40	13	’s	’s	PART
ejpam-3424	40	14	generalized	generalize	VERB
ejpam-3424	40	15	lah	lah	PROPN
ejpam-3424	40	16	numbers	number	NOUN
ejpam-3424	40	17	lmk	lmk	PROPN
ejpam-3424	40	18	,	,	PUNCT
ejpam-3424	40	19	h	h	NOUN
ejpam-3424	40	20	,	,	PUNCT
ejpam-3424	40	21	n	n	CCONJ
ejpam-3424	40	22	in	in	ADP
ejpam-3424	40	23	(	(	PUNCT
ejpam-3424	40	24	8)	8)	NUM
ejpam-3424	40	25	reduce	reduce	VERB
ejpam-3424	40	26	to	to	ADP
ejpam-3424	40	27	the	the	DET
ejpam-3424	40	28	ordinary	ordinary	ADJ
ejpam-3424	40	29	lah	lah	NOUN
ejpam-3424	40	30	numbers	number	NOUN
ejpam-3424	40	31	ln	ln	ADJ
ejpam-3424	40	32	,	,	PUNCT
ejpam-3424	40	33	m	m	VERB
ejpam-3424	40	34	in	in	ADP
ejpam-3424	40	35	(	(	PUNCT
ejpam-3424	40	36	12	12	NUM
ejpam-3424	40	37	)	)	PUNCT
ejpam-3424	40	38	and	and	CCONJ
ejpam-3424	40	39	(	(	PUNCT
ejpam-3424	40	40	13	13	NUM
ejpam-3424	40	41	)	)	PUNCT
ejpam-3424	40	42	for	for	ADP
ejpam-3424	40	43	h	h	NOUN
ejpam-3424	40	44	=	=	SYM
ejpam-3424	40	45	1	1	NUM
ejpam-3424	40	46	and	and	CCONJ
ejpam-3424	40	47	k	k	NOUN
ejpam-3424	40	48	=	=	NOUN
ejpam-3424	40	49	2	2	X
ejpam-3424	40	50	.	.	X
ejpam-3424	40	51	that	that	PRON
ejpam-3424	40	52	is	be	AUX
ejpam-3424	40	53	,	,	PUNCT
ejpam-3424	40	54	lm2,1,n	lm2,1,n	X
ejpam-3424	40	55	=	=	SYM
ejpam-3424	40	56	ln	ln	ADJ
ejpam-3424	40	57	,	,	PUNCT
ejpam-3424	40	58	m	m	VERB
ejpam-3424	40	59	=	=	ADJ
ejpam-3424	40	60	lm1,2,n	lm1,2,n	PROPN
ejpam-3424	40	61	r.	r.	PROPN
ejpam-3424	40	62	corcino	corcino	PROPN
ejpam-3424	40	63	,	,	PUNCT
ejpam-3424	40	64	c.	c.	PROPN
ejpam-3424	40	65	corcino	corcino	PROPN
ejpam-3424	40	66	,	,	PUNCT
ejpam-3424	40	67	g.	g.	PROPN
ejpam-3424	40	68	rama	rama	PROPN
ejpam-3424	40	69	/	/	SYM
ejpam-3424	40	70	eur	eur	PROPN
ejpam-3424	40	71	.	.	PUNCT
ejpam-3424	41	1	j.	j.	PROPN
ejpam-3424	41	2	pure	pure	PROPN
ejpam-3424	41	3	appl	appl	PROPN
ejpam-3424	41	4	.	.	PROPN
ejpam-3424	41	5	math	math	PROPN
ejpam-3424	41	6	,	,	PUNCT
ejpam-3424	41	7	12	12	NUM
ejpam-3424	41	8	(	(	PUNCT
ejpam-3424	41	9	3	3	NUM
ejpam-3424	41	10	)	)	PUNCT
ejpam-3424	41	11	(	(	PUNCT
ejpam-3424	41	12	2019	2019	NUM
ejpam-3424	41	13	)	)	PUNCT
ejpam-3424	41	14	,	,	PUNCT
ejpam-3424	41	15	1069	1069	NUM
ejpam-3424	41	16	-	-	SYM
ejpam-3424	41	17	1081	1081	NUM
ejpam-3424	41	18	1072	1072	NUM
ejpam-3424	41	19	moreover	moreover	ADV
ejpam-3424	41	20	,	,	PUNCT
ejpam-3424	41	21	(	(	PUNCT
ejpam-3424	41	22	4	4	NUM
ejpam-3424	41	23	)	)	PUNCT
ejpam-3424	41	24	and	and	CCONJ
ejpam-3424	41	25	(	(	PUNCT
ejpam-3424	41	26	5	5	X
ejpam-3424	41	27	)	)	PUNCT
ejpam-3424	41	28	give	give	NOUN
ejpam-3424	41	29	{	{	PUNCT
ejpam-3424	41	30	cm1,n	cm1,n	PROPN
ejpam-3424	41	31	,	,	PUNCT
ejpam-3424	41	32	d	d	PROPN
ejpam-3424	41	33	m	m	VERB
ejpam-3424	41	34	1,n	1,n	NUM
ejpam-3424	41	35	}	}	PUNCT
ejpam-3424	41	36	=	=	SYM
ejpam-3424	41	37	{	{	PUNCT
ejpam-3424	41	38	(	(	PUNCT
ejpam-3424	41	39	−1)n−m	−1)n−m	X
ejpam-3424	41	40	[	[	PUNCT
ejpam-3424	41	41	n	n	X
ejpam-3424	41	42	m	m	VERB
ejpam-3424	41	43	]	]	PUNCT
ejpam-3424	41	44	,	,	PUNCT
ejpam-3424	41	45	{	{	PUNCT
ejpam-3424	41	46	n	n	ADV
ejpam-3424	41	47	m	m	VERB
ejpam-3424	41	48	}	}	PUNCT
ejpam-3424	41	49	}	}	PUNCT
ejpam-3424	41	50	{	{	PUNCT
ejpam-3424	41	51	cm2,n	cm2,n	ADJ
ejpam-3424	41	52	,	,	PUNCT
ejpam-3424	41	53	d	d	PROPN
ejpam-3424	41	54	m	m	VERB
ejpam-3424	41	55	2,n	2,n	NUM
ejpam-3424	41	56	}	}	PUNCT
ejpam-3424	41	57	=	=	SYM
ejpam-3424	41	58	{	{	PUNCT
ejpam-3424	41	59	(	(	PUNCT
ejpam-3424	41	60	−1)n	−1)n	X
ejpam-3424	41	61	[	[	PUNCT
ejpam-3424	41	62	n	n	X
ejpam-3424	41	63	m	m	VERB
ejpam-3424	41	64	]	]	PUNCT
ejpam-3424	41	65	,	,	PUNCT
ejpam-3424	41	66	(	(	PUNCT
ejpam-3424	41	67	−1)n	−1)n	X
ejpam-3424	41	68	{	{	PUNCT
ejpam-3424	41	69	n	n	NOUN
ejpam-3424	41	70	m	m	VERB
ejpam-3424	41	71	}	}	PUNCT
ejpam-3424	41	72	}	}	PUNCT
ejpam-3424	41	73	,	,	PUNCT
ejpam-3424	41	74	where	where	SCONJ
ejpam-3424	41	75	[	[	PUNCT
ejpam-3424	41	76	n	n	X
ejpam-3424	41	77	k	k	X
ejpam-3424	41	78	]	]	X
ejpam-3424	41	79	is	be	AUX
ejpam-3424	41	80	the	the	DET
ejpam-3424	41	81	karamata	karamata	ADJ
ejpam-3424	41	82	-	-	PUNCT
ejpam-3424	41	83	knuth	knuth	NOUN
ejpam-3424	41	84	notation	notation	NOUN
ejpam-3424	41	85	for	for	ADP
ejpam-3424	41	86	the	the	DET
ejpam-3424	41	87	unsigned	unsigned	ADJ
ejpam-3424	41	88	stirling	stirling	NOUN
ejpam-3424	41	89	numbers	number	NOUN
ejpam-3424	41	90	of	of	ADP
ejpam-3424	41	91	the	the	DET
ejpam-3424	41	92	first	first	ADJ
ejpam-3424	41	93	kind	kind	NOUN
ejpam-3424	41	94	.	.	PUNCT
ejpam-3424	42	1	the	the	DET
ejpam-3424	42	2	whitney	whitney	PROPN
ejpam-3424	42	3	numbers	number	NOUN
ejpam-3424	42	4	of	of	ADP
ejpam-3424	42	5	the	the	DET
ejpam-3424	42	6	first	first	ADJ
ejpam-3424	42	7	kind	kind	NOUN
ejpam-3424	42	8	wα(n	wα(n	NOUN
ejpam-3424	42	9	,	,	PUNCT
ejpam-3424	42	10	m	m	NOUN
ejpam-3424	42	11	)	)	PUNCT
ejpam-3424	42	12	and	and	CCONJ
ejpam-3424	42	13	second	second	ADJ
ejpam-3424	42	14	kind	kind	NOUN
ejpam-3424	42	15	wα(n	wα(n	NOUN
ejpam-3424	42	16	,	,	PUNCT
ejpam-3424	42	17	m	m	NOUN
ejpam-3424	42	18	)	)	PUNCT
ejpam-3424	42	19	of	of	ADP
ejpam-3424	42	20	dowling	dowle	VERB
ejpam-3424	42	21	lattices	lattice	NOUN
ejpam-3424	42	22	are	be	AUX
ejpam-3424	42	23	defined	define	VERB
ejpam-3424	42	24	in	in	ADP
ejpam-3424	42	25	the	the	DET
ejpam-3424	42	26	paper	paper	NOUN
ejpam-3424	42	27	of	of	ADP
ejpam-3424	42	28	benoumhani	benoumhani	NOUN
ejpam-3424	43	1	[	[	X
ejpam-3424	43	2	1	1	NUM
ejpam-3424	43	3	]	]	PUNCT
ejpam-3424	43	4	as	as	ADP
ejpam-3424	43	5	the	the	DET
ejpam-3424	43	6	coefficient	coefficient	NOUN
ejpam-3424	43	7	of	of	ADP
ejpam-3424	43	8	the	the	DET
ejpam-3424	43	9	following	follow	VERB
ejpam-3424	43	10	equations	equation	NOUN
ejpam-3424	43	11	,	,	PUNCT
ejpam-3424	43	12	αn	αn	INTJ
ejpam-3424	43	13	(	(	PUNCT
ejpam-3424	43	14	x−	x−	PROPN
ejpam-3424	43	15	1	1	NUM
ejpam-3424	43	16	α	α	NOUN
ejpam-3424	43	17	)	)	PUNCT
ejpam-3424	43	18	n	n	PROPN
ejpam-3424	43	19	=	=	SYM
ejpam-3424	43	20	n∑	n∑	PROPN
ejpam-3424	43	21	m=0	m=0	PROPN
ejpam-3424	43	22	wα(n	wα(n	NOUN
ejpam-3424	43	23	,	,	PUNCT
ejpam-3424	43	24	m)xm	m)xm	PROPN
ejpam-3424	43	25	(	(	PUNCT
ejpam-3424	43	26	14	14	NUM
ejpam-3424	43	27	)	)	PUNCT
ejpam-3424	43	28	xn	xn	PUNCT
ejpam-3424	44	1	=	=	SYM
ejpam-3424	44	2	n∑	n∑	PROPN
ejpam-3424	44	3	m=0	m=0	PROPN
ejpam-3424	44	4	αmwα(n	αmwα(n	PROPN
ejpam-3424	44	5	,	,	PUNCT
ejpam-3424	44	6	m	m	NOUN
ejpam-3424	44	7	)	)	PUNCT
ejpam-3424	44	8	(	(	PUNCT
ejpam-3424	44	9	x−	x−	PROPN
ejpam-3424	44	10	1	1	NUM
ejpam-3424	44	11	α	α	NOUN
ejpam-3424	44	12	)	)	PUNCT
ejpam-3424	44	13	m	m	VERB
ejpam-3424	44	14	(	(	PUNCT
ejpam-3424	44	15	15	15	NUM
ejpam-3424	44	16	)	)	PUNCT
ejpam-3424	44	17	which	which	PRON
ejpam-3424	44	18	can	can	AUX
ejpam-3424	44	19	be	be	AUX
ejpam-3424	44	20	written	write	VERB
ejpam-3424	44	21	as	as	ADP
ejpam-3424	44	22	(	(	PUNCT
ejpam-3424	44	23	x−	x−	PROPN
ejpam-3424	44	24	1|α)n	1|α)n	NUM
ejpam-3424	44	25	=	=	SYM
ejpam-3424	44	26	n∑	n∑	PROPN
ejpam-3424	44	27	m=0	m=0	PROPN
ejpam-3424	44	28	wα(n	wα(n	NOUN
ejpam-3424	44	29	,	,	PUNCT
ejpam-3424	44	30	m)xm	m)xm	PROPN
ejpam-3424	44	31	(	(	PUNCT
ejpam-3424	44	32	16	16	NUM
ejpam-3424	44	33	)	)	PUNCT
ejpam-3424	44	34	xn	xn	PUNCT
ejpam-3424	45	1	=	=	SYM
ejpam-3424	45	2	n∑	n∑	PROPN
ejpam-3424	45	3	m=0	m=0	PROPN
ejpam-3424	45	4	wα(n	wα(n	PROPN
ejpam-3424	45	5	,	,	PUNCT
ejpam-3424	45	6	m)(x−	m)(x−	PROPN
ejpam-3424	45	7	1|α)m	1|α)m	NUM
ejpam-3424	45	8	(	(	PUNCT
ejpam-3424	45	9	17	17	NUM
ejpam-3424	45	10	)	)	PUNCT
ejpam-3424	45	11	where	where	SCONJ
ejpam-3424	45	12	α	α	NOUN
ejpam-3424	45	13	is	be	AUX
ejpam-3424	45	14	a	a	DET
ejpam-3424	45	15	positive	positive	ADJ
ejpam-3424	45	16	integer	integer	NOUN
ejpam-3424	45	17	and	and	CCONJ
ejpam-3424	45	18	(	(	PUNCT
ejpam-3424	45	19	x|α)m	x|α)m	PUNCT
ejpam-3424	45	20	=	=	SYM
ejpam-3424	45	21	∏m−1	∏m−1	PROPN
ejpam-3424	45	22	i=0	i=0	PROPN
ejpam-3424	45	23	(	(	PUNCT
ejpam-3424	45	24	x−	x−	PROPN
ejpam-3424	45	25	iα	iα	PROPN
ejpam-3424	45	26	)	)	PUNCT
ejpam-3424	45	27	.	.	PUNCT
ejpam-3424	46	1	it	it	PRON
ejpam-3424	46	2	can	can	AUX
ejpam-3424	46	3	easily	easily	ADV
ejpam-3424	46	4	be	be	AUX
ejpam-3424	46	5	shown	show	VERB
ejpam-3424	46	6	that	that	SCONJ
ejpam-3424	46	7	n∑	n∑	PROPN
ejpam-3424	46	8	k	k	PROPN
ejpam-3424	47	1	=	=	PROPN
ejpam-3424	47	2	j	j	X
ejpam-3424	47	3	wα(n	wα(n	NOUN
ejpam-3424	47	4	,	,	PUNCT
ejpam-3424	47	5	k)wα(k	k)wα(k	PROPN
ejpam-3424	47	6	,	,	PUNCT
ejpam-3424	47	7	j	j	NOUN
ejpam-3424	47	8	)	)	PUNCT
ejpam-3424	47	9	=	=	SYM
ejpam-3424	48	1	n∑	n∑	PROPN
ejpam-3424	48	2	k	k	PROPN
ejpam-3424	49	1	=	=	PROPN
ejpam-3424	49	2	j	j	X
ejpam-3424	49	3	wα(n	wα(n	NOUN
ejpam-3424	49	4	,	,	PUNCT
ejpam-3424	49	5	k)wα(k	k)wα(k	PROPN
ejpam-3424	49	6	,	,	PUNCT
ejpam-3424	49	7	j	j	NOUN
ejpam-3424	49	8	)	)	PUNCT
ejpam-3424	49	9	=	=	SYM
ejpam-3424	49	10	δn	δn	PROPN
ejpam-3424	49	11	,	,	PUNCT
ejpam-3424	49	12	j	j	PROPN
ejpam-3424	49	13	(	(	PUNCT
ejpam-3424	49	14	18	18	NUM
ejpam-3424	49	15	)	)	PUNCT
ejpam-3424	49	16	fn	fn	NOUN
ejpam-3424	49	17	=	=	SYM
ejpam-3424	49	18	n∑	n∑	PROPN
ejpam-3424	49	19	k=0	k=0	PROPN
ejpam-3424	49	20	wα(n	wα(n	NOUN
ejpam-3424	49	21	,	,	PUNCT
ejpam-3424	49	22	k)gk	k)gk	PROPN
ejpam-3424	49	23	⇐	⇐	ADJ
ejpam-3424	49	24	⇒	⇒	NOUN
ejpam-3424	49	25	gn	gn	PROPN
ejpam-3424	50	1	=	=	PUNCT
ejpam-3424	50	2	n∑	n∑	PROPN
ejpam-3424	50	3	k=0	k=0	PROPN
ejpam-3424	50	4	wα(n	wα(n	NOUN
ejpam-3424	50	5	,	,	PUNCT
ejpam-3424	50	6	k)fk	k)fk	PROPN
ejpam-3424	50	7	.	.	PUNCT
ejpam-3424	51	1	(	(	PUNCT
ejpam-3424	51	2	19	19	NUM
ejpam-3424	51	3	)	)	PUNCT
ejpam-3424	51	4	when	when	SCONJ
ejpam-3424	51	5	qk(x	qk(x	NOUN
ejpam-3424	51	6	,	,	PUNCT
ejpam-3424	51	7	n	n	CCONJ
ejpam-3424	51	8	)	)	PUNCT
ejpam-3424	51	9	=	=	SYM
ejpam-3424	51	10	(	(	PUNCT
ejpam-3424	51	11	(	(	PUNCT
ejpam-3424	51	12	−1)k−1x−	−1)k−1x−	X
ejpam-3424	51	13	1|α)n	1|α)n	NUM
ejpam-3424	51	14	,	,	PUNCT
ejpam-3424	51	15	equations	equation	NOUN
ejpam-3424	51	16	(	(	PUNCT
ejpam-3424	51	17	4	4	NUM
ejpam-3424	51	18	)	)	PUNCT
ejpam-3424	51	19	and	and	CCONJ
ejpam-3424	51	20	(	(	PUNCT
ejpam-3424	51	21	5	5	X
ejpam-3424	51	22	)	)	PUNCT
ejpam-3424	51	23	yield	yield	NOUN
ejpam-3424	51	24	equations	equation	NOUN
ejpam-3424	51	25	(	(	PUNCT
ejpam-3424	51	26	16	16	NUM
ejpam-3424	51	27	)	)	PUNCT
ejpam-3424	51	28	and	and	CCONJ
ejpam-3424	51	29	(	(	PUNCT
ejpam-3424	51	30	17	17	NUM
ejpam-3424	51	31	)	)	PUNCT
ejpam-3424	51	32	,	,	PUNCT
ejpam-3424	51	33	respectively	respectively	ADV
ejpam-3424	51	34	.	.	PUNCT
ejpam-3424	52	1	this	this	PRON
ejpam-3424	52	2	implies	imply	VERB
ejpam-3424	52	3	that	that	SCONJ
ejpam-3424	52	4	{	{	PUNCT
ejpam-3424	52	5	cm1,n	cm1,n	PROPN
ejpam-3424	52	6	,	,	PUNCT
ejpam-3424	52	7	d	d	PROPN
ejpam-3424	52	8	m	m	VERB
ejpam-3424	52	9	1,n	1,n	NUM
ejpam-3424	52	10	}	}	PUNCT
ejpam-3424	52	11	=	=	SYM
ejpam-3424	52	12	{	{	PUNCT
ejpam-3424	52	13	wα(n	wα(n	NOUN
ejpam-3424	52	14	,	,	PUNCT
ejpam-3424	52	15	m),wα(n	m),wα(n	NOUN
ejpam-3424	52	16	,	,	PUNCT
ejpam-3424	52	17	m	m	NOUN
ejpam-3424	52	18	)	)	PUNCT
ejpam-3424	52	19	}	}	PUNCT
ejpam-3424	52	20	and	and	CCONJ
ejpam-3424	52	21	{	{	PUNCT
ejpam-3424	52	22	cm2,n	cm2,n	ADJ
ejpam-3424	52	23	,	,	PUNCT
ejpam-3424	52	24	d	d	PROPN
ejpam-3424	52	25	m	m	VERB
ejpam-3424	52	26	2,n	2,n	NUM
ejpam-3424	52	27	}	}	PUNCT
ejpam-3424	52	28	=	=	SYM
ejpam-3424	52	29	{	{	PUNCT
ejpam-3424	52	30	(	(	PUNCT
ejpam-3424	52	31	−1)mwα(n	−1)mwα(n	NOUN
ejpam-3424	52	32	,	,	PUNCT
ejpam-3424	52	33	m	m	NOUN
ejpam-3424	52	34	)	)	PUNCT
ejpam-3424	52	35	,	,	PUNCT
ejpam-3424	52	36	(	(	PUNCT
ejpam-3424	52	37	−1)nwα(n	−1)nwα(n	NOUN
ejpam-3424	52	38	,	,	PUNCT
ejpam-3424	52	39	m	m	NOUN
ejpam-3424	52	40	)	)	PUNCT
ejpam-3424	52	41	}	}	PUNCT
ejpam-3424	52	42	.	.	PUNCT
ejpam-3424	53	1	from	from	ADP
ejpam-3424	53	2	the	the	DET
ejpam-3424	53	3	definition	definition	NOUN
ejpam-3424	53	4	of	of	ADP
ejpam-3424	53	5	whitney	whitney	PROPN
ejpam-3424	53	6	numbers	number	NOUN
ejpam-3424	53	7	,	,	PUNCT
ejpam-3424	53	8	we	we	PRON
ejpam-3424	53	9	may	may	AUX
ejpam-3424	53	10	also	also	ADV
ejpam-3424	53	11	define	define	VERB
ejpam-3424	53	12	whitney	whitney	NOUN
ejpam-3424	53	13	-	-	PUNCT
ejpam-3424	53	14	lah	lah	PROPN
ejpam-3424	53	15	numbers	number	NOUN
ejpam-3424	53	16	denoted	denote	VERB
ejpam-3424	53	17	by	by	ADP
ejpam-3424	53	18	lwn	lwn	NOUN
ejpam-3424	53	19	,	,	PUNCT
ejpam-3424	53	20	m(α	m(α	PROPN
ejpam-3424	53	21	)	)	PUNCT
ejpam-3424	53	22	as	as	ADP
ejpam-3424	53	23	the	the	DET
ejpam-3424	53	24	coefficients	coefficient	NOUN
ejpam-3424	53	25	of	of	ADP
ejpam-3424	53	26	the	the	DET
ejpam-3424	53	27	following	follow	VERB
ejpam-3424	53	28	relations	relation	NOUN
ejpam-3424	53	29	,	,	PUNCT
ejpam-3424	53	30	(	(	PUNCT
ejpam-3424	53	31	−x−	−x−	NOUN
ejpam-3424	53	32	1|α)n	1|α)n	NUM
ejpam-3424	53	33	=	=	SYM
ejpam-3424	53	34	n∑	n∑	PROPN
ejpam-3424	53	35	m=0	m=0	PROPN
ejpam-3424	53	36	lwn	lwn	PROPN
ejpam-3424	53	37	,	,	PUNCT
ejpam-3424	53	38	m(α)(x−	m(α)(x−	NOUN
ejpam-3424	53	39	1|α)m	1|α)m	NUM
ejpam-3424	53	40	(	(	PUNCT
ejpam-3424	53	41	20	20	NUM
ejpam-3424	53	42	)	)	PUNCT
ejpam-3424	53	43	r.	r.	PROPN
ejpam-3424	53	44	corcino	corcino	PROPN
ejpam-3424	53	45	,	,	PUNCT
ejpam-3424	53	46	c.	c.	PROPN
ejpam-3424	53	47	corcino	corcino	PROPN
ejpam-3424	53	48	,	,	PUNCT
ejpam-3424	53	49	g.	g.	PROPN
ejpam-3424	53	50	rama	rama	PROPN
ejpam-3424	53	51	/	/	SYM
ejpam-3424	53	52	eur	eur	PROPN
ejpam-3424	53	53	.	.	PUNCT
ejpam-3424	54	1	j.	j.	PROPN
ejpam-3424	54	2	pure	pure	PROPN
ejpam-3424	54	3	appl	appl	PROPN
ejpam-3424	54	4	.	.	PROPN
ejpam-3424	54	5	math	math	PROPN
ejpam-3424	54	6	,	,	PUNCT
ejpam-3424	54	7	12	12	NUM
ejpam-3424	54	8	(	(	PUNCT
ejpam-3424	54	9	3	3	NUM
ejpam-3424	54	10	)	)	PUNCT
ejpam-3424	54	11	(	(	PUNCT
ejpam-3424	54	12	2019	2019	NUM
ejpam-3424	54	13	)	)	PUNCT
ejpam-3424	54	14	,	,	PUNCT
ejpam-3424	54	15	1069	1069	NUM
ejpam-3424	54	16	-	-	SYM
ejpam-3424	54	17	1081	1081	NUM
ejpam-3424	54	18	1073	1073	NUM
ejpam-3424	54	19	(	(	PUNCT
ejpam-3424	54	20	x−	x−	PROPN
ejpam-3424	54	21	1|α)n	1|α)n	NUM
ejpam-3424	54	22	=	=	SYM
ejpam-3424	54	23	n∑	n∑	PROPN
ejpam-3424	54	24	m=0	m=0	PROPN
ejpam-3424	54	25	lwn	lwn	PROPN
ejpam-3424	54	26	,	,	PUNCT
ejpam-3424	54	27	m(α)(−x−	m(α)(−x−	PROPN
ejpam-3424	54	28	1|α)m	1|α)m	NUM
ejpam-3424	54	29	.	.	PUNCT
ejpam-3424	55	1	(	(	PUNCT
ejpam-3424	55	2	21	21	NUM
ejpam-3424	55	3	)	)	PUNCT
ejpam-3424	55	4	by	by	ADP
ejpam-3424	55	5	assigning	assign	VERB
ejpam-3424	55	6	qk(x	qk(x	NOUN
ejpam-3424	55	7	,	,	PUNCT
ejpam-3424	55	8	n	n	CCONJ
ejpam-3424	55	9	)	)	PUNCT
ejpam-3424	55	10	=	=	SYM
ejpam-3424	55	11	(	(	PUNCT
ejpam-3424	55	12	(	(	PUNCT
ejpam-3424	55	13	−1)k−1x−	−1)k−1x−	X
ejpam-3424	55	14	1|α)n	1|α)n	NUM
ejpam-3424	55	15	,	,	PUNCT
ejpam-3424	55	16	(	(	PUNCT
ejpam-3424	55	17	8)	8)	NUM
ejpam-3424	55	18	gives	give	VERB
ejpam-3424	55	19	lm2,1,n	lm2,1,n	NOUN
ejpam-3424	55	20	=	=	SYM
ejpam-3424	55	21	lwn	lwn	NOUN
ejpam-3424	55	22	,	,	PUNCT
ejpam-3424	55	23	m(α	m(α	PROPN
ejpam-3424	55	24	)	)	PUNCT
ejpam-3424	55	25	=	=	PUNCT
ejpam-3424	55	26	lm1,2,n	lm1,2,n	PROPN
ejpam-3424	55	27	.	.	PUNCT
ejpam-3424	56	1	hence	hence	ADV
ejpam-3424	56	2	,	,	PUNCT
ejpam-3424	56	3	with	with	ADP
ejpam-3424	56	4	k	k	PROPN
ejpam-3424	56	5	=	=	SYM
ejpam-3424	56	6	2	2	NUM
ejpam-3424	56	7	and	and	CCONJ
ejpam-3424	56	8	h	h	NOUN
ejpam-3424	56	9	=	=	NOUN
ejpam-3424	56	10	1	1	NUM
ejpam-3424	56	11	,	,	PUNCT
ejpam-3424	56	12	(	(	PUNCT
ejpam-3424	56	13	10	10	NUM
ejpam-3424	56	14	)	)	PUNCT
ejpam-3424	56	15	yields	yield	NOUN
ejpam-3424	56	16	lwn	lwn	NOUN
ejpam-3424	56	17	,	,	PUNCT
ejpam-3424	56	18	j(α	j(α	PROPN
ejpam-3424	56	19	)	)	PUNCT
ejpam-3424	56	20	=	=	SYM
ejpam-3424	57	1	n∑	n∑	NOUN
ejpam-3424	57	2	k	k	PROPN
ejpam-3424	58	1	=	=	ADJ
ejpam-3424	58	2	j	j	PROPN
ejpam-3424	58	3	(	(	PUNCT
ejpam-3424	58	4	−1)kwα(n	−1)kwα(n	NOUN
ejpam-3424	58	5	,	,	PUNCT
ejpam-3424	58	6	k)wα(k	k)wα(k	PROPN
ejpam-3424	58	7	,	,	PUNCT
ejpam-3424	58	8	j	j	NOUN
ejpam-3424	58	9	)	)	PUNCT
ejpam-3424	58	10	.	.	PUNCT
ejpam-3424	59	1	(	(	PUNCT
ejpam-3424	59	2	22	22	NUM
ejpam-3424	59	3	)	)	PUNCT
ejpam-3424	59	4	the	the	DET
ejpam-3424	59	5	dowling	dowling	NOUN
ejpam-3424	59	6	numbers	number	NOUN
ejpam-3424	59	7	,	,	PUNCT
ejpam-3424	59	8	denoted	denote	VERB
ejpam-3424	59	9	by	by	ADP
ejpam-3424	59	10	dn(α	dn(α	NOUN
ejpam-3424	59	11	)	)	PUNCT
ejpam-3424	59	12	,	,	PUNCT
ejpam-3424	59	13	can	can	AUX
ejpam-3424	59	14	be	be	AUX
ejpam-3424	59	15	defined	define	VERB
ejpam-3424	59	16	as	as	ADP
ejpam-3424	59	17	the	the	DET
ejpam-3424	59	18	sum	sum	NOUN
ejpam-3424	59	19	of	of	ADP
ejpam-3424	59	20	whitney	whitney	PROPN
ejpam-3424	59	21	numbers	number	NOUN
ejpam-3424	59	22	of	of	ADP
ejpam-3424	59	23	the	the	DET
ejpam-3424	59	24	second	second	ADJ
ejpam-3424	59	25	kind	kind	NOUN
ejpam-3424	59	26	wα(n	wα(n	NOUN
ejpam-3424	59	27	,	,	PUNCT
ejpam-3424	59	28	m	m	NOUN
ejpam-3424	59	29	)	)	PUNCT
ejpam-3424	59	30	,	,	PUNCT
ejpam-3424	59	31	i.e.	i.e.	X
ejpam-3424	59	32	dn(α	dn(α	PUNCT
ejpam-3424	59	33	)	)	PUNCT
ejpam-3424	60	1	=	=	SYM
ejpam-3424	60	2	n∑	n∑	PROPN
ejpam-3424	60	3	m=0	m=0	PROPN
ejpam-3424	60	4	wα(n	wα(n	X
ejpam-3424	60	5	,	,	PUNCT
ejpam-3424	60	6	m	m	NOUN
ejpam-3424	60	7	)	)	PUNCT
ejpam-3424	60	8	.	.	PUNCT
ejpam-3424	61	1	(	(	PUNCT
ejpam-3424	61	2	23	23	NUM
ejpam-3424	61	3	)	)	PUNCT
ejpam-3424	61	4	using	use	VERB
ejpam-3424	61	5	the	the	DET
ejpam-3424	61	6	inverse	inverse	NOUN
ejpam-3424	61	7	relation	relation	NOUN
ejpam-3424	61	8	in	in	ADP
ejpam-3424	61	9	(	(	PUNCT
ejpam-3424	61	10	19	19	NUM
ejpam-3424	61	11	)	)	PUNCT
ejpam-3424	61	12	,	,	PUNCT
ejpam-3424	61	13	we	we	PRON
ejpam-3424	61	14	have	have	VERB
ejpam-3424	61	15	wα(n	wα(n	NOUN
ejpam-3424	61	16	,	,	PUNCT
ejpam-3424	61	17	k	k	NOUN
ejpam-3424	61	18	)	)	PUNCT
ejpam-3424	62	1	=	=	SYM
ejpam-3424	62	2	n∑	n∑	X
ejpam-3424	62	3	j=0	j=0	PROPN
ejpam-3424	62	4	(	(	PUNCT
ejpam-3424	62	5	−1)nwα(n	−1)nwα(n	NOUN
ejpam-3424	62	6	,	,	PUNCT
ejpam-3424	62	7	j)lwj	j)lwj	PROPN
ejpam-3424	62	8	,	,	PUNCT
ejpam-3424	62	9	k(α	k(α	PROPN
ejpam-3424	62	10	)	)	PUNCT
ejpam-3424	62	11	thus	thus	ADV
ejpam-3424	62	12	,	,	PUNCT
ejpam-3424	62	13	the	the	DET
ejpam-3424	62	14	dowling	dowling	NOUN
ejpam-3424	62	15	numbers	number	NOUN
ejpam-3424	62	16	equal	equal	ADJ
ejpam-3424	62	17	dn(α	dn(α	PUNCT
ejpam-3424	62	18	)	)	PUNCT
ejpam-3424	62	19	=	=	SYM
ejpam-3424	62	20	n∑	n∑	X
ejpam-3424	62	21	j=0	j=0	PROPN
ejpam-3424	62	22	(	(	PUNCT
ejpam-3424	62	23	−1)n−j	−1)n−j	PUNCT
ejpam-3424	62	24	[	[	PUNCT
ejpam-3424	62	25	j∑	j∑	X
ejpam-3424	62	26	k=0	k=0	PROPN
ejpam-3424	62	27	(	(	PUNCT
ejpam-3424	62	28	−1)jlwj	−1)jlwj	NOUN
ejpam-3424	62	29	,	,	PUNCT
ejpam-3424	62	30	k(α	k(α	PROPN
ejpam-3424	62	31	)	)	PUNCT
ejpam-3424	62	32	]	]	PUNCT
ejpam-3424	62	33	wα(n	wα(n	NOUN
ejpam-3424	62	34	,	,	PUNCT
ejpam-3424	62	35	j	j	PROPN
ejpam-3424	62	36	)	)	PUNCT
ejpam-3424	62	37	.	.	PUNCT
ejpam-3424	63	1	(	(	PUNCT
ejpam-3424	63	2	24	24	NUM
ejpam-3424	63	3	)	)	PUNCT
ejpam-3424	63	4	in	in	ADP
ejpam-3424	63	5	this	this	DET
ejpam-3424	63	6	paper	paper	NOUN
ejpam-3424	63	7	,	,	PUNCT
ejpam-3424	63	8	we	we	PRON
ejpam-3424	63	9	establish	establish	VERB
ejpam-3424	63	10	more	more	ADJ
ejpam-3424	63	11	properties	property	NOUN
ejpam-3424	63	12	of	of	ADP
ejpam-3424	63	13	tauber	tauber	PROPN
ejpam-3424	63	14	’s	’s	PART
ejpam-3424	63	15	generalized	generalize	VERB
ejpam-3424	63	16	stirling	stirling	NOUN
ejpam-3424	63	17	numbers	number	NOUN
ejpam-3424	63	18	as	as	ADV
ejpam-3424	63	19	well	well	ADV
ejpam-3424	63	20	as	as	ADP
ejpam-3424	63	21	some	some	DET
ejpam-3424	63	22	properties	property	NOUN
ejpam-3424	63	23	of	of	ADP
ejpam-3424	63	24	the	the	DET
ejpam-3424	63	25	generalized	generalized	ADJ
ejpam-3424	63	26	bell	bell	NOUN
ejpam-3424	63	27	numbers	number	NOUN
ejpam-3424	63	28	.	.	PUNCT
ejpam-3424	64	1	2	2	X
ejpam-3424	64	2	.	.	X
ejpam-3424	64	3	some	some	DET
ejpam-3424	64	4	recurrence	recurrence	NOUN
ejpam-3424	64	5	relations	relation	NOUN
ejpam-3424	64	6	tauber	tauber	PROPN
ejpam-3424	64	7	’s	’s	PART
ejpam-3424	64	8	generalized	generalize	VERB
ejpam-3424	64	9	stirling	stirling	NOUN
ejpam-3424	64	10	numbers	number	NOUN
ejpam-3424	64	11	of	of	ADP
ejpam-3424	64	12	the	the	DET
ejpam-3424	64	13	first	first	ADJ
ejpam-3424	64	14	and	and	CCONJ
ejpam-3424	64	15	second	second	ADJ
ejpam-3424	64	16	kind	kind	NOUN
ejpam-3424	64	17	and	and	CCONJ
ejpam-3424	64	18	tauber	tauber	PROPN
ejpam-3424	64	19	’s	’s	PART
ejpam-3424	64	20	generalized	generalize	VERB
ejpam-3424	64	21	lah	lah	NOUN
ejpam-3424	64	22	numbers	number	NOUN
ejpam-3424	64	23	are	be	AUX
ejpam-3424	64	24	known	know	VERB
ejpam-3424	64	25	to	to	PART
ejpam-3424	64	26	have	have	VERB
ejpam-3424	64	27	triangular	triangular	NOUN
ejpam-3424	64	28	recurrence	recurrence	NOUN
ejpam-3424	64	29	relations	relation	NOUN
ejpam-3424	64	30	.	.	PUNCT
ejpam-3424	65	1	in	in	ADP
ejpam-3424	65	2	this	this	DET
ejpam-3424	65	3	section	section	NOUN
ejpam-3424	65	4	,	,	PUNCT
ejpam-3424	65	5	we	we	PRON
ejpam-3424	65	6	establish	establish	VERB
ejpam-3424	65	7	other	other	ADJ
ejpam-3424	65	8	forms	form	NOUN
ejpam-3424	65	9	of	of	ADP
ejpam-3424	65	10	recurrence	recurrence	NOUN
ejpam-3424	65	11	relations	relation	NOUN
ejpam-3424	65	12	for	for	ADP
ejpam-3424	65	13	tauber	tauber	PROPN
ejpam-3424	65	14	’s	’s	PART
ejpam-3424	65	15	generalized	generalize	VERB
ejpam-3424	65	16	stirling	stirling	NOUN
ejpam-3424	65	17	numbers	number	NOUN
ejpam-3424	65	18	of	of	ADP
ejpam-3424	65	19	the	the	DET
ejpam-3424	65	20	first	first	ADJ
ejpam-3424	65	21	and	and	CCONJ
ejpam-3424	65	22	second	second	ADJ
ejpam-3424	65	23	kind	kind	NOUN
ejpam-3424	65	24	and	and	CCONJ
ejpam-3424	65	25	tauber	tauber	PROPN
ejpam-3424	65	26	’s	’s	PART
ejpam-3424	65	27	generalized	generalize	VERB
ejpam-3424	65	28	lah	lah	NOUN
ejpam-3424	65	29	numbers	number	NOUN
ejpam-3424	65	30	.	.	PUNCT
ejpam-3424	66	1	the	the	DET
ejpam-3424	66	2	following	follow	VERB
ejpam-3424	66	3	theorems	theorem	NOUN
ejpam-3424	66	4	contain	contain	VERB
ejpam-3424	66	5	the	the	DET
ejpam-3424	66	6	vertical	vertical	ADJ
ejpam-3424	66	7	recurrence	recurrence	NOUN
ejpam-3424	66	8	relation	relation	PROPN
ejpam-3424	66	9	.	.	PUNCT
ejpam-3424	67	1	theorem	theorem	VERB
ejpam-3424	67	2	2.1	2.1	NUM
ejpam-3424	67	3	.	.	PUNCT
ejpam-3424	68	1	tauber	tauber	PROPN
ejpam-3424	68	2	’s	’s	PART
ejpam-3424	68	3	generalized	generalize	VERB
ejpam-3424	68	4	stirling	stirling	NOUN
ejpam-3424	68	5	numbers	number	NOUN
ejpam-3424	68	6	of	of	ADP
ejpam-3424	68	7	the	the	DET
ejpam-3424	68	8	first	first	ADJ
ejpam-3424	68	9	kind	kind	NOUN
ejpam-3424	68	10	cnm	cnm	PROPN
ejpam-3424	68	11	satisfy	satisfy	VERB
ejpam-3424	68	12	the	the	DET
ejpam-3424	68	13	following	follow	VERB
ejpam-3424	68	14	vertical	vertical	ADJ
ejpam-3424	68	15	recurrence	recurrence	PROPN
ejpam-3424	68	16	relation	relation	NOUN
ejpam-3424	68	17	,	,	PUNCT
ejpam-3424	68	18	cmn	cmn	VERB
ejpam-3424	68	19	=	=	PUNCT
ejpam-3424	69	1	n−m+1∑	n−m+1∑	PROPN
ejpam-3424	69	2	i=1	i=1	PROPN
ejpam-3424	69	3	i−1∏	i−1∏	PUNCT
ejpam-3424	69	4	j=0	j=0	VERB
ejpam-3424	69	5	m(n+	m(n+	PROPN
ejpam-3424	69	6	1−	1−	NUM
ejpam-3424	69	7	j	j	NOUN
ejpam-3424	69	8	)	)	PUNCT
ejpam-3424	70	1	n(n−	n(n−	VERB
ejpam-3424	70	2	i+	i+	NUM
ejpam-3424	70	3	1)cm−1	1)cm−1	PROPN
ejpam-3424	70	4	n−i	n−i	PROPN
ejpam-3424	70	5	(	(	PUNCT
ejpam-3424	70	6	25	25	NUM
ejpam-3424	70	7	)	)	PUNCT
ejpam-3424	70	8	where	where	SCONJ
ejpam-3424	70	9	m(n+	m(n+	X
ejpam-3424	70	10	1	1	NUM
ejpam-3424	70	11	)	)	PUNCT
ejpam-3424	70	12	=	=	SYM
ejpam-3424	70	13	1,m(n+	1,m(n+	NUM
ejpam-3424	70	14	2	2	NUM
ejpam-3424	70	15	)	)	PUNCT
ejpam-3424	70	16	=	=	SYM
ejpam-3424	71	1	1	1	X
ejpam-3424	71	2	.	.	PUNCT
ejpam-3424	71	3	r.	r.	PROPN
ejpam-3424	71	4	corcino	corcino	PROPN
ejpam-3424	71	5	,	,	PUNCT
ejpam-3424	71	6	c.	c.	PROPN
ejpam-3424	71	7	corcino	corcino	PROPN
ejpam-3424	71	8	,	,	PUNCT
ejpam-3424	71	9	g.	g.	PROPN
ejpam-3424	71	10	rama	rama	PROPN
ejpam-3424	71	11	/	/	SYM
ejpam-3424	71	12	eur	eur	PROPN
ejpam-3424	71	13	.	.	PUNCT
ejpam-3424	72	1	j.	j.	PROPN
ejpam-3424	72	2	pure	pure	PROPN
ejpam-3424	72	3	appl	appl	PROPN
ejpam-3424	72	4	.	.	PROPN
ejpam-3424	72	5	math	math	PROPN
ejpam-3424	72	6	,	,	PUNCT
ejpam-3424	72	7	12	12	NUM
ejpam-3424	72	8	(	(	PUNCT
ejpam-3424	72	9	3	3	NUM
ejpam-3424	72	10	)	)	PUNCT
ejpam-3424	72	11	(	(	PUNCT
ejpam-3424	72	12	2019	2019	NUM
ejpam-3424	72	13	)	)	PUNCT
ejpam-3424	72	14	,	,	PUNCT
ejpam-3424	72	15	1069	1069	NUM
ejpam-3424	72	16	-	-	SYM
ejpam-3424	72	17	1081	1081	NUM
ejpam-3424	72	18	1074	1074	NUM
ejpam-3424	72	19	proof	proof	NOUN
ejpam-3424	72	20	.	.	PUNCT
ejpam-3424	73	1	from	from	ADP
ejpam-3424	73	2	the	the	DET
ejpam-3424	73	3	triangular	triangular	NOUN
ejpam-3424	73	4	recurrence	recurrence	NOUN
ejpam-3424	73	5	relation	relation	NOUN
ejpam-3424	73	6	(	(	PUNCT
ejpam-3424	73	7	6	6	NUM
ejpam-3424	73	8	)	)	PUNCT
ejpam-3424	73	9	,	,	PUNCT
ejpam-3424	73	10	that	that	PRON
ejpam-3424	73	11	is	is	ADV
ejpam-3424	73	12	cmn	cmn	NOUN
ejpam-3424	73	13	=	=	PUNCT
ejpam-3424	73	14	m(n)cmn−1	m(n)cmn−1	PROPN
ejpam-3424	74	1	+	+	NOUN
ejpam-3424	74	2	n(n)cm−1	n(n)cm−1	ADJ
ejpam-3424	74	3	n−1	n−1	PROPN
ejpam-3424	74	4	=	=	SYM
ejpam-3424	74	5	n(n)cm−1	n(n)cm−1	NOUN
ejpam-3424	74	6	n−1	n−1	PROPN
ejpam-3424	74	7	+	+	NOUN
ejpam-3424	74	8	m(n)cmn−1	m(n)cmn−1	X
ejpam-3424	74	9	.	.	PUNCT
ejpam-3424	75	1	since	since	SCONJ
ejpam-3424	75	2	cmn−1	cmn−1	PROPN
ejpam-3424	75	3	=	=	PUNCT
ejpam-3424	75	4	m(n−	m(n−	PROPN
ejpam-3424	75	5	1)cmn−2	1)cmn−2	NUM
ejpam-3424	75	6	+	+	NOUN
ejpam-3424	75	7	n(n−	n(n−	PROPN
ejpam-3424	75	8	1)cm−1	1)cm−1	PROPN
ejpam-3424	75	9	n−2	n−2	PROPN
ejpam-3424	75	10	then	then	ADV
ejpam-3424	75	11	cmn	cmn	VERB
ejpam-3424	75	12	=	=	PUNCT
ejpam-3424	75	13	n(n)cm−1	n(n)cm−1	NOUN
ejpam-3424	75	14	n−1	n−1	PROPN
ejpam-3424	75	15	+	+	PROPN
ejpam-3424	75	16	m(n)n(n−	m(n)n(n−	PROPN
ejpam-3424	75	17	1)cm−1	1)cm−1	PROPN
ejpam-3424	75	18	n−2	n−2	PROPN
ejpam-3424	76	1	+	+	PROPN
ejpam-3424	76	2	m(n)m(n−	m(n)m(n−	PROPN
ejpam-3424	76	3	1)cmn−2	1)cmn−2	NUM
ejpam-3424	76	4	.	.	PUNCT
ejpam-3424	77	1	continuing	continue	VERB
ejpam-3424	77	2	in	in	ADP
ejpam-3424	77	3	this	this	DET
ejpam-3424	77	4	manner	manner	NOUN
ejpam-3424	77	5	,	,	PUNCT
ejpam-3424	77	6	cmn	cmn	VERB
ejpam-3424	77	7	=	=	NOUN
ejpam-3424	77	8	n(n)cm−1	n(n)cm−1	NOUN
ejpam-3424	78	1	n−1	n−1	PROPN
ejpam-3424	78	2	+	+	PROPN
ejpam-3424	78	3	m(n)n(n−	m(n)n(n−	ADJ
ejpam-3424	78	4	1)cm−1	1)cm−1	PROPN
ejpam-3424	78	5	n−2	n−2	PROPN
ejpam-3424	78	6	+	+	X
ejpam-3424	78	7	.	.	PUNCT
ejpam-3424	78	8	.	.	PUNCT
ejpam-3424	78	9	.+m(n	.+m(n	PUNCT
ejpam-3424	78	10	)	)	PUNCT
ejpam-3424	78	11	.	.	PUNCT
ejpam-3424	78	12	.	.	PUNCT
ejpam-3424	79	1	.m(m+	.m(m+	PUNCT
ejpam-3424	80	1	1)n(m)cm−1	1)n(m)cm−1	NUM
ejpam-3424	81	1	m−1	m−1	PROPN
ejpam-3424	81	2	+	+	ADJ
ejpam-3424	81	3	m(n	m(n	NOUN
ejpam-3424	81	4	)	)	PUNCT
ejpam-3424	81	5	.	.	PUNCT
ejpam-3424	82	1	.	.	PUNCT
ejpam-3424	83	1	.m(m+	.m(m+	PUNCT
ejpam-3424	84	1	1)m(m)cmm−1	1)m(m)cmm−1	NUM
ejpam-3424	84	2	.	.	PUNCT
ejpam-3424	85	1	by	by	ADP
ejpam-3424	85	2	definition	definition	NOUN
ejpam-3424	85	3	,	,	PUNCT
ejpam-3424	85	4	the	the	DET
ejpam-3424	85	5	last	last	ADJ
ejpam-3424	85	6	term	term	NOUN
ejpam-3424	85	7	is	be	AUX
ejpam-3424	85	8	equal	equal	ADJ
ejpam-3424	85	9	to	to	ADP
ejpam-3424	85	10	zero	zero	NUM
ejpam-3424	85	11	.	.	PUNCT
ejpam-3424	86	1	thus	thus	ADV
ejpam-3424	86	2	,	,	PUNCT
ejpam-3424	86	3	cmn	cmn	VERB
ejpam-3424	86	4	=	=	PUNCT
ejpam-3424	86	5	n−m+1∑	n−m+1∑	PROPN
ejpam-3424	86	6	i=1	i=1	X
ejpam-3424	87	1	[	[	X
ejpam-3424	87	2	m(n+	m(n+	NOUN
ejpam-3424	87	3	1	1	NUM
ejpam-3424	87	4	)	)	PUNCT
ejpam-3424	87	5	.	.	PUNCT
ejpam-3424	88	1	.	.	PUNCT
ejpam-3424	89	1	.m(n−	.m(n−	PUNCT
ejpam-3424	90	1	i+	i+	PUNCT
ejpam-3424	90	2	2)n(n−	2)n(n−	NUM
ejpam-3424	90	3	i+	i+	PUNCT
ejpam-3424	90	4	1)]cm−1	1)]cm−1	PROPN
ejpam-3424	90	5	n−i	n−i	PROPN
ejpam-3424	90	6	where	where	SCONJ
ejpam-3424	90	7	m(n+	m(n+	X
ejpam-3424	90	8	1	1	NUM
ejpam-3424	90	9	)	)	PUNCT
ejpam-3424	90	10	=	=	SYM
ejpam-3424	90	11	1,m(n+	1,m(n+	NUM
ejpam-3424	90	12	2	2	NUM
ejpam-3424	90	13	)	)	PUNCT
ejpam-3424	90	14	=	=	SYM
ejpam-3424	90	15	1	1	X
ejpam-3424	90	16	.	.	X
ejpam-3424	90	17	theorem	theorem	VERB
ejpam-3424	90	18	2.2	2.2	NUM
ejpam-3424	90	19	.	.	PUNCT
ejpam-3424	91	1	tauber	tauber	PROPN
ejpam-3424	91	2	’s	’s	PART
ejpam-3424	91	3	generalized	generalize	VERB
ejpam-3424	91	4	stirling	stirling	NOUN
ejpam-3424	91	5	numbers	number	NOUN
ejpam-3424	91	6	of	of	ADP
ejpam-3424	91	7	the	the	DET
ejpam-3424	91	8	second	second	ADJ
ejpam-3424	91	9	kind	kind	NOUN
ejpam-3424	91	10	dm	dm	AUX
ejpam-3424	91	11	n	n	PRON
ejpam-3424	91	12	satisfy	satisfy	VERB
ejpam-3424	91	13	the	the	DET
ejpam-3424	91	14	following	follow	VERB
ejpam-3424	91	15	vertical	vertical	ADJ
ejpam-3424	91	16	recurrence	recurrence	NOUN
ejpam-3424	91	17	relation	relation	NOUN
ejpam-3424	91	18	,	,	PUNCT
ejpam-3424	91	19	dm	dm	PROPN
ejpam-3424	91	20	n	n	NOUN
ejpam-3424	91	21	=	=	NOUN
ejpam-3424	91	22	n−m+1∑	n−m+1∑	PROPN
ejpam-3424	91	23	i=1	i=1	PROPN
ejpam-3424	92	1	(	(	PUNCT
ejpam-3424	92	2	−1)i−1	−1)i−1	PROPN
ejpam-3424	92	3	(	(	PUNCT
ejpam-3424	92	4	m(m+	m(m+	PROPN
ejpam-3424	92	5	1))i−1	1))i−1	NUM
ejpam-3424	92	6	(	(	PUNCT
ejpam-3424	92	7	n(m+	n(m+	NOUN
ejpam-3424	92	8	1))i	1))i	NUM
ejpam-3424	92	9	dm−1	dm−1	NOUN
ejpam-3424	92	10	n−i	n−i	NOUN
ejpam-3424	92	11	.	.	PUNCT
ejpam-3424	93	1	(	(	PUNCT
ejpam-3424	93	2	26	26	NUM
ejpam-3424	93	3	)	)	PUNCT
ejpam-3424	93	4	proof	proof	NOUN
ejpam-3424	93	5	.	.	PUNCT
ejpam-3424	94	1	from	from	ADP
ejpam-3424	94	2	the	the	DET
ejpam-3424	94	3	triangular	triangular	NOUN
ejpam-3424	94	4	recurrence	recurrence	NOUN
ejpam-3424	94	5	relation	relation	NOUN
ejpam-3424	94	6	(	(	PUNCT
ejpam-3424	94	7	7	7	NUM
ejpam-3424	94	8	)	)	PUNCT
ejpam-3424	94	9	,	,	PUNCT
ejpam-3424	94	10	dm	dm	PROPN
ejpam-3424	94	11	n	n	NOUN
ejpam-3424	94	12	=	=	SYM
ejpam-3424	94	13	−m(m+	−m(m+	ADP
ejpam-3424	94	14	1	1	X
ejpam-3424	94	15	)	)	PUNCT
ejpam-3424	94	16	n(m+	n(m+	NOUN
ejpam-3424	94	17	1	1	NUM
ejpam-3424	94	18	)	)	PUNCT
ejpam-3424	94	19	dm	dm	NOUN
ejpam-3424	94	20	n−1	n−1	PROPN
ejpam-3424	95	1	+	+	CCONJ
ejpam-3424	95	2	1	1	NUM
ejpam-3424	95	3	n(m+	n(m+	NUM
ejpam-3424	95	4	1	1	NUM
ejpam-3424	95	5	)	)	PUNCT
ejpam-3424	95	6	dm−1	dm−1	NOUN
ejpam-3424	95	7	n−1	n−1	PROPN
ejpam-3424	95	8	since	since	SCONJ
ejpam-3424	95	9	dm	dm	PROPN
ejpam-3424	95	10	n−1	n−1	PROPN
ejpam-3424	95	11	=	=	PUNCT
ejpam-3424	95	12	−m(m+	−m(m+	ADP
ejpam-3424	95	13	1	1	X
ejpam-3424	95	14	)	)	PUNCT
ejpam-3424	95	15	n(m+	n(m+	NOUN
ejpam-3424	95	16	1	1	NUM
ejpam-3424	95	17	)	)	PUNCT
ejpam-3424	95	18	dm	dm	PROPN
ejpam-3424	95	19	n−2	n−2	PROPN
ejpam-3424	96	1	+	+	CCONJ
ejpam-3424	96	2	1	1	NUM
ejpam-3424	96	3	n(m+	n(m+	NUM
ejpam-3424	96	4	1	1	NUM
ejpam-3424	96	5	)	)	PUNCT
ejpam-3424	96	6	dm−1	dm−1	NOUN
ejpam-3424	96	7	n−2	n−2	PROPN
ejpam-3424	97	1	,	,	PUNCT
ejpam-3424	97	2	then	then	ADV
ejpam-3424	97	3	dm	dm	PROPN
ejpam-3424	97	4	n	n	NOUN
ejpam-3424	97	5	=	=	SYM
ejpam-3424	97	6	1	1	NUM
ejpam-3424	97	7	n(m+	n(m+	NUM
ejpam-3424	97	8	1	1	NUM
ejpam-3424	97	9	)	)	PUNCT
ejpam-3424	97	10	dm−1	dm−1	NOUN
ejpam-3424	97	11	n−1	n−1	PROPN
ejpam-3424	97	12	−	−	PROPN
ejpam-3424	97	13	m(m+	m(m+	VERB
ejpam-3424	97	14	1	1	NUM
ejpam-3424	97	15	)	)	PUNCT
ejpam-3424	97	16	(	(	PUNCT
ejpam-3424	97	17	n(m+	n(m+	X
ejpam-3424	97	18	1))2	1))2	NUM
ejpam-3424	97	19	dm−1	dm−1	NOUN
ejpam-3424	97	20	n−2	n−2	PROPN
ejpam-3424	98	1	+	+	CCONJ
ejpam-3424	98	2	(	(	PUNCT
ejpam-3424	98	3	m(m+	m(m+	NUM
ejpam-3424	98	4	1))2	1))2	NUM
ejpam-3424	98	5	(	(	PUNCT
ejpam-3424	98	6	n(m+	n(m+	X
ejpam-3424	98	7	1))2	1))2	NUM
ejpam-3424	98	8	dm	dm	PROPN
ejpam-3424	98	9	n−2	n−2	PROPN
ejpam-3424	98	10	.	.	PUNCT
ejpam-3424	99	1	continuing	continue	VERB
ejpam-3424	99	2	in	in	ADP
ejpam-3424	99	3	this	this	DET
ejpam-3424	99	4	manner	manner	NOUN
ejpam-3424	99	5	,	,	PUNCT
ejpam-3424	99	6	dm	dm	PROPN
ejpam-3424	99	7	n	n	NOUN
ejpam-3424	99	8	=	=	SYM
ejpam-3424	99	9	1	1	NUM
ejpam-3424	99	10	n(m+	n(m+	NUM
ejpam-3424	99	11	1	1	NUM
ejpam-3424	99	12	)	)	PUNCT
ejpam-3424	99	13	dm−1	dm−1	NOUN
ejpam-3424	99	14	n−1	n−1	PROPN
ejpam-3424	99	15	−	−	PROPN
ejpam-3424	99	16	m(m+	m(m+	VERB
ejpam-3424	99	17	1	1	NUM
ejpam-3424	99	18	)	)	PUNCT
ejpam-3424	99	19	(	(	PUNCT
ejpam-3424	99	20	n(m+	n(m+	X
ejpam-3424	99	21	1))2	1))2	NUM
ejpam-3424	99	22	dm−1	dm−1	NOUN
ejpam-3424	99	23	n−2	n−2	PROPN
ejpam-3424	100	1	+	+	X
ejpam-3424	100	2	.	.	PUNCT
ejpam-3424	100	3	.	.	PUNCT
ejpam-3424	101	1	.+	.+	NOUN
ejpam-3424	101	2	(	(	PUNCT
ejpam-3424	101	3	−1)n−m	−1)n−m	X
ejpam-3424	101	4	(	(	PUNCT
ejpam-3424	101	5	m(m+	m(m+	NUM
ejpam-3424	101	6	1))n−m	1))n−m	NUM
ejpam-3424	101	7	(	(	PUNCT
ejpam-3424	101	8	n(m+	n(m+	NOUN
ejpam-3424	101	9	1))n−m+1	1))n−m+1	NUM
ejpam-3424	101	10	dm−1	dm−1	NOUN
ejpam-3424	101	11	m−1	m−1	PROPN
ejpam-3424	101	12	r.	r.	PROPN
ejpam-3424	101	13	corcino	corcino	PROPN
ejpam-3424	101	14	,	,	PUNCT
ejpam-3424	101	15	c.	c.	PROPN
ejpam-3424	101	16	corcino	corcino	PROPN
ejpam-3424	101	17	,	,	PUNCT
ejpam-3424	101	18	g.	g.	PROPN
ejpam-3424	101	19	rama	rama	PROPN
ejpam-3424	101	20	/	/	SYM
ejpam-3424	101	21	eur	eur	PROPN
ejpam-3424	101	22	.	.	PUNCT
ejpam-3424	102	1	j.	j.	PROPN
ejpam-3424	102	2	pure	pure	PROPN
ejpam-3424	102	3	appl	appl	PROPN
ejpam-3424	102	4	.	.	PROPN
ejpam-3424	102	5	math	math	PROPN
ejpam-3424	102	6	,	,	PUNCT
ejpam-3424	102	7	12	12	NUM
ejpam-3424	102	8	(	(	PUNCT
ejpam-3424	102	9	3	3	NUM
ejpam-3424	102	10	)	)	PUNCT
ejpam-3424	102	11	(	(	PUNCT
ejpam-3424	102	12	2019	2019	NUM
ejpam-3424	102	13	)	)	PUNCT
ejpam-3424	102	14	,	,	PUNCT
ejpam-3424	102	15	1069	1069	NUM
ejpam-3424	102	16	-	-	SYM
ejpam-3424	102	17	1081	1081	NUM
ejpam-3424	102	18	1075	1075	NUM
ejpam-3424	102	19	+	+	CCONJ
ejpam-3424	102	20	(	(	PUNCT
ejpam-3424	102	21	−1)n−m+1	−1)n−m+1	X
ejpam-3424	102	22	(	(	PUNCT
ejpam-3424	102	23	m(m+	m(m+	X
ejpam-3424	102	24	1))n−m+1	1))n−m+1	X
ejpam-3424	102	25	(	(	PUNCT
ejpam-3424	102	26	n(m+	n(m+	NOUN
ejpam-3424	102	27	1))n−m+1	1))n−m+1	NUM
ejpam-3424	102	28	dm	dm	PROPN
ejpam-3424	102	29	m−1	m−1	PROPN
ejpam-3424	102	30	.	.	PUNCT
ejpam-3424	103	1	by	by	ADP
ejpam-3424	103	2	definition	definition	NOUN
ejpam-3424	103	3	,	,	PUNCT
ejpam-3424	103	4	the	the	DET
ejpam-3424	103	5	last	last	ADJ
ejpam-3424	103	6	term	term	NOUN
ejpam-3424	103	7	is	be	AUX
ejpam-3424	103	8	equal	equal	ADJ
ejpam-3424	103	9	to	to	ADP
ejpam-3424	103	10	zero	zero	NUM
ejpam-3424	103	11	.	.	PUNCT
ejpam-3424	104	1	thus	thus	ADV
ejpam-3424	104	2	,	,	PUNCT
ejpam-3424	104	3	dm	dm	PROPN
ejpam-3424	104	4	n	n	PROPN
ejpam-3424	104	5	=	=	NOUN
ejpam-3424	104	6	n−m+1∑	n−m+1∑	PROPN
ejpam-3424	104	7	i=1	i=1	PROPN
ejpam-3424	104	8	(	(	PUNCT
ejpam-3424	104	9	−1)i−1	−1)i−1	PROPN
ejpam-3424	104	10	(	(	PUNCT
ejpam-3424	104	11	m(m+	m(m+	PROPN
ejpam-3424	104	12	1))i−1	1))i−1	NUM
ejpam-3424	104	13	(	(	PUNCT
ejpam-3424	104	14	n(m+	n(m+	NOUN
ejpam-3424	104	15	1))i	1))i	NUM
ejpam-3424	104	16	dm−1	dm−1	NOUN
ejpam-3424	104	17	n−i	n−i	NOUN
ejpam-3424	104	18	.	.	PUNCT
ejpam-3424	105	1	theorem	theorem	VERB
ejpam-3424	105	2	2.3	2.3	NUM
ejpam-3424	105	3	.	.	PUNCT
ejpam-3424	106	1	tauber	tauber	PROPN
ejpam-3424	106	2	’s	’s	PART
ejpam-3424	106	3	generalized	generalize	VERB
ejpam-3424	106	4	lah	lah	PROPN
ejpam-3424	106	5	numbers	number	NOUN
ejpam-3424	106	6	lmk	lmk	PROPN
ejpam-3424	106	7	,	,	PUNCT
ejpam-3424	106	8	h	h	NOUN
ejpam-3424	106	9	,	,	PUNCT
ejpam-3424	106	10	n	n	PRON
ejpam-3424	106	11	satisfy	satisfy	VERB
ejpam-3424	106	12	the	the	DET
ejpam-3424	106	13	following	follow	VERB
ejpam-3424	106	14	vertical	vertical	ADJ
ejpam-3424	106	15	recurrence	recurrence	PROPN
ejpam-3424	106	16	relation	relation	PROPN
ejpam-3424	106	17	,	,	PUNCT
ejpam-3424	106	18	lmk	lmk	PROPN
ejpam-3424	106	19	,	,	PUNCT
ejpam-3424	106	20	h	h	NOUN
ejpam-3424	106	21	,	,	PUNCT
ejpam-3424	106	22	n	n	PROPN
ejpam-3424	106	23	=	=	NUM
ejpam-3424	106	24	n−m+1∑	n−m+1∑	PROPN
ejpam-3424	106	25	i=1	i=1	PROPN
ejpam-3424	107	1			PUNCT
ejpam-3424	107	2	i−1∏	i−1∏	PROPN
ejpam-3424	107	3	j=0	j=0	PROPN
ejpam-3424	107	4	[	[	PUNCT
ejpam-3424	107	5	mk(n+	mk(n+	PROPN
ejpam-3424	107	6	1−	1−	NUM
ejpam-3424	107	7	j)−	j)−	PROPN
ejpam-3424	107	8	nk(n+	nk(n+	PROPN
ejpam-3424	108	1	1−	1−	NUM
ejpam-3424	108	2	j)mh(m+	j)mh(m+	NOUN
ejpam-3424	108	3	1	1	NUM
ejpam-3424	108	4	)	)	PUNCT
ejpam-3424	108	5	nh(m+	nh(m+	NUM
ejpam-3424	108	6	1	1	NUM
ejpam-3424	108	7	)	)	PUNCT
ejpam-3424	108	8	]	]	PUNCT
ejpam-3424	109	1			PROPN
ejpam-3424	109	2	nk(n−	nk(n−	PROPN
ejpam-3424	109	3	i+	i+	X
ejpam-3424	109	4	1	1	NUM
ejpam-3424	109	5	)	)	PUNCT
ejpam-3424	109	6	nh(m	nh(m	NOUN
ejpam-3424	109	7	)	)	PUNCT
ejpam-3424	109	8	lm−1	lm−1	PROPN
ejpam-3424	109	9	k	k	PROPN
ejpam-3424	109	10	,	,	PUNCT
ejpam-3424	109	11	h	h	NOUN
ejpam-3424	109	12	,	,	PUNCT
ejpam-3424	109	13	n−i	n−i	NOUN
ejpam-3424	109	14	where	where	SCONJ
ejpam-3424	109	15	[	[	PUNCT
ejpam-3424	109	16	mk(n+	mk(n+	PROPN
ejpam-3424	109	17	1)−	1)−	PROPN
ejpam-3424	109	18	nk(n+	nk(n+	PROPN
ejpam-3424	109	19	1)mh(m+	1)mh(m+	NOUN
ejpam-3424	109	20	1	1	NUM
ejpam-3424	109	21	)	)	PUNCT
ejpam-3424	109	22	nh(m+	nh(m+	NUM
ejpam-3424	109	23	1	1	NUM
ejpam-3424	109	24	)	)	PUNCT
ejpam-3424	109	25	]	]	PUNCT
ejpam-3424	109	26	=	=	PUNCT
ejpam-3424	109	27	1	1	X
ejpam-3424	109	28	.	.	PUNCT
ejpam-3424	109	29	proof	proof	NOUN
ejpam-3424	109	30	.	.	PUNCT
ejpam-3424	110	1	from	from	ADP
ejpam-3424	110	2	the	the	DET
ejpam-3424	110	3	triangular	triangular	NOUN
ejpam-3424	110	4	recurrence	recurrence	NOUN
ejpam-3424	110	5	relation	relation	NOUN
ejpam-3424	110	6	(	(	PUNCT
ejpam-3424	110	7	9	9	NUM
ejpam-3424	110	8	)	)	PUNCT
ejpam-3424	110	9	,	,	PUNCT
ejpam-3424	110	10	that	that	PRON
ejpam-3424	110	11	is	be	AUX
ejpam-3424	110	12	lmk	lmk	PROPN
ejpam-3424	110	13	,	,	PUNCT
ejpam-3424	110	14	h	h	NOUN
ejpam-3424	110	15	,	,	PUNCT
ejpam-3424	110	16	n	n	NOUN
ejpam-3424	110	17	=	=	PUNCT
ejpam-3424	110	18	[	[	PUNCT
ejpam-3424	110	19	mk(n)−	mk(n)−	NOUN
ejpam-3424	110	20	nk(n)mh(m+	nk(n)mh(m+	NOUN
ejpam-3424	110	21	1	1	NUM
ejpam-3424	110	22	)	)	PUNCT
ejpam-3424	110	23	nh(m+	nh(m+	NUM
ejpam-3424	110	24	1	1	NUM
ejpam-3424	110	25	)	)	PUNCT
ejpam-3424	110	26	]	]	PUNCT
ejpam-3424	111	1	lmk	lmk	PROPN
ejpam-3424	111	2	,	,	PUNCT
ejpam-3424	111	3	h	h	NOUN
ejpam-3424	111	4	,	,	PUNCT
ejpam-3424	111	5	n−1	n−1	PROPN
ejpam-3424	111	6	+	+	NUM
ejpam-3424	111	7	nk(n	nk(n	NOUN
ejpam-3424	111	8	)	)	PUNCT
ejpam-3424	111	9	nh(m	nh(m	NUM
ejpam-3424	111	10	)	)	PUNCT
ejpam-3424	111	11	lm−1	lm−1	PROPN
ejpam-3424	111	12	k	k	PROPN
ejpam-3424	111	13	,	,	PUNCT
ejpam-3424	111	14	h	h	NOUN
ejpam-3424	111	15	,	,	PUNCT
ejpam-3424	111	16	n−1	n−1	PROPN
ejpam-3424	111	17	=	=	PUNCT
ejpam-3424	111	18	nk(n	nk(n	X
ejpam-3424	111	19	)	)	PUNCT
ejpam-3424	111	20	nh(m	nh(m	ADP
ejpam-3424	111	21	)	)	PUNCT
ejpam-3424	111	22	lm−1	lm−1	PROPN
ejpam-3424	111	23	k	k	PROPN
ejpam-3424	111	24	,	,	PUNCT
ejpam-3424	111	25	h	h	NOUN
ejpam-3424	111	26	,	,	PUNCT
ejpam-3424	111	27	n−1	n−1	PROPN
ejpam-3424	111	28	+	+	PUNCT
ejpam-3424	111	29	[	[	PUNCT
ejpam-3424	111	30	mk(n)−	mk(n)−	NOUN
ejpam-3424	111	31	nk(n)mh(m+	nk(n)mh(m+	NOUN
ejpam-3424	111	32	1	1	NUM
ejpam-3424	111	33	)	)	PUNCT
ejpam-3424	111	34	nh(m+	nh(m+	NUM
ejpam-3424	111	35	1	1	NUM
ejpam-3424	111	36	)	)	PUNCT
ejpam-3424	111	37	]	]	PUNCT
ejpam-3424	112	1	lmk	lmk	PROPN
ejpam-3424	112	2	,	,	PUNCT
ejpam-3424	112	3	h	h	NOUN
ejpam-3424	112	4	,	,	PUNCT
ejpam-3424	112	5	n−1	n−1	PROPN
ejpam-3424	112	6	.	.	PROPN
ejpam-3424	112	7	since	since	SCONJ
ejpam-3424	112	8	lmk	lmk	PROPN
ejpam-3424	112	9	,	,	PUNCT
ejpam-3424	112	10	h	h	NOUN
ejpam-3424	112	11	,	,	PUNCT
ejpam-3424	112	12	n−1	n−1	PROPN
ejpam-3424	112	13	=	=	PUNCT
ejpam-3424	112	14	[	[	PUNCT
ejpam-3424	112	15	mk(n−	mk(n−	PROPN
ejpam-3424	112	16	1)−	1)−	PROPN
ejpam-3424	112	17	nk(n−	nk(n−	PROPN
ejpam-3424	112	18	1)mh(m+	1)mh(m+	NOUN
ejpam-3424	112	19	1	1	NUM
ejpam-3424	112	20	)	)	PUNCT
ejpam-3424	112	21	nh(m+	nh(m+	NUM
ejpam-3424	112	22	1	1	NUM
ejpam-3424	112	23	)	)	PUNCT
ejpam-3424	112	24	]	]	PUNCT
ejpam-3424	113	1	lmk	lmk	PROPN
ejpam-3424	113	2	,	,	PUNCT
ejpam-3424	113	3	h	h	NOUN
ejpam-3424	113	4	,	,	PUNCT
ejpam-3424	113	5	n−2	n−2	PROPN
ejpam-3424	113	6	+	+	CCONJ
ejpam-3424	113	7	nk(n−	nk(n−	PROPN
ejpam-3424	113	8	1	1	NUM
ejpam-3424	113	9	)	)	PUNCT
ejpam-3424	113	10	nh(m	nh(m	NOUN
ejpam-3424	113	11	)	)	PUNCT
ejpam-3424	113	12	lm−1	lm−1	PROPN
ejpam-3424	113	13	k	k	PROPN
ejpam-3424	113	14	,	,	PUNCT
ejpam-3424	113	15	h	h	NOUN
ejpam-3424	113	16	,	,	PUNCT
ejpam-3424	113	17	n−2	n−2	PROPN
ejpam-3424	113	18	,	,	PUNCT
ejpam-3424	113	19	then	then	ADV
ejpam-3424	113	20	lmk	lmk	PROPN
ejpam-3424	113	21	,	,	PUNCT
ejpam-3424	113	22	h	h	NOUN
ejpam-3424	113	23	,	,	PUNCT
ejpam-3424	113	24	n	n	NOUN
ejpam-3424	113	25	=	=	PUNCT
ejpam-3424	113	26	nk(n	nk(n	X
ejpam-3424	113	27	)	)	PUNCT
ejpam-3424	113	28	nh(m	nh(m	ADP
ejpam-3424	113	29	)	)	PUNCT
ejpam-3424	113	30	lm−1	lm−1	PROPN
ejpam-3424	113	31	k	k	PROPN
ejpam-3424	113	32	,	,	PUNCT
ejpam-3424	113	33	h	h	NOUN
ejpam-3424	113	34	,	,	PUNCT
ejpam-3424	113	35	n−1	n−1	PROPN
ejpam-3424	113	36	+	+	CCONJ
ejpam-3424	113	37	nk(n−	nk(n−	PROPN
ejpam-3424	113	38	1	1	NUM
ejpam-3424	113	39	)	)	PUNCT
ejpam-3424	113	40	nh(m	nh(m	PUNCT
ejpam-3424	113	41	)	)	PUNCT
ejpam-3424	114	1	[	[	PUNCT
ejpam-3424	114	2	mk(n)−	mk(n)−	NOUN
ejpam-3424	114	3	nk(n)mh(m+	nk(n)mh(m+	NOUN
ejpam-3424	114	4	1	1	NUM
ejpam-3424	114	5	)	)	PUNCT
ejpam-3424	114	6	nh(m+	nh(m+	NUM
ejpam-3424	114	7	1	1	NUM
ejpam-3424	114	8	)	)	PUNCT
ejpam-3424	114	9	]	]	PUNCT
ejpam-3424	114	10	lm−1	lm−1	PROPN
ejpam-3424	114	11	k	k	PROPN
ejpam-3424	114	12	,	,	PUNCT
ejpam-3424	114	13	h	h	NOUN
ejpam-3424	114	14	,	,	PUNCT
ejpam-3424	114	15	n−2	n−2	PROPN
ejpam-3424	114	16	+	+	CCONJ
ejpam-3424	114	17	[	[	PUNCT
ejpam-3424	114	18	mk(n)−	mk(n)−	NOUN
ejpam-3424	114	19	nk(n)mh(m+	nk(n)mh(m+	NOUN
ejpam-3424	114	20	1	1	NUM
ejpam-3424	114	21	)	)	PUNCT
ejpam-3424	114	22	nh(m+	nh(m+	NUM
ejpam-3424	114	23	1	1	NUM
ejpam-3424	114	24	)	)	PUNCT
ejpam-3424	114	25	]	]	PUNCT
ejpam-3424	114	26	[	[	PUNCT
ejpam-3424	114	27	mk(n−	mk(n−	PROPN
ejpam-3424	114	28	1)−	1)−	PROPN
ejpam-3424	114	29	nk(n−	nk(n−	PROPN
ejpam-3424	114	30	1)mh(m+	1)mh(m+	NOUN
ejpam-3424	114	31	1	1	NUM
ejpam-3424	114	32	)	)	PUNCT
ejpam-3424	114	33	nh(m+	nh(m+	NUM
ejpam-3424	114	34	1	1	NUM
ejpam-3424	114	35	)	)	PUNCT
ejpam-3424	114	36	]	]	PUNCT
ejpam-3424	114	37	×	×	PROPN
ejpam-3424	114	38	[	[	PUNCT
ejpam-3424	114	39	lmk	lmk	PROPN
ejpam-3424	114	40	,	,	PUNCT
ejpam-3424	114	41	h	h	NOUN
ejpam-3424	114	42	,	,	PUNCT
ejpam-3424	114	43	n−2	n−2	PROPN
ejpam-3424	114	44	]	]	PUNCT
ejpam-3424	114	45	.	.	PUNCT
ejpam-3424	115	1	continuing	continue	VERB
ejpam-3424	115	2	in	in	ADP
ejpam-3424	115	3	this	this	DET
ejpam-3424	115	4	manner	manner	NOUN
ejpam-3424	115	5	,	,	PUNCT
ejpam-3424	115	6	lmk	lmk	PROPN
ejpam-3424	115	7	,	,	PUNCT
ejpam-3424	115	8	h	h	NOUN
ejpam-3424	115	9	,	,	PUNCT
ejpam-3424	115	10	n	n	NOUN
ejpam-3424	115	11	=	=	PUNCT
ejpam-3424	115	12	nk(n	nk(n	X
ejpam-3424	115	13	)	)	PUNCT
ejpam-3424	115	14	nh(m	nh(m	ADP
ejpam-3424	115	15	)	)	PUNCT
ejpam-3424	115	16	lm−1	lm−1	PROPN
ejpam-3424	115	17	k	k	PROPN
ejpam-3424	115	18	,	,	PUNCT
ejpam-3424	115	19	h	h	NOUN
ejpam-3424	115	20	,	,	PUNCT
ejpam-3424	115	21	n−1	n−1	PROPN
ejpam-3424	115	22	+	+	PUNCT
ejpam-3424	115	23	[	[	PUNCT
ejpam-3424	115	24	mk(n)−	mk(n)−	NOUN
ejpam-3424	115	25	nk(n)mh(m+	nk(n)mh(m+	NOUN
ejpam-3424	115	26	1	1	NUM
ejpam-3424	115	27	)	)	PUNCT
ejpam-3424	115	28	nh(m+	nh(m+	NUM
ejpam-3424	115	29	1	1	NUM
ejpam-3424	115	30	)	)	PUNCT
ejpam-3424	115	31	]	]	PUNCT
ejpam-3424	115	32	nk(n−	nk(n−	PROPN
ejpam-3424	115	33	1	1	NUM
ejpam-3424	115	34	)	)	PUNCT
ejpam-3424	115	35	nh(m	nh(m	NOUN
ejpam-3424	115	36	)	)	PUNCT
ejpam-3424	115	37	lm−1	lm−1	PROPN
ejpam-3424	115	38	k	k	PROPN
ejpam-3424	115	39	,	,	PUNCT
ejpam-3424	115	40	h	h	NOUN
ejpam-3424	115	41	,	,	PUNCT
ejpam-3424	115	42	n−2	n−2	PROPN
ejpam-3424	115	43	+	+	X
ejpam-3424	115	44	.	.	PUNCT
ejpam-3424	115	45	.	.	PUNCT
ejpam-3424	116	1	.+	.+	NOUN
ejpam-3424	116	2	[	[	PUNCT
ejpam-3424	116	3	mk(n)−	mk(n)−	NOUN
ejpam-3424	116	4	nk(n)mh(m+	nk(n)mh(m+	NOUN
ejpam-3424	116	5	1	1	NUM
ejpam-3424	116	6	)	)	PUNCT
ejpam-3424	116	7	nh(m+	nh(m+	NUM
ejpam-3424	116	8	1	1	NUM
ejpam-3424	116	9	)	)	PUNCT
ejpam-3424	116	10	]	]	PUNCT
ejpam-3424	116	11	.	.	PUNCT
ejpam-3424	116	12	.	.	PUNCT
ejpam-3424	116	13	.	.	PUNCT
ejpam-3424	117	1	[	[	PUNCT
ejpam-3424	117	2	mk(m+	mk(m+	PROPN
ejpam-3424	117	3	1)−	1)−	PROPN
ejpam-3424	117	4	nk(m+	nk(m+	NOUN
ejpam-3424	117	5	1)mh(m+	1)mh(m+	NOUN
ejpam-3424	117	6	1	1	NUM
ejpam-3424	117	7	)	)	PUNCT
ejpam-3424	117	8	nh(m+	nh(m+	NUM
ejpam-3424	117	9	1	1	NUM
ejpam-3424	117	10	)	)	PUNCT
ejpam-3424	117	11	]	]	PUNCT
ejpam-3424	118	1	r.	r.	PROPN
ejpam-3424	118	2	corcino	corcino	PROPN
ejpam-3424	118	3	,	,	PUNCT
ejpam-3424	118	4	c.	c.	PROPN
ejpam-3424	118	5	corcino	corcino	PROPN
ejpam-3424	118	6	,	,	PUNCT
ejpam-3424	118	7	g.	g.	PROPN
ejpam-3424	118	8	rama	rama	PROPN
ejpam-3424	118	9	/	/	SYM
ejpam-3424	118	10	eur	eur	PROPN
ejpam-3424	118	11	.	.	PUNCT
ejpam-3424	119	1	j.	j.	PROPN
ejpam-3424	119	2	pure	pure	PROPN
ejpam-3424	119	3	appl	appl	PROPN
ejpam-3424	119	4	.	.	PROPN
ejpam-3424	119	5	math	math	PROPN
ejpam-3424	119	6	,	,	PUNCT
ejpam-3424	119	7	12	12	NUM
ejpam-3424	119	8	(	(	PUNCT
ejpam-3424	119	9	3	3	NUM
ejpam-3424	119	10	)	)	PUNCT
ejpam-3424	119	11	(	(	PUNCT
ejpam-3424	119	12	2019	2019	NUM
ejpam-3424	119	13	)	)	PUNCT
ejpam-3424	119	14	,	,	PUNCT
ejpam-3424	119	15	1069	1069	NUM
ejpam-3424	119	16	-	-	SYM
ejpam-3424	119	17	1081	1081	NUM
ejpam-3424	119	18	1076	1076	NUM
ejpam-3424	119	19	nk(m	nk(m	NOUN
ejpam-3424	119	20	)	)	PUNCT
ejpam-3424	119	21	nh(m	nh(m	ADP
ejpam-3424	119	22	)	)	PUNCT
ejpam-3424	119	23	lm−1	lm−1	PROPN
ejpam-3424	119	24	k	k	PROPN
ejpam-3424	119	25	,	,	PUNCT
ejpam-3424	119	26	h	h	NOUN
ejpam-3424	119	27	,	,	PUNCT
ejpam-3424	119	28	m−1	m−1	PROPN
ejpam-3424	119	29	+	+	PROPN
ejpam-3424	119	30	[	[	PUNCT
ejpam-3424	119	31	mk(n)−	mk(n)−	NOUN
ejpam-3424	119	32	nk(n)mh(m+	nk(n)mh(m+	NOUN
ejpam-3424	119	33	1	1	NUM
ejpam-3424	119	34	)	)	PUNCT
ejpam-3424	119	35	nh(m+	nh(m+	NUM
ejpam-3424	119	36	1	1	NUM
ejpam-3424	119	37	)	)	PUNCT
ejpam-3424	119	38	]	]	PUNCT
ejpam-3424	119	39	.	.	PUNCT
ejpam-3424	119	40	.	.	PUNCT
ejpam-3424	119	41	.	.	PUNCT
ejpam-3424	120	1	[	[	PUNCT
ejpam-3424	120	2	mk(m+	mk(m+	PROPN
ejpam-3424	120	3	1)−	1)−	PROPN
ejpam-3424	120	4	nk(m+	nk(m+	NOUN
ejpam-3424	120	5	1)mh(m+	1)mh(m+	NOUN
ejpam-3424	120	6	1	1	NUM
ejpam-3424	120	7	)	)	PUNCT
ejpam-3424	120	8	nh(m+	nh(m+	NUM
ejpam-3424	120	9	1	1	NUM
ejpam-3424	120	10	)	)	PUNCT
ejpam-3424	120	11	]	]	PUNCT
ejpam-3424	121	1	[	[	PUNCT
ejpam-3424	121	2	mk(m)−	mk(m)−	NOUN
ejpam-3424	121	3	nk(m)mh(m+	nk(m)mh(m+	NOUN
ejpam-3424	121	4	1	1	NUM
ejpam-3424	121	5	)	)	PUNCT
ejpam-3424	121	6	nh(m+	nh(m+	NUM
ejpam-3424	121	7	1	1	NUM
ejpam-3424	121	8	)	)	PUNCT
ejpam-3424	121	9	]	]	PUNCT
ejpam-3424	121	10	lmk	lmk	PROPN
ejpam-3424	121	11	,	,	PUNCT
ejpam-3424	121	12	h	h	NOUN
ejpam-3424	121	13	,	,	PUNCT
ejpam-3424	121	14	m−1	m−1	PROPN
ejpam-3424	121	15	.	.	PUNCT
ejpam-3424	122	1	by	by	ADP
ejpam-3424	122	2	definition	definition	NOUN
ejpam-3424	122	3	,	,	PUNCT
ejpam-3424	122	4	the	the	DET
ejpam-3424	122	5	last	last	ADJ
ejpam-3424	122	6	term	term	NOUN
ejpam-3424	122	7	is	be	AUX
ejpam-3424	122	8	equal	equal	ADJ
ejpam-3424	122	9	to	to	ADP
ejpam-3424	122	10	zero	zero	NUM
ejpam-3424	122	11	.	.	PUNCT
ejpam-3424	123	1	thus	thus	ADV
ejpam-3424	123	2	,	,	PUNCT
ejpam-3424	123	3	lmk	lmk	PROPN
ejpam-3424	123	4	,	,	PUNCT
ejpam-3424	123	5	h	h	NOUN
ejpam-3424	123	6	,	,	PUNCT
ejpam-3424	123	7	n	n	PROPN
ejpam-3424	123	8	=	=	NUM
ejpam-3424	123	9	n−m+1∑	n−m+1∑	PROPN
ejpam-3424	123	10	i=1	i=1	PROPN
ejpam-3424	124	1	[	[	PUNCT
ejpam-3424	124	2	mk(n+	mk(n+	PROPN
ejpam-3424	124	3	1)−	1)−	PROPN
ejpam-3424	124	4	nk(n+	nk(n+	PROPN
ejpam-3424	124	5	1)mh(m+	1)mh(m+	NOUN
ejpam-3424	124	6	1	1	NUM
ejpam-3424	124	7	)	)	PUNCT
ejpam-3424	124	8	nh(m+	nh(m+	NUM
ejpam-3424	124	9	1	1	NUM
ejpam-3424	124	10	)	)	PUNCT
ejpam-3424	124	11	]	]	PUNCT
ejpam-3424	124	12	.	.	PUNCT
ejpam-3424	124	13	.	.	PUNCT
ejpam-3424	124	14	.	.	PUNCT
ejpam-3424	125	1	[	[	PUNCT
ejpam-3424	125	2	mk(n−	mk(n−	ADJ
ejpam-3424	125	3	i+	i+	PUNCT
ejpam-3424	125	4	2)−	2)−	PROPN
ejpam-3424	125	5	nk(n−	nk(n−	PROPN
ejpam-3424	125	6	i+	i+	X
ejpam-3424	125	7	2)mh(m+	2)mh(m+	NOUN
ejpam-3424	125	8	1	1	NUM
ejpam-3424	125	9	)	)	PUNCT
ejpam-3424	125	10	nh(m+	nh(m+	NUM
ejpam-3424	125	11	1	1	NUM
ejpam-3424	125	12	)	)	PUNCT
ejpam-3424	125	13	]	]	PUNCT
ejpam-3424	126	1	nk(n−	nk(n−	PROPN
ejpam-3424	126	2	i+	i+	NUM
ejpam-3424	126	3	1	1	NUM
ejpam-3424	126	4	)	)	PUNCT
ejpam-3424	126	5	nh(m	nh(m	NOUN
ejpam-3424	126	6	)	)	PUNCT
ejpam-3424	126	7	lm−1	lm−1	PROPN
ejpam-3424	126	8	k	k	PROPN
ejpam-3424	126	9	,	,	PUNCT
ejpam-3424	126	10	h	h	NOUN
ejpam-3424	126	11	,	,	PUNCT
ejpam-3424	126	12	n−i	n−i	NOUN
ejpam-3424	126	13	where	where	SCONJ
ejpam-3424	126	14	[	[	PUNCT
ejpam-3424	126	15	mk(n+	mk(n+	PROPN
ejpam-3424	126	16	1)−	1)−	PROPN
ejpam-3424	126	17	nk(n+	nk(n+	PROPN
ejpam-3424	126	18	1)mh(m+	1)mh(m+	NOUN
ejpam-3424	126	19	1	1	NUM
ejpam-3424	126	20	)	)	PUNCT
ejpam-3424	126	21	nh(m+	nh(m+	NUM
ejpam-3424	126	22	1	1	NUM
ejpam-3424	126	23	)	)	PUNCT
ejpam-3424	126	24	]	]	PUNCT
ejpam-3424	127	1	=	=	PUNCT
ejpam-3424	127	2	1	1	X
ejpam-3424	127	3	.	.	NOUN
ejpam-3424	127	4	3	3	NUM
ejpam-3424	127	5	.	.	X
ejpam-3424	128	1	some	some	DET
ejpam-3424	128	2	explicit	explicit	ADJ
ejpam-3424	128	3	formulas	formula	NOUN
ejpam-3424	128	4	consider	consider	VERB
ejpam-3424	128	5	the	the	DET
ejpam-3424	128	6	generating	generate	VERB
ejpam-3424	128	7	function	function	NOUN
ejpam-3424	128	8	ψm(t	ψm(t	NOUN
ejpam-3424	128	9	)	)	PUNCT
ejpam-3424	128	10	for	for	ADP
ejpam-3424	128	11	tauber	tauber	PROPN
ejpam-3424	128	12	’s	’s	PART
ejpam-3424	128	13	generalized	generalize	VERB
ejpam-3424	128	14	stirling	stirling	NOUN
ejpam-3424	128	15	numbers	number	NOUN
ejpam-3424	128	16	of	of	ADP
ejpam-3424	128	17	the	the	DET
ejpam-3424	128	18	second	second	ADJ
ejpam-3424	128	19	kind	kind	NOUN
ejpam-3424	128	20	given	give	VERB
ejpam-3424	128	21	by	by	ADP
ejpam-3424	128	22	ψm(t	ψm(t	NOUN
ejpam-3424	128	23	)	)	PUNCT
ejpam-3424	128	24	=	=	PUNCT
ejpam-3424	129	1	∑	∑	PUNCT
ejpam-3424	129	2	n≥m	n≥m	NOUN
ejpam-3424	129	3	dm	dm	PROPN
ejpam-3424	129	4	k	k	NOUN
ejpam-3424	129	5	,	,	PUNCT
ejpam-3424	129	6	nt	not	PART
ejpam-3424	129	7	n	n	CCONJ
ejpam-3424	129	8	(	(	PUNCT
ejpam-3424	129	9	27	27	NUM
ejpam-3424	129	10	)	)	PUNCT
ejpam-3424	129	11	where	where	SCONJ
ejpam-3424	129	12	ψ0(t	ψ0(t	VERB
ejpam-3424	129	13	)	)	PUNCT
ejpam-3424	129	14	=	=	SYM
ejpam-3424	129	15	1	1	X
ejpam-3424	129	16	.	.	PUNCT
ejpam-3424	130	1	using	use	VERB
ejpam-3424	130	2	the	the	DET
ejpam-3424	130	3	recurrence	recurrence	NOUN
ejpam-3424	130	4	relation	relation	NOUN
ejpam-3424	130	5	in	in	ADP
ejpam-3424	130	6	(	(	PUNCT
ejpam-3424	130	7	7	7	NUM
ejpam-3424	130	8	)	)	PUNCT
ejpam-3424	130	9	,	,	PUNCT
ejpam-3424	130	10	we	we	PRON
ejpam-3424	130	11	have	have	VERB
ejpam-3424	130	12	ψm(t	ψm(t	NOUN
ejpam-3424	130	13	)	)	PUNCT
ejpam-3424	131	1	=	=	PUNCT
ejpam-3424	131	2	∑	∑	PUNCT
ejpam-3424	131	3	n≥m	n≥m	NOUN
ejpam-3424	131	4	{	{	PUNCT
ejpam-3424	131	5	−m(m+	−m(m+	SYM
ejpam-3424	131	6	1	1	NUM
ejpam-3424	131	7	)	)	PUNCT
ejpam-3424	131	8	n(m+	n(m+	NUM
ejpam-3424	131	9	1	1	NUM
ejpam-3424	131	10	)	)	PUNCT
ejpam-3424	131	11	dm	dm	PROPN
ejpam-3424	131	12	k	k	NOUN
ejpam-3424	131	13	,	,	PUNCT
ejpam-3424	131	14	n−1	n−1	PROPN
ejpam-3424	132	1	+	+	CCONJ
ejpam-3424	133	1	1	1	NUM
ejpam-3424	133	2	n(m+	n(m+	NUM
ejpam-3424	133	3	1	1	NUM
ejpam-3424	133	4	)	)	PUNCT
ejpam-3424	133	5	dm−1	dm−1	NOUN
ejpam-3424	133	6	k	k	NOUN
ejpam-3424	133	7	,	,	PUNCT
ejpam-3424	133	8	n−1	n−1	PROPN
ejpam-3424	133	9	}	}	PUNCT
ejpam-3424	133	10	tn	tn	NOUN
ejpam-3424	134	1	=	=	SYM
ejpam-3424	134	2	−m(m+	−m(m+	ADP
ejpam-3424	134	3	1	1	X
ejpam-3424	134	4	)	)	PUNCT
ejpam-3424	134	5	n(m+	n(m+	NUM
ejpam-3424	134	6	1	1	NUM
ejpam-3424	134	7	)	)	PUNCT
ejpam-3424	134	8	t	t	NOUN
ejpam-3424	134	9	∑	∑	PROPN
ejpam-3424	134	10	n≥m	n≥m	NOUN
ejpam-3424	134	11	dm	dm	PROPN
ejpam-3424	134	12	k	k	NOUN
ejpam-3424	134	13	,	,	PUNCT
ejpam-3424	134	14	n−1	n−1	PROPN
ejpam-3424	134	15	t	t	PROPN
ejpam-3424	134	16	n−1	n−1	PROPN
ejpam-3424	135	1	+	+	NUM
ejpam-3424	135	2	t	t	PROPN
ejpam-3424	135	3	n(m+	n(m+	NOUN
ejpam-3424	135	4	1	1	NUM
ejpam-3424	135	5	)	)	PUNCT
ejpam-3424	135	6	∑	∑	PUNCT
ejpam-3424	135	7	n≥m	n≥m	NOUN
ejpam-3424	135	8	dm−1	dm−1	PROPN
ejpam-3424	135	9	k	k	PROPN
ejpam-3424	135	10	,	,	PUNCT
ejpam-3424	135	11	n−1	n−1	PROPN
ejpam-3424	135	12	t	t	NOUN
ejpam-3424	135	13	n−1	n−1	NOUN
ejpam-3424	135	14	=	=	PUNCT
ejpam-3424	135	15	−m(m+	−m(m+	ADP
ejpam-3424	135	16	1	1	X
ejpam-3424	135	17	)	)	PUNCT
ejpam-3424	135	18	n(m+	n(m+	NUM
ejpam-3424	135	19	1	1	NUM
ejpam-3424	135	20	)	)	PUNCT
ejpam-3424	135	21	tψm(t	tψm(t	NOUN
ejpam-3424	135	22	)	)	PUNCT
ejpam-3424	136	1	+	+	NUM
ejpam-3424	136	2	t	t	NOUN
ejpam-3424	136	3	n(m+	n(m+	VERB
ejpam-3424	136	4	1	1	NUM
ejpam-3424	136	5	)	)	PUNCT
ejpam-3424	136	6	ψm−1(t	ψm−1(t	ADJ
ejpam-3424	136	7	)	)	PUNCT
ejpam-3424	136	8	.	.	PUNCT
ejpam-3424	137	1	hence	hence	ADV
ejpam-3424	137	2	,	,	PUNCT
ejpam-3424	137	3	ψm(t	ψm(t	NOUN
ejpam-3424	137	4	)	)	PUNCT
ejpam-3424	138	1	=	=	SYM
ejpam-3424	138	2	t	t	NOUN
ejpam-3424	138	3	n(m+	n(m+	NOUN
ejpam-3424	138	4	1	1	NUM
ejpam-3424	138	5	+	+	NUM
ejpam-3424	138	6	m(m+	m(m+	VERB
ejpam-3424	138	7	1)t	1)t	PROPN
ejpam-3424	138	8	ψm−1(t	ψm−1(t	PROPN
ejpam-3424	138	9	)	)	PUNCT
ejpam-3424	138	10	.	.	PUNCT
ejpam-3424	139	1	by	by	ADP
ejpam-3424	139	2	backward	backward	ADJ
ejpam-3424	139	3	substitution	substitution	NOUN
ejpam-3424	139	4	,	,	PUNCT
ejpam-3424	139	5	we	we	PRON
ejpam-3424	139	6	have	have	VERB
ejpam-3424	139	7	ψm(t	ψm(t	NOUN
ejpam-3424	139	8	)	)	PUNCT
ejpam-3424	140	1	=	=	SYM
ejpam-3424	140	2	tm∏m−1	tm∏m−1	NOUN
ejpam-3424	140	3	i=0	i=0	PROPN
ejpam-3424	140	4	[	[	X
ejpam-3424	140	5	n(m+	n(m+	NOUN
ejpam-3424	140	6	1−	1−	NUM
ejpam-3424	140	7	i	i	NOUN
ejpam-3424	140	8	)	)	PUNCT
ejpam-3424	141	1	+	+	PUNCT
ejpam-3424	141	2	m(m+	m(m+	X
ejpam-3424	141	3	1−	1−	NUM
ejpam-3424	141	4	i)t	i)t	NOUN
ejpam-3424	141	5	]	]	PUNCT
ejpam-3424	141	6	.	.	PUNCT
ejpam-3424	142	1	this	this	DET
ejpam-3424	142	2	result	result	NOUN
ejpam-3424	142	3	is	be	AUX
ejpam-3424	142	4	stated	state	VERB
ejpam-3424	142	5	formally	formally	ADV
ejpam-3424	142	6	in	in	ADP
ejpam-3424	142	7	the	the	DET
ejpam-3424	142	8	following	following	NOUN
ejpam-3424	142	9	theorem	theorem	PROPN
ejpam-3424	142	10	.	.	PROPN
ejpam-3424	142	11	r.	r.	PROPN
ejpam-3424	142	12	corcino	corcino	PROPN
ejpam-3424	142	13	,	,	PUNCT
ejpam-3424	142	14	c.	c.	PROPN
ejpam-3424	142	15	corcino	corcino	PROPN
ejpam-3424	142	16	,	,	PUNCT
ejpam-3424	142	17	g.	g.	PROPN
ejpam-3424	142	18	rama	rama	PROPN
ejpam-3424	142	19	/	/	SYM
ejpam-3424	142	20	eur	eur	PROPN
ejpam-3424	142	21	.	.	PUNCT
ejpam-3424	143	1	j.	j.	PROPN
ejpam-3424	143	2	pure	pure	PROPN
ejpam-3424	143	3	appl	appl	PROPN
ejpam-3424	143	4	.	.	PROPN
ejpam-3424	143	5	math	math	PROPN
ejpam-3424	143	6	,	,	PUNCT
ejpam-3424	143	7	12	12	NUM
ejpam-3424	143	8	(	(	PUNCT
ejpam-3424	143	9	3	3	NUM
ejpam-3424	143	10	)	)	PUNCT
ejpam-3424	143	11	(	(	PUNCT
ejpam-3424	143	12	2019	2019	NUM
ejpam-3424	143	13	)	)	PUNCT
ejpam-3424	143	14	,	,	PUNCT
ejpam-3424	143	15	1069	1069	NUM
ejpam-3424	143	16	-	-	SYM
ejpam-3424	143	17	1081	1081	NUM
ejpam-3424	143	18	1077	1077	NUM
ejpam-3424	143	19	theorem	theorem	VERB
ejpam-3424	143	20	3.1	3.1	NUM
ejpam-3424	143	21	.	.	PUNCT
ejpam-3424	144	1	the	the	DET
ejpam-3424	144	2	rational	rational	ADJ
ejpam-3424	144	3	generating	generating	NOUN
ejpam-3424	144	4	function	function	NOUN
ejpam-3424	144	5	for	for	ADP
ejpam-3424	144	6	tauber	tauber	PROPN
ejpam-3424	144	7	’s	’s	PART
ejpam-3424	144	8	generalized	generalize	VERB
ejpam-3424	144	9	stirling	stirling	NOUN
ejpam-3424	144	10	numbers	number	NOUN
ejpam-3424	144	11	of	of	ADP
ejpam-3424	144	12	the	the	DET
ejpam-3424	144	13	second	second	ADJ
ejpam-3424	144	14	kind	kind	NOUN
ejpam-3424	144	15	is	be	AUX
ejpam-3424	144	16	given	give	VERB
ejpam-3424	144	17	by∑	by∑	ADJ
ejpam-3424	144	18	n≥m	n≥m	NOUN
ejpam-3424	144	19	dm	dm	PROPN
ejpam-3424	144	20	k	k	NOUN
ejpam-3424	144	21	,	,	PUNCT
ejpam-3424	144	22	nt	not	PART
ejpam-3424	144	23	n	n	NOUN
ejpam-3424	144	24	=	=	NOUN
ejpam-3424	144	25	tm∏m−1	tm∏m−1	NOUN
ejpam-3424	144	26	i=0	i=0	PROPN
ejpam-3424	145	1	[	[	X
ejpam-3424	145	2	n(m+	n(m+	NOUN
ejpam-3424	145	3	1−	1−	NUM
ejpam-3424	145	4	i	i	NOUN
ejpam-3424	145	5	)	)	PUNCT
ejpam-3424	146	1	+	+	PUNCT
ejpam-3424	146	2	m(m+	m(m+	X
ejpam-3424	146	3	1−	1−	NUM
ejpam-3424	146	4	i)t	i)t	NOUN
ejpam-3424	146	5	]	]	PUNCT
ejpam-3424	146	6	.	.	PUNCT
ejpam-3424	147	1	as	as	ADP
ejpam-3424	147	2	a	a	DET
ejpam-3424	147	3	consequence	consequence	NOUN
ejpam-3424	147	4	of	of	ADP
ejpam-3424	147	5	this	this	DET
ejpam-3424	147	6	rational	rational	ADJ
ejpam-3424	147	7	generating	generating	NOUN
ejpam-3424	147	8	function	function	NOUN
ejpam-3424	147	9	,	,	PUNCT
ejpam-3424	147	10	we	we	PRON
ejpam-3424	147	11	have	have	VERB
ejpam-3424	147	12	the	the	DET
ejpam-3424	147	13	following	follow	VERB
ejpam-3424	147	14	explicit	explicit	ADJ
ejpam-3424	147	15	formula	formula	NOUN
ejpam-3424	147	16	in	in	ADP
ejpam-3424	147	17	symmetric	symmetric	ADJ
ejpam-3424	147	18	function	function	NOUN
ejpam-3424	147	19	form	form	NOUN
ejpam-3424	147	20	.	.	PUNCT
ejpam-3424	148	1	theorem	theorem	VERB
ejpam-3424	148	2	3.2	3.2	NUM
ejpam-3424	148	3	.	.	PUNCT
ejpam-3424	149	1	tauber	tauber	PROPN
ejpam-3424	149	2	’s	’s	PART
ejpam-3424	149	3	generalized	generalize	VERB
ejpam-3424	149	4	stirling	stirling	NOUN
ejpam-3424	149	5	numbers	number	NOUN
ejpam-3424	149	6	of	of	ADP
ejpam-3424	149	7	the	the	DET
ejpam-3424	149	8	second	second	ADJ
ejpam-3424	149	9	kind	kind	NOUN
ejpam-3424	149	10	are	be	AUX
ejpam-3424	149	11	given	give	VERB
ejpam-3424	149	12	by	by	ADP
ejpam-3424	149	13	dm	dm	PROPN
ejpam-3424	149	14	k	k	PROPN
ejpam-3424	149	15	,	,	PUNCT
ejpam-3424	149	16	n	n	PROPN
ejpam-3424	149	17	=	=	SYM
ejpam-3424	149	18	1∏m−1	1∏m−1	NUM
ejpam-3424	149	19	i=0	i=0	PROPN
ejpam-3424	149	20	n(m+	n(m+	X
ejpam-3424	149	21	1−	1−	NUM
ejpam-3424	149	22	i	i	NOUN
ejpam-3424	149	23	)	)	PUNCT
ejpam-3424	149	24	∑	∑	PUNCT
ejpam-3424	149	25	s1+s2+	s1+s2+	ADV
ejpam-3424	149	26	...	...	SYM
ejpam-3424	149	27	+sm	+sm	X
ejpam-3424	149	28	=	=	SYM
ejpam-3424	149	29	n−m	n−m	PROPN
ejpam-3424	149	30	m∏	m∏	PROPN
ejpam-3424	149	31	i=0	i=0	PROPN
ejpam-3424	150	1	[	[	PUNCT
ejpam-3424	150	2	−m(m+	−m(m+	X
ejpam-3424	150	3	1−	1−	NUM
ejpam-3424	150	4	i	i	NOUN
ejpam-3424	150	5	)	)	PUNCT
ejpam-3424	150	6	n(m+	n(m+	X
ejpam-3424	150	7	1−	1−	NUM
ejpam-3424	150	8	i	i	NOUN
ejpam-3424	150	9	)	)	PUNCT
ejpam-3424	150	10	]	]	X
ejpam-3424	150	11	si	si	X
ejpam-3424	150	12	.	.	PUNCT
ejpam-3424	150	13	proof	proof	NOUN
ejpam-3424	150	14	.	.	PUNCT
ejpam-3424	151	1	using	use	VERB
ejpam-3424	151	2	the	the	DET
ejpam-3424	151	3	rational	rational	ADJ
ejpam-3424	151	4	generating	generating	NOUN
ejpam-3424	151	5	function	function	NOUN
ejpam-3424	151	6	in	in	ADP
ejpam-3424	151	7	theorem	theorem	NOUN
ejpam-3424	151	8	3.1	3.1	NUM
ejpam-3424	151	9	,	,	PUNCT
ejpam-3424	151	10	we	we	PRON
ejpam-3424	151	11	get∑	get∑	AUX
ejpam-3424	151	12	n≥m	n≥m	NOUN
ejpam-3424	151	13	dm	dm	PROPN
ejpam-3424	151	14	k	k	NOUN
ejpam-3424	151	15	,	,	PUNCT
ejpam-3424	151	16	nt	not	PART
ejpam-3424	151	17	n	n	NOUN
ejpam-3424	151	18	=	=	NOUN
ejpam-3424	151	19	tm∏m−1	tm∏m−1	NOUN
ejpam-3424	151	20	i=0	i=0	PROPN
ejpam-3424	152	1	[	[	X
ejpam-3424	152	2	n(m+	n(m+	NOUN
ejpam-3424	152	3	1−	1−	NUM
ejpam-3424	152	4	i	i	NOUN
ejpam-3424	152	5	)	)	PUNCT
ejpam-3424	153	1	+	+	PUNCT
ejpam-3424	153	2	m(m+	m(m+	X
ejpam-3424	153	3	1−	1−	NUM
ejpam-3424	153	4	i)t	i)t	NOUN
ejpam-3424	153	5	]	]	PUNCT
ejpam-3424	153	6	=	=	SYM
ejpam-3424	153	7	tm∏m−1	tm∏m−1	NOUN
ejpam-3424	153	8	i=0	i=0	PROPN
ejpam-3424	153	9	n(m+	n(m+	X
ejpam-3424	153	10	1−	1−	NUM
ejpam-3424	153	11	i	i	NOUN
ejpam-3424	153	12	)	)	PUNCT
ejpam-3424	154	1	m−1∏	m−1∏	PROPN
ejpam-3424	154	2	i=0	i=0	PROPN
ejpam-3424	154	3	1	1	NUM
ejpam-3424	154	4	[	[	SYM
ejpam-3424	154	5	1−	1−	NUM
ejpam-3424	154	6	(	(	PUNCT
ejpam-3424	154	7	−m(m+1−i	−m(m+1−i	NOUN
ejpam-3424	154	8	)	)	PUNCT
ejpam-3424	154	9	n(m+1−i	n(m+1−i	PROPN
ejpam-3424	154	10	)	)	PUNCT
ejpam-3424	154	11	)	)	PUNCT
ejpam-3424	155	1	t	t	X
ejpam-3424	155	2	]	]	PUNCT
ejpam-3424	156	1	=	=	PUNCT
ejpam-3424	156	2	tm∏m−1	tm∏m−1	NOUN
ejpam-3424	156	3	i=0	i=0	PROPN
ejpam-3424	156	4	n(m+	n(m+	X
ejpam-3424	156	5	1−	1−	NUM
ejpam-3424	156	6	i	i	NOUN
ejpam-3424	156	7	)	)	PUNCT
ejpam-3424	156	8	m−1∏	m−1∏	PROPN
ejpam-3424	156	9	i=0	i=0	PROPN
ejpam-3424	156	10	∑	∑	PUNCT
ejpam-3424	156	11	n≥0	n≥0	PROPN
ejpam-3424	156	12	(	(	PUNCT
ejpam-3424	156	13	−m(m+	−m(m+	X
ejpam-3424	156	14	1−	1−	NUM
ejpam-3424	156	15	i	i	NOUN
ejpam-3424	156	16	)	)	PUNCT
ejpam-3424	156	17	n(m+	n(m+	X
ejpam-3424	156	18	1−	1−	NUM
ejpam-3424	156	19	i	i	NOUN
ejpam-3424	156	20	)	)	PUNCT
ejpam-3424	156	21	)	)	PUNCT
ejpam-3424	156	22	n	n	PRON
ejpam-3424	156	23	tn	tn	NOUN
ejpam-3424	156	24	=	=	SYM
ejpam-3424	156	25	tm∏m−1	tm∏m−1	NOUN
ejpam-3424	156	26	i=0	i=0	PROPN
ejpam-3424	156	27	n(m+	n(m+	X
ejpam-3424	156	28	1−	1−	NUM
ejpam-3424	156	29	i	i	NOUN
ejpam-3424	156	30	)	)	PUNCT
ejpam-3424	156	31	∑	∑	PUNCT
ejpam-3424	156	32	n≥m	n≥m	INTJ
ejpam-3424	156	33	∑	∑	PUNCT
ejpam-3424	156	34	s1+s2+	s1+s2+	ADV
ejpam-3424	156	35	...	...	SYM
ejpam-3424	156	36	+sm	+sm	X
ejpam-3424	156	37	=	=	SYM
ejpam-3424	156	38	n−m	n−m	PROPN
ejpam-3424	156	39	m∏	m∏	PROPN
ejpam-3424	156	40	i=0	i=0	PROPN
ejpam-3424	156	41	[	[	PUNCT
ejpam-3424	156	42	−m(m+	−m(m+	X
ejpam-3424	156	43	1−	1−	NUM
ejpam-3424	156	44	i	i	NOUN
ejpam-3424	156	45	)	)	PUNCT
ejpam-3424	156	46	n(m+	n(m+	X
ejpam-3424	156	47	1−	1−	NUM
ejpam-3424	156	48	i	i	NOUN
ejpam-3424	156	49	)	)	PUNCT
ejpam-3424	156	50	]	]	PUNCT
ejpam-3424	156	51	si	si	PROPN
ejpam-3424	156	52	tsi	tsi	PROPN
ejpam-3424	156	53	=	=	PUNCT
ejpam-3424	156	54	∑	∑	PROPN
ejpam-3424	156	55	n≥m	n≥m	NOUN
ejpam-3424	156	56	{	{	PUNCT
ejpam-3424	156	57	tm∏m−1	tm∏m−1	NOUN
ejpam-3424	156	58	i=0	i=0	PROPN
ejpam-3424	156	59	n(m+	n(m+	X
ejpam-3424	156	60	1−	1−	NUM
ejpam-3424	156	61	i	i	NOUN
ejpam-3424	156	62	)	)	PUNCT
ejpam-3424	156	63	∑	∑	PUNCT
ejpam-3424	156	64	s1+s2+	s1+s2+	ADV
ejpam-3424	156	65	...	...	SYM
ejpam-3424	156	66	+sm	+sm	X
ejpam-3424	156	67	=	=	SYM
ejpam-3424	156	68	n−m	n−m	PROPN
ejpam-3424	156	69	m∏	m∏	PROPN
ejpam-3424	156	70	i=0	i=0	PROPN
ejpam-3424	156	71	[	[	PUNCT
ejpam-3424	156	72	−m(m+	−m(m+	X
ejpam-3424	156	73	1−	1−	NUM
ejpam-3424	156	74	i	i	NOUN
ejpam-3424	156	75	)	)	PUNCT
ejpam-3424	156	76	n(m+	n(m+	X
ejpam-3424	156	77	1−	1−	NUM
ejpam-3424	156	78	i	i	NOUN
ejpam-3424	156	79	)	)	PUNCT
ejpam-3424	156	80	]	]	PUNCT
ejpam-3424	156	81	si	si	X
ejpam-3424	156	82	}	}	PUNCT
ejpam-3424	156	83	tn	tn	PROPN
ejpam-3424	156	84	comparing	compare	VERB
ejpam-3424	156	85	coefficients	coefficient	NOUN
ejpam-3424	156	86	of	of	ADP
ejpam-3424	156	87	tn	tn	NOUN
ejpam-3424	156	88	completes	complete	VERB
ejpam-3424	156	89	the	the	DET
ejpam-3424	156	90	proof	proof	NOUN
ejpam-3424	156	91	of	of	ADP
ejpam-3424	156	92	the	the	DET
ejpam-3424	156	93	theorem	theorem	NOUN
ejpam-3424	156	94	.	.	PUNCT
ejpam-3424	157	1	one	one	NUM
ejpam-3424	157	2	of	of	ADP
ejpam-3424	157	3	the	the	DET
ejpam-3424	157	4	objectives	objective	NOUN
ejpam-3424	157	5	of	of	ADP
ejpam-3424	157	6	this	this	DET
ejpam-3424	157	7	study	study	NOUN
ejpam-3424	157	8	is	be	AUX
ejpam-3424	157	9	to	to	PART
ejpam-3424	157	10	establish	establish	VERB
ejpam-3424	157	11	a	a	DET
ejpam-3424	157	12	new	new	ADJ
ejpam-3424	157	13	explicit	explicit	ADJ
ejpam-3424	157	14	formula	formula	NOUN
ejpam-3424	157	15	for	for	ADP
ejpam-3424	157	16	tauber	tauber	PROPN
ejpam-3424	157	17	’s	’s	PART
ejpam-3424	157	18	generalized	generalize	VERB
ejpam-3424	157	19	bell	bell	NOUN
ejpam-3424	157	20	numbers	number	NOUN
ejpam-3424	157	21	,	,	PUNCT
ejpam-3424	157	22	which	which	PRON
ejpam-3424	157	23	is	be	AUX
ejpam-3424	157	24	analogous	analogous	ADJ
ejpam-3424	157	25	to	to	ADP
ejpam-3424	157	26	the	the	DET
ejpam-3424	157	27	qi	qi	NOUN
ejpam-3424	157	28	formula	formula	NOUN
ejpam-3424	157	29	.	.	PUNCT
ejpam-3424	158	1	to	to	PART
ejpam-3424	158	2	derive	derive	VERB
ejpam-3424	158	3	the	the	DET
ejpam-3424	158	4	desired	desire	VERB
ejpam-3424	158	5	formula	formula	NOUN
ejpam-3424	158	6	,	,	PUNCT
ejpam-3424	158	7	we	we	PRON
ejpam-3424	158	8	need	need	VERB
ejpam-3424	158	9	to	to	PART
ejpam-3424	158	10	establish	establish	VERB
ejpam-3424	158	11	the	the	DET
ejpam-3424	158	12	following	follow	VERB
ejpam-3424	158	13	relations	relation	NOUN
ejpam-3424	158	14	.	.	PUNCT
ejpam-3424	159	1	theorem	theorem	VERB
ejpam-3424	159	2	3.3	3.3	NUM
ejpam-3424	159	3	.	.	PUNCT
ejpam-3424	160	1	tauber	tauber	PROPN
ejpam-3424	160	2	’s	’s	PART
ejpam-3424	160	3	generalized	generalize	VERB
ejpam-3424	160	4	stirling	stirling	NOUN
ejpam-3424	160	5	numbers	number	NOUN
ejpam-3424	160	6	of	of	ADP
ejpam-3424	160	7	the	the	DET
ejpam-3424	160	8	first	first	ADJ
ejpam-3424	160	9	and	and	CCONJ
ejpam-3424	160	10	second	second	ADJ
ejpam-3424	160	11	kind	kind	NOUN
ejpam-3424	160	12	satisfy	satisfy	VERB
ejpam-3424	160	13	the	the	DET
ejpam-3424	160	14	following	follow	VERB
ejpam-3424	160	15	orthogonality	orthogonality	NOUN
ejpam-3424	160	16	relation	relation	NOUN
ejpam-3424	160	17	for	for	ADP
ejpam-3424	160	18	a	a	DET
ejpam-3424	160	19	given	give	VERB
ejpam-3424	160	20	sequence	sequence	NOUN
ejpam-3424	160	21	of	of	ADP
ejpam-3424	160	22	polynomials	polynomial	NOUN
ejpam-3424	160	23	qk(x	qk(x	NOUN
ejpam-3424	160	24	,	,	PUNCT
ejpam-3424	160	25	n	n	CCONJ
ejpam-3424	160	26	)	)	PUNCT
ejpam-3424	160	27	,	,	PUNCT
ejpam-3424	160	28	n∑	n∑	NOUN
ejpam-3424	160	29	m	m	PRON
ejpam-3424	160	30	=	=	NOUN
ejpam-3424	160	31	s	s	X
ejpam-3424	160	32	c	c	NOUN
ejpam-3424	160	33	m	m	VERB
ejpam-3424	160	34	k	k	NOUN
ejpam-3424	160	35	,	,	PUNCT
ejpam-3424	160	36	nd	nd	NOUN
ejpam-3424	160	37	s	s	X
ejpam-3424	160	38	k	k	NOUN
ejpam-3424	160	39	,	,	PUNCT
ejpam-3424	160	40	m	m	VERB
ejpam-3424	160	41	=	=	SYM
ejpam-3424	160	42	n∑	n∑	NOUN
ejpam-3424	160	43	m	m	PROPN
ejpam-3424	160	44	=	=	NOUN
ejpam-3424	160	45	s	s	X
ejpam-3424	160	46	d	d	NOUN
ejpam-3424	160	47	m	m	VERB
ejpam-3424	160	48	k	k	NOUN
ejpam-3424	160	49	,	,	PUNCT
ejpam-3424	160	50	nc	nc	PROPN
ejpam-3424	160	51	s	s	PROPN
ejpam-3424	160	52	k	k	PROPN
ejpam-3424	160	53	,	,	PUNCT
ejpam-3424	160	54	m	m	VERB
ejpam-3424	160	55	=	=	NOUN
ejpam-3424	160	56	δsn	δsn	NOUN
ejpam-3424	160	57	=	=	PUNCT
ejpam-3424	160	58	{	{	PUNCT
ejpam-3424	160	59	0	0	NUM
ejpam-3424	160	60	,	,	PUNCT
ejpam-3424	160	61	if	if	SCONJ
ejpam-3424	160	62	n	n	PROPN
ejpam-3424	160	63	6=	6=	SYM
ejpam-3424	160	64	s	s	ADP
ejpam-3424	160	65	1	1	NUM
ejpam-3424	160	66	,	,	PUNCT
ejpam-3424	160	67	if	if	SCONJ
ejpam-3424	160	68	n	n	ADV
ejpam-3424	160	69	=	=	SYM
ejpam-3424	160	70	s	s	VERB
ejpam-3424	160	71	where	where	SCONJ
ejpam-3424	160	72	k	k	NOUN
ejpam-3424	160	73	=	=	SYM
ejpam-3424	160	74	1	1	NUM
ejpam-3424	160	75	,	,	PUNCT
ejpam-3424	160	76	2	2	NUM
ejpam-3424	160	77	.	.	PUNCT
ejpam-3424	160	78	r.	r.	PROPN
ejpam-3424	160	79	corcino	corcino	PROPN
ejpam-3424	160	80	,	,	PUNCT
ejpam-3424	160	81	c.	c.	PROPN
ejpam-3424	160	82	corcino	corcino	PROPN
ejpam-3424	160	83	,	,	PUNCT
ejpam-3424	160	84	g.	g.	PROPN
ejpam-3424	160	85	rama	rama	PROPN
ejpam-3424	160	86	/	/	SYM
ejpam-3424	160	87	eur	eur	PROPN
ejpam-3424	160	88	.	.	PUNCT
ejpam-3424	161	1	j.	j.	PROPN
ejpam-3424	161	2	pure	pure	PROPN
ejpam-3424	161	3	appl	appl	PROPN
ejpam-3424	161	4	.	.	PROPN
ejpam-3424	161	5	math	math	PROPN
ejpam-3424	161	6	,	,	PUNCT
ejpam-3424	161	7	12	12	NUM
ejpam-3424	161	8	(	(	PUNCT
ejpam-3424	161	9	3	3	NUM
ejpam-3424	161	10	)	)	PUNCT
ejpam-3424	161	11	(	(	PUNCT
ejpam-3424	161	12	2019	2019	NUM
ejpam-3424	161	13	)	)	PUNCT
ejpam-3424	161	14	,	,	PUNCT
ejpam-3424	161	15	1069	1069	NUM
ejpam-3424	161	16	-	-	SYM
ejpam-3424	161	17	1081	1081	NUM
ejpam-3424	161	18	1078	1078	NUM
ejpam-3424	161	19	proof	proof	NOUN
ejpam-3424	161	20	.	.	PUNCT
ejpam-3424	162	1	note	note	VERB
ejpam-3424	162	2	that	that	SCONJ
ejpam-3424	162	3	(	(	PUNCT
ejpam-3424	162	4	5	5	X
ejpam-3424	162	5	)	)	PUNCT
ejpam-3424	162	6	can	can	AUX
ejpam-3424	162	7	be	be	AUX
ejpam-3424	162	8	written	write	VERB
ejpam-3424	162	9	as	as	ADP
ejpam-3424	162	10	xm	xm	PROPN
ejpam-3424	162	11	=	=	PUNCT
ejpam-3424	162	12	m∑	m∑	NOUN
ejpam-3424	162	13	s=0	s=0	PROPN
ejpam-3424	163	1	d	d	NOUN
ejpam-3424	163	2	s	s	PROPN
ejpam-3424	163	3	k	k	NOUN
ejpam-3424	163	4	,	,	PUNCT
ejpam-3424	163	5	mqk(x	mqk(x	PROPN
ejpam-3424	163	6	,	,	PUNCT
ejpam-3424	163	7	s	s	NOUN
ejpam-3424	163	8	)	)	PUNCT
ejpam-3424	163	9	.	.	PUNCT
ejpam-3424	164	1	(	(	PUNCT
ejpam-3424	164	2	28	28	NUM
ejpam-3424	164	3	)	)	PUNCT
ejpam-3424	164	4	substitute	substitute	NOUN
ejpam-3424	164	5	(	(	PUNCT
ejpam-3424	164	6	28	28	NUM
ejpam-3424	164	7	)	)	PUNCT
ejpam-3424	164	8	into	into	ADP
ejpam-3424	164	9	(	(	PUNCT
ejpam-3424	164	10	4	4	NUM
ejpam-3424	164	11	)	)	PUNCT
ejpam-3424	164	12	,	,	PUNCT
ejpam-3424	164	13	then	then	ADV
ejpam-3424	164	14	qk(x	qk(x	NOUN
ejpam-3424	164	15	,	,	PUNCT
ejpam-3424	164	16	n	n	CCONJ
ejpam-3424	164	17	)	)	PUNCT
ejpam-3424	164	18	=	=	SYM
ejpam-3424	165	1	n∑	n∑	PROPN
ejpam-3424	165	2	m=0	m=0	PROPN
ejpam-3424	166	1	c	c	PROPN
ejpam-3424	166	2	m	m	VERB
ejpam-3424	166	3	k	k	NOUN
ejpam-3424	166	4	,	,	PUNCT
ejpam-3424	166	5	nx	nx	PROPN
ejpam-3424	166	6	m	m	NOUN
ejpam-3424	166	7	=	=	SYM
ejpam-3424	166	8	n∑	n∑	PROPN
ejpam-3424	166	9	m=0	m=0	PROPN
ejpam-3424	166	10	c	c	PROPN
ejpam-3424	166	11	m	m	VERB
ejpam-3424	166	12	k	k	NOUN
ejpam-3424	166	13	,	,	PUNCT
ejpam-3424	166	14	n	n	PRON
ejpam-3424	166	15	m∑	m∑	X
ejpam-3424	166	16	s=0	s=0	PROPN
ejpam-3424	167	1	d	d	X
ejpam-3424	167	2	s	s	PROPN
ejpam-3424	167	3	k	k	NOUN
ejpam-3424	167	4	,	,	PUNCT
ejpam-3424	167	5	mqk(x	mqk(x	PROPN
ejpam-3424	167	6	,	,	PUNCT
ejpam-3424	167	7	s	s	PART
ejpam-3424	167	8	)	)	PUNCT
ejpam-3424	167	9	=	=	SYM
ejpam-3424	167	10	n∑	n∑	PROPN
ejpam-3424	167	11	m=0	m=0	PROPN
ejpam-3424	167	12	m∑	m∑	VERB
ejpam-3424	167	13	s=0	s=0	PROPN
ejpam-3424	167	14	c	c	NOUN
ejpam-3424	167	15	m	m	VERB
ejpam-3424	167	16	k	k	ADJ
ejpam-3424	167	17	,	,	PUNCT
ejpam-3424	167	18	nd	nd	NOUN
ejpam-3424	167	19	s	s	X
ejpam-3424	167	20	k	k	NOUN
ejpam-3424	167	21	,	,	PUNCT
ejpam-3424	167	22	mqk(x	mqk(x	PROPN
ejpam-3424	167	23	,	,	PUNCT
ejpam-3424	167	24	s	s	PART
ejpam-3424	167	25	)	)	PUNCT
ejpam-3424	167	26	=	=	SYM
ejpam-3424	167	27	n∑	n∑	PROPN
ejpam-3424	167	28	s=0	s=0	PROPN
ejpam-3424	167	29	{	{	PUNCT
ejpam-3424	167	30	n∑	n∑	NOUN
ejpam-3424	167	31	m	m	PROPN
ejpam-3424	167	32	=	=	NOUN
ejpam-3424	167	33	s	s	X
ejpam-3424	167	34	c	c	NOUN
ejpam-3424	167	35	m	m	VERB
ejpam-3424	167	36	k	k	NOUN
ejpam-3424	167	37	,	,	PUNCT
ejpam-3424	167	38	nd	nd	NOUN
ejpam-3424	167	39	s	s	X
ejpam-3424	167	40	k	k	NOUN
ejpam-3424	167	41	,	,	PUNCT
ejpam-3424	167	42	m	m	VERB
ejpam-3424	167	43	}	}	PUNCT
ejpam-3424	167	44	qk(x	qk(x	NOUN
ejpam-3424	167	45	,	,	PUNCT
ejpam-3424	167	46	s	s	PART
ejpam-3424	167	47	)	)	PUNCT
ejpam-3424	167	48	.	.	PUNCT
ejpam-3424	168	1	thus	thus	ADV
ejpam-3424	168	2	,	,	PUNCT
ejpam-3424	168	3	n∑	n∑	PROPN
ejpam-3424	168	4	m	m	PROPN
ejpam-3424	168	5	=	=	NOUN
ejpam-3424	168	6	s	s	X
ejpam-3424	168	7	c	c	NOUN
ejpam-3424	168	8	m	m	VERB
ejpam-3424	168	9	k	k	NOUN
ejpam-3424	168	10	,	,	PUNCT
ejpam-3424	168	11	nd	nd	NOUN
ejpam-3424	168	12	s	s	X
ejpam-3424	168	13	k	k	NOUN
ejpam-3424	168	14	,	,	PUNCT
ejpam-3424	168	15	m	m	VERB
ejpam-3424	168	16	=	=	NOUN
ejpam-3424	168	17	δsn	δsn	NOUN
ejpam-3424	168	18	=	=	PUNCT
ejpam-3424	168	19	{	{	PUNCT
ejpam-3424	168	20	0	0	NUM
ejpam-3424	168	21	,	,	PUNCT
ejpam-3424	168	22	if	if	SCONJ
ejpam-3424	168	23	n	n	PROPN
ejpam-3424	168	24	6=	6=	SYM
ejpam-3424	168	25	s	s	ADP
ejpam-3424	168	26	1	1	NUM
ejpam-3424	168	27	,	,	PUNCT
ejpam-3424	168	28	if	if	SCONJ
ejpam-3424	168	29	n	n	PROPN
ejpam-3424	168	30	=	=	SYM
ejpam-3424	168	31	s	s	PROPN
ejpam-3424	168	32	.	.	PUNCT
ejpam-3424	169	1	similarly	similarly	ADV
ejpam-3424	169	2	,	,	PUNCT
ejpam-3424	169	3	(	(	PUNCT
ejpam-3424	169	4	4	4	X
ejpam-3424	169	5	)	)	PUNCT
ejpam-3424	169	6	can	can	AUX
ejpam-3424	169	7	be	be	AUX
ejpam-3424	169	8	written	write	VERB
ejpam-3424	169	9	as	as	ADP
ejpam-3424	169	10	qk(x	qk(x	NOUN
ejpam-3424	169	11	,	,	PUNCT
ejpam-3424	169	12	m	m	NOUN
ejpam-3424	169	13	)	)	PUNCT
ejpam-3424	169	14	=	=	PUNCT
ejpam-3424	170	1	m∑	m∑	CCONJ
ejpam-3424	170	2	s=0	s=0	PROPN
ejpam-3424	171	1	c	c	NOUN
ejpam-3424	171	2	s	s	PART
ejpam-3424	171	3	k	k	NOUN
ejpam-3424	171	4	,	,	PUNCT
ejpam-3424	171	5	mx	mx	PROPN
ejpam-3424	171	6	s.	s.	PROPN
ejpam-3424	171	7	(	(	PUNCT
ejpam-3424	171	8	29	29	NUM
ejpam-3424	171	9	)	)	PUNCT
ejpam-3424	171	10	substitute	substitute	NOUN
ejpam-3424	171	11	(	(	PUNCT
ejpam-3424	171	12	29	29	NUM
ejpam-3424	171	13	)	)	PUNCT
ejpam-3424	171	14	into	into	ADP
ejpam-3424	171	15	(	(	PUNCT
ejpam-3424	171	16	5	5	NUM
ejpam-3424	171	17	)	)	PUNCT
ejpam-3424	171	18	,	,	PUNCT
ejpam-3424	171	19	then	then	ADV
ejpam-3424	171	20	xn	xn	PROPN
ejpam-3424	172	1	=	=	SYM
ejpam-3424	172	2	n∑	n∑	PROPN
ejpam-3424	172	3	m=0	m=0	PROPN
ejpam-3424	173	1	d	d	PROPN
ejpam-3424	173	2	m	m	VERB
ejpam-3424	173	3	k	k	NOUN
ejpam-3424	173	4	,	,	PUNCT
ejpam-3424	173	5	nqk(x	nqk(x	PROPN
ejpam-3424	173	6	,	,	PUNCT
ejpam-3424	173	7	m	m	NOUN
ejpam-3424	173	8	)	)	PUNCT
ejpam-3424	173	9	=	=	SYM
ejpam-3424	174	1	n∑	n∑	PROPN
ejpam-3424	174	2	m=0	m=0	PROPN
ejpam-3424	175	1	d	d	PROPN
ejpam-3424	175	2	m	m	VERB
ejpam-3424	175	3	k	k	NOUN
ejpam-3424	175	4	,	,	PUNCT
ejpam-3424	175	5	n	n	PRON
ejpam-3424	175	6	m∑	m∑	X
ejpam-3424	175	7	s=0	s=0	PROPN
ejpam-3424	176	1	c	c	NOUN
ejpam-3424	176	2	s	s	PART
ejpam-3424	176	3	k	k	NOUN
ejpam-3424	176	4	,	,	PUNCT
ejpam-3424	176	5	mx	mx	PROPN
ejpam-3424	176	6	s	s	PROPN
ejpam-3424	176	7	=	=	SYM
ejpam-3424	176	8	n∑	n∑	PROPN
ejpam-3424	176	9	m=0	m=0	PROPN
ejpam-3424	176	10	m∑	m∑	VERB
ejpam-3424	176	11	s=0	s=0	PROPN
ejpam-3424	177	1	d	d	NOUN
ejpam-3424	177	2	m	m	VERB
ejpam-3424	177	3	k	k	NOUN
ejpam-3424	177	4	,	,	PUNCT
ejpam-3424	177	5	nc	nc	PROPN
ejpam-3424	177	6	s	s	PROPN
ejpam-3424	177	7	k	k	PROPN
ejpam-3424	177	8	,	,	PUNCT
ejpam-3424	177	9	mx	mx	PROPN
ejpam-3424	177	10	s	s	PROPN
ejpam-3424	177	11	=	=	PROPN
ejpam-3424	177	12	n∑	n∑	PROPN
ejpam-3424	177	13	s=0	s=0	PROPN
ejpam-3424	177	14	{	{	PUNCT
ejpam-3424	177	15	n∑	n∑	NOUN
ejpam-3424	177	16	m	m	PROPN
ejpam-3424	177	17	=	=	NOUN
ejpam-3424	177	18	s	s	X
ejpam-3424	177	19	d	d	NOUN
ejpam-3424	177	20	m	m	VERB
ejpam-3424	177	21	k	k	NOUN
ejpam-3424	177	22	,	,	PUNCT
ejpam-3424	177	23	nc	nc	PROPN
ejpam-3424	177	24	s	s	PROPN
ejpam-3424	177	25	k	k	PROPN
ejpam-3424	177	26	,	,	PUNCT
ejpam-3424	177	27	m	m	VERB
ejpam-3424	177	28	}	}	PUNCT
ejpam-3424	177	29	xs	xs	PROPN
ejpam-3424	177	30	.	.	PUNCT
ejpam-3424	178	1	thus	thus	ADV
ejpam-3424	178	2	,	,	PUNCT
ejpam-3424	178	3	n∑	n∑	PROPN
ejpam-3424	178	4	m	m	PROPN
ejpam-3424	178	5	=	=	NOUN
ejpam-3424	178	6	s	s	X
ejpam-3424	178	7	d	d	NOUN
ejpam-3424	178	8	m	m	VERB
ejpam-3424	178	9	k	k	NOUN
ejpam-3424	178	10	,	,	PUNCT
ejpam-3424	178	11	nc	nc	PROPN
ejpam-3424	178	12	s	s	PROPN
ejpam-3424	178	13	k	k	PROPN
ejpam-3424	178	14	,	,	PUNCT
ejpam-3424	178	15	m	m	VERB
ejpam-3424	178	16	=	=	NOUN
ejpam-3424	178	17	δsn	δsn	NOUN
ejpam-3424	178	18	=	=	PUNCT
ejpam-3424	178	19	{	{	PUNCT
ejpam-3424	178	20	0	0	NUM
ejpam-3424	178	21	,	,	PUNCT
ejpam-3424	178	22	if	if	SCONJ
ejpam-3424	178	23	n	n	PROPN
ejpam-3424	178	24	6=	6=	SYM
ejpam-3424	178	25	s	s	ADP
ejpam-3424	178	26	1	1	NUM
ejpam-3424	178	27	,	,	PUNCT
ejpam-3424	178	28	if	if	SCONJ
ejpam-3424	178	29	n	n	PROPN
ejpam-3424	178	30	=	=	SYM
ejpam-3424	178	31	s	s	PART
ejpam-3424	178	32	.	.	PUNCT
ejpam-3424	179	1	consequently	consequently	ADV
ejpam-3424	179	2	,	,	PUNCT
ejpam-3424	179	3	n∑	n∑	PROPN
ejpam-3424	179	4	m	m	PROPN
ejpam-3424	179	5	=	=	NOUN
ejpam-3424	179	6	s	s	X
ejpam-3424	179	7	c	c	NOUN
ejpam-3424	179	8	m	m	VERB
ejpam-3424	179	9	k	k	NOUN
ejpam-3424	179	10	,	,	PUNCT
ejpam-3424	179	11	nd	nd	NOUN
ejpam-3424	179	12	s	s	AUX
ejpam-3424	179	13	k	k	NOUN
ejpam-3424	179	14	,	,	PUNCT
ejpam-3424	179	15	m	m	VERB
ejpam-3424	179	16	=	=	SYM
ejpam-3424	179	17	n∑	n∑	NOUN
ejpam-3424	179	18	m	m	PROPN
ejpam-3424	179	19	=	=	NOUN
ejpam-3424	179	20	s	s	X
ejpam-3424	179	21	d	d	NOUN
ejpam-3424	179	22	m	m	VERB
ejpam-3424	179	23	k	k	NOUN
ejpam-3424	179	24	,	,	PUNCT
ejpam-3424	179	25	nc	nc	PROPN
ejpam-3424	179	26	s	s	PROPN
ejpam-3424	179	27	k	k	PROPN
ejpam-3424	179	28	,	,	PUNCT
ejpam-3424	179	29	m	m	VERB
ejpam-3424	179	30	=	=	ADJ
ejpam-3424	179	31	δsn	δsn	PROPN
ejpam-3424	179	32	.	.	PUNCT
ejpam-3424	180	1	(	(	PUNCT
ejpam-3424	180	2	30	30	NUM
ejpam-3424	180	3	)	)	PUNCT
ejpam-3424	180	4	r.	r.	PROPN
ejpam-3424	180	5	corcino	corcino	PROPN
ejpam-3424	180	6	,	,	PUNCT
ejpam-3424	180	7	c.	c.	PROPN
ejpam-3424	180	8	corcino	corcino	PROPN
ejpam-3424	180	9	,	,	PUNCT
ejpam-3424	180	10	g.	g.	PROPN
ejpam-3424	180	11	rama	rama	PROPN
ejpam-3424	180	12	/	/	SYM
ejpam-3424	180	13	eur	eur	PROPN
ejpam-3424	180	14	.	.	PUNCT
ejpam-3424	181	1	j.	j.	PROPN
ejpam-3424	181	2	pure	pure	PROPN
ejpam-3424	181	3	appl	appl	PROPN
ejpam-3424	181	4	.	.	PROPN
ejpam-3424	181	5	math	math	PROPN
ejpam-3424	181	6	,	,	PUNCT
ejpam-3424	181	7	12	12	NUM
ejpam-3424	181	8	(	(	PUNCT
ejpam-3424	181	9	3	3	NUM
ejpam-3424	181	10	)	)	PUNCT
ejpam-3424	181	11	(	(	PUNCT
ejpam-3424	181	12	2019	2019	NUM
ejpam-3424	181	13	)	)	PUNCT
ejpam-3424	181	14	,	,	PUNCT
ejpam-3424	181	15	1069	1069	NUM
ejpam-3424	181	16	-	-	SYM
ejpam-3424	181	17	1081	1081	NUM
ejpam-3424	181	18	1079	1079	NUM
ejpam-3424	181	19	theorem	theorem	VERB
ejpam-3424	181	20	3.4	3.4	NUM
ejpam-3424	181	21	.	.	PUNCT
ejpam-3424	182	1	the	the	DET
ejpam-3424	182	2	tauber	tauber	PROPN
ejpam-3424	182	3	’s	’s	PART
ejpam-3424	182	4	generalized	generalize	VERB
ejpam-3424	182	5	stirling	stirling	NOUN
ejpam-3424	182	6	numbers	number	NOUN
ejpam-3424	182	7	of	of	ADP
ejpam-3424	182	8	the	the	DET
ejpam-3424	182	9	first	first	ADJ
ejpam-3424	182	10	and	and	CCONJ
ejpam-3424	182	11	second	second	ADJ
ejpam-3424	182	12	kind	kind	NOUN
ejpam-3424	182	13	are	be	AUX
ejpam-3424	182	14	inverses	inverse	NOUN
ejpam-3424	182	15	,	,	PUNCT
ejpam-3424	182	16	fn	fn	NOUN
ejpam-3424	182	17	=	=	SYM
ejpam-3424	182	18	n∑	n∑	PROPN
ejpam-3424	182	19	m=0	m=0	PROPN
ejpam-3424	183	1	c	c	PROPN
ejpam-3424	183	2	m	m	VERB
ejpam-3424	183	3	k	k	NOUN
ejpam-3424	183	4	,	,	PUNCT
ejpam-3424	183	5	ngm	ngm	PROPN
ejpam-3424	183	6	⇐	⇐	PROPN
ejpam-3424	183	7	⇒	⇒	PROPN
ejpam-3424	183	8	gn	gn	PROPN
ejpam-3424	184	1	=	=	PUNCT
ejpam-3424	184	2	n∑	n∑	PROPN
ejpam-3424	184	3	m=0	m=0	PROPN
ejpam-3424	185	1	d	d	PROPN
ejpam-3424	185	2	m	m	VERB
ejpam-3424	185	3	k	k	NOUN
ejpam-3424	185	4	,	,	PUNCT
ejpam-3424	185	5	nfm	nfm	PROPN
ejpam-3424	185	6	(	(	PUNCT
ejpam-3424	185	7	31	31	NUM
ejpam-3424	185	8	)	)	PUNCT
ejpam-3424	185	9	for	for	ADP
ejpam-3424	185	10	k	k	PROPN
ejpam-3424	185	11	=	=	SYM
ejpam-3424	185	12	1	1	NUM
ejpam-3424	185	13	,	,	PUNCT
ejpam-3424	185	14	2	2	NUM
ejpam-3424	185	15	.	.	PUNCT
ejpam-3424	185	16	proof	proof	NOUN
ejpam-3424	185	17	.	.	PUNCT
ejpam-3424	186	1	n∑	n∑	PROPN
ejpam-3424	186	2	m=0	m=0	PROPN
ejpam-3424	187	1	d	d	PROPN
ejpam-3424	187	2	m	m	VERB
ejpam-3424	187	3	k	k	NOUN
ejpam-3424	187	4	,	,	PUNCT
ejpam-3424	187	5	nfm	nfm	PROPN
ejpam-3424	187	6	=	=	SYM
ejpam-3424	187	7	n∑	n∑	PROPN
ejpam-3424	187	8	m=0	m=0	PROPN
ejpam-3424	188	1	d	d	PROPN
ejpam-3424	188	2	m	m	VERB
ejpam-3424	188	3	k	k	NOUN
ejpam-3424	188	4	,	,	PUNCT
ejpam-3424	188	5	n	n	PRON
ejpam-3424	188	6	m∑	m∑	X
ejpam-3424	188	7	s=0	s=0	PROPN
ejpam-3424	188	8	c	c	PROPN
ejpam-3424	188	9	s	s	PART
ejpam-3424	188	10	k	k	NOUN
ejpam-3424	188	11	,	,	PUNCT
ejpam-3424	188	12	mgs	mgs	NOUN
ejpam-3424	188	13	=	=	SYM
ejpam-3424	188	14	n∑	n∑	PROPN
ejpam-3424	188	15	m=0	m=0	PROPN
ejpam-3424	188	16	m∑	m∑	VERB
ejpam-3424	188	17	s=0	s=0	PROPN
ejpam-3424	189	1	d	d	NOUN
ejpam-3424	189	2	m	m	VERB
ejpam-3424	189	3	k	k	NOUN
ejpam-3424	189	4	,	,	PUNCT
ejpam-3424	189	5	nc	nc	PROPN
ejpam-3424	189	6	s	s	PROPN
ejpam-3424	189	7	k	k	PROPN
ejpam-3424	189	8	,	,	PUNCT
ejpam-3424	189	9	mgs	mgs	NOUN
ejpam-3424	189	10	=	=	SYM
ejpam-3424	189	11	n∑	n∑	PROPN
ejpam-3424	189	12	s=0	s=0	PROPN
ejpam-3424	189	13	{	{	PUNCT
ejpam-3424	189	14	n∑	n∑	NOUN
ejpam-3424	189	15	m	m	PROPN
ejpam-3424	189	16	=	=	NOUN
ejpam-3424	189	17	s	s	X
ejpam-3424	189	18	d	d	NOUN
ejpam-3424	189	19	m	m	VERB
ejpam-3424	189	20	k	k	NOUN
ejpam-3424	189	21	,	,	PUNCT
ejpam-3424	189	22	nc	nc	PROPN
ejpam-3424	189	23	s	s	PROPN
ejpam-3424	189	24	k	k	PROPN
ejpam-3424	189	25	,	,	PUNCT
ejpam-3424	189	26	m	m	VERB
ejpam-3424	189	27	}	}	PUNCT
ejpam-3424	189	28	gs	gs	NOUN
ejpam-3424	190	1	=	=	PUNCT
ejpam-3424	190	2	n∑	n∑	PROPN
ejpam-3424	190	3	s=0	s=0	PROPN
ejpam-3424	190	4	δsngs	δsng	NOUN
ejpam-3424	190	5	=	=	SYM
ejpam-3424	190	6	δnngn	δnngn	X
ejpam-3424	190	7	=	=	SYM
ejpam-3424	190	8	gn	gn	X
ejpam-3424	190	9	conversely	conversely	ADV
ejpam-3424	190	10	,	,	PUNCT
ejpam-3424	190	11	n∑	n∑	PROPN
ejpam-3424	190	12	m=0	m=0	PROPN
ejpam-3424	191	1	c	c	PROPN
ejpam-3424	191	2	m	m	VERB
ejpam-3424	191	3	k	k	NOUN
ejpam-3424	191	4	,	,	PUNCT
ejpam-3424	191	5	ngm	ngm	PROPN
ejpam-3424	191	6	=	=	SYM
ejpam-3424	191	7	n∑	n∑	PROPN
ejpam-3424	191	8	m=0	m=0	PROPN
ejpam-3424	192	1	c	c	PROPN
ejpam-3424	192	2	m	m	VERB
ejpam-3424	192	3	k	k	NOUN
ejpam-3424	192	4	,	,	PUNCT
ejpam-3424	192	5	n	n	PRON
ejpam-3424	192	6	m∑	m∑	X
ejpam-3424	192	7	s=0	s=0	PROPN
ejpam-3424	193	1	d	d	X
ejpam-3424	193	2	s	s	PART
ejpam-3424	193	3	k	k	NOUN
ejpam-3424	193	4	,	,	PUNCT
ejpam-3424	193	5	mfs	mfs	PROPN
ejpam-3424	193	6	=	=	SYM
ejpam-3424	193	7	n∑	n∑	PROPN
ejpam-3424	193	8	m=0	m=0	PROPN
ejpam-3424	193	9	m∑	m∑	VERB
ejpam-3424	193	10	s=0	s=0	PROPN
ejpam-3424	193	11	c	c	NOUN
ejpam-3424	193	12	m	m	VERB
ejpam-3424	193	13	k	k	ADJ
ejpam-3424	193	14	,	,	PUNCT
ejpam-3424	193	15	nd	nd	PROPN
ejpam-3424	193	16	s	s	X
ejpam-3424	193	17	k	k	NOUN
ejpam-3424	193	18	,	,	PUNCT
ejpam-3424	193	19	mfs	mfs	NOUN
ejpam-3424	193	20	=	=	SYM
ejpam-3424	193	21	n∑	n∑	ADJ
ejpam-3424	193	22	s=0	s=0	PROPN
ejpam-3424	193	23	{	{	PUNCT
ejpam-3424	193	24	n∑	n∑	NOUN
ejpam-3424	193	25	m	m	PROPN
ejpam-3424	193	26	=	=	NOUN
ejpam-3424	193	27	s	s	X
ejpam-3424	193	28	c	c	NOUN
ejpam-3424	193	29	m	m	VERB
ejpam-3424	193	30	k	k	NOUN
ejpam-3424	193	31	,	,	PUNCT
ejpam-3424	193	32	nd	nd	NOUN
ejpam-3424	193	33	s	s	X
ejpam-3424	193	34	k	k	NOUN
ejpam-3424	193	35	,	,	PUNCT
ejpam-3424	193	36	m	m	VERB
ejpam-3424	193	37	}	}	PUNCT
ejpam-3424	193	38	fs	fs	ADP
ejpam-3424	193	39	=	=	PUNCT
ejpam-3424	193	40	n∑	n∑	PROPN
ejpam-3424	193	41	s=0	s=0	PROPN
ejpam-3424	193	42	δsnfs	δsnfs	NOUN
ejpam-3424	193	43	=	=	SYM
ejpam-3424	193	44	δnnfn	δnnfn	PROPN
ejpam-3424	193	45	=	=	SYM
ejpam-3424	193	46	fn	fn	NOUN
ejpam-3424	193	47	theorem	theorem	NOUN
ejpam-3424	193	48	3.5	3.5	NUM
ejpam-3424	193	49	.	.	PUNCT
ejpam-3424	194	1	the	the	DET
ejpam-3424	194	2	bell	bell	PROPN
ejpam-3424	194	3	numbers	number	NOUN
ejpam-3424	194	4	bh	bh	PROPN
ejpam-3424	194	5	,	,	PUNCT
ejpam-3424	194	6	n	n	PRON
ejpam-3424	194	7	can	can	AUX
ejpam-3424	194	8	be	be	AUX
ejpam-3424	194	9	computed	compute	VERB
ejpam-3424	194	10	in	in	ADP
ejpam-3424	194	11	terms	term	NOUN
ejpam-3424	194	12	of	of	ADP
ejpam-3424	194	13	tauber	tauber	PROPN
ejpam-3424	194	14	’s	’s	PART
ejpam-3424	194	15	generalized	generalize	VERB
ejpam-3424	194	16	lah	lah	NOUN
ejpam-3424	194	17	and	and	CCONJ
ejpam-3424	194	18	stirling	stirling	NOUN
ejpam-3424	194	19	numbers	number	NOUN
ejpam-3424	194	20	of	of	ADP
ejpam-3424	194	21	the	the	DET
ejpam-3424	194	22	second	second	ADJ
ejpam-3424	194	23	kind	kind	NOUN
ejpam-3424	194	24	.	.	PUNCT
ejpam-3424	195	1	that	that	PRON
ejpam-3424	195	2	is	is	ADV
ejpam-3424	195	3	,	,	PUNCT
ejpam-3424	195	4	bh	bh	NOUN
ejpam-3424	195	5	,	,	PUNCT
ejpam-3424	195	6	n	n	PROPN
ejpam-3424	195	7	=	=	SYM
ejpam-3424	195	8	n∑	n∑	PROPN
ejpam-3424	195	9	s=0	s=0	PROPN
ejpam-3424	195	10	{	{	PUNCT
ejpam-3424	195	11	n∑	n∑	PROPN
ejpam-3424	195	12	m=0	m=0	PROPN
ejpam-3424	195	13	lmk	lmk	PROPN
ejpam-3424	195	14	,	,	PUNCT
ejpam-3424	195	15	h	h	NOUN
ejpam-3424	195	16	,	,	PUNCT
ejpam-3424	195	17	s	s	PART
ejpam-3424	195	18	}	}	PUNCT
ejpam-3424	195	19	ds	ds	PROPN
ejpam-3424	195	20	k	k	X
ejpam-3424	195	21	,	,	PUNCT
ejpam-3424	195	22	n.	n.	PROPN
ejpam-3424	195	23	(	(	PUNCT
ejpam-3424	195	24	32	32	NUM
ejpam-3424	195	25	)	)	PUNCT
ejpam-3424	195	26	proof	proof	NOUN
ejpam-3424	195	27	.	.	PUNCT
ejpam-3424	196	1	from	from	ADP
ejpam-3424	196	2	the	the	DET
ejpam-3424	196	3	inverse	inverse	NOUN
ejpam-3424	196	4	relation	relation	NOUN
ejpam-3424	196	5	(	(	PUNCT
ejpam-3424	196	6	31	31	NUM
ejpam-3424	196	7	)	)	PUNCT
ejpam-3424	196	8	of	of	ADP
ejpam-3424	196	9	tauber	tauber	PROPN
ejpam-3424	196	10	’s	’s	PART
ejpam-3424	196	11	generalized	generalize	VERB
ejpam-3424	196	12	stirling	stirling	NOUN
ejpam-3424	196	13	numbers	number	NOUN
ejpam-3424	196	14	of	of	ADP
ejpam-3424	196	15	the	the	DET
ejpam-3424	196	16	first	first	ADJ
ejpam-3424	196	17	and	and	CCONJ
ejpam-3424	196	18	second	second	ADJ
ejpam-3424	196	19	kind	kind	NOUN
ejpam-3424	196	20	,	,	PUNCT
ejpam-3424	196	21	fn	fn	NOUN
ejpam-3424	196	22	=	=	SYM
ejpam-3424	196	23	n∑	n∑	PROPN
ejpam-3424	196	24	s=0	s=0	PROPN
ejpam-3424	196	25	csk	csk	PROPN
ejpam-3424	196	26	,	,	PUNCT
ejpam-3424	196	27	ngs	ng	NOUN
ejpam-3424	196	28	⇐	⇐	ADJ
ejpam-3424	196	29	⇒	⇒	PROPN
ejpam-3424	196	30	gn	gn	PROPN
ejpam-3424	197	1	=	=	PUNCT
ejpam-3424	197	2	n∑	n∑	PROPN
ejpam-3424	197	3	s=0	s=0	PROPN
ejpam-3424	197	4	ds	ds	PROPN
ejpam-3424	197	5	k	k	PROPN
ejpam-3424	197	6	,	,	PUNCT
ejpam-3424	197	7	nfs	nfs	PROPN
ejpam-3424	197	8	.	.	PUNCT
ejpam-3424	198	1	(	(	PUNCT
ejpam-3424	198	2	33	33	NUM
ejpam-3424	198	3	)	)	PUNCT
ejpam-3424	198	4	r.	r.	PROPN
ejpam-3424	198	5	corcino	corcino	PROPN
ejpam-3424	198	6	,	,	PUNCT
ejpam-3424	198	7	c.	c.	PROPN
ejpam-3424	198	8	corcino	corcino	PROPN
ejpam-3424	198	9	,	,	PUNCT
ejpam-3424	198	10	g.	g.	PROPN
ejpam-3424	198	11	rama	rama	PROPN
ejpam-3424	198	12	/	/	SYM
ejpam-3424	198	13	eur	eur	PROPN
ejpam-3424	198	14	.	.	PUNCT
ejpam-3424	199	1	j.	j.	PROPN
ejpam-3424	199	2	pure	pure	PROPN
ejpam-3424	199	3	appl	appl	PROPN
ejpam-3424	199	4	.	.	PROPN
ejpam-3424	199	5	math	math	PROPN
ejpam-3424	199	6	,	,	PUNCT
ejpam-3424	199	7	12	12	NUM
ejpam-3424	199	8	(	(	PUNCT
ejpam-3424	199	9	3	3	NUM
ejpam-3424	199	10	)	)	PUNCT
ejpam-3424	199	11	(	(	PUNCT
ejpam-3424	199	12	2019	2019	NUM
ejpam-3424	199	13	)	)	PUNCT
ejpam-3424	199	14	,	,	PUNCT
ejpam-3424	199	15	1069	1069	NUM
ejpam-3424	199	16	-	-	SYM
ejpam-3424	199	17	1081	1081	NUM
ejpam-3424	199	18	1080	1080	NUM
ejpam-3424	199	19	consider	consider	VERB
ejpam-3424	199	20	(	(	PUNCT
ejpam-3424	199	21	10	10	NUM
ejpam-3424	199	22	)	)	PUNCT
ejpam-3424	199	23	and	and	CCONJ
ejpam-3424	199	24	let	let	VERB
ejpam-3424	199	25	gs	gs	NOUN
ejpam-3424	199	26	=	=	NOUN
ejpam-3424	200	1	dm	dm	NUM
ejpam-3424	200	2	h	h	NOUN
ejpam-3424	200	3	,	,	PUNCT
ejpam-3424	200	4	s	s	PART
ejpam-3424	200	5	and	and	CCONJ
ejpam-3424	200	6	fn	fn	NOUN
ejpam-3424	200	7	=	=	NOUN
ejpam-3424	200	8	lmk	lmk	PROPN
ejpam-3424	200	9	,	,	PUNCT
ejpam-3424	200	10	h	h	NOUN
ejpam-3424	200	11	,	,	PUNCT
ejpam-3424	200	12	n	n	CCONJ
ejpam-3424	200	13	,	,	PUNCT
ejpam-3424	200	14	by	by	ADP
ejpam-3424	200	15	(	(	PUNCT
ejpam-3424	200	16	33	33	NUM
ejpam-3424	200	17	)	)	PUNCT
ejpam-3424	200	18	,	,	PUNCT
ejpam-3424	200	19	dm	dm	NOUN
ejpam-3424	200	20	h	h	NOUN
ejpam-3424	200	21	,	,	PUNCT
ejpam-3424	200	22	n	n	PROPN
ejpam-3424	200	23	=	=	SYM
ejpam-3424	200	24	n∑	n∑	NOUN
ejpam-3424	200	25	s=0	s=0	X
ejpam-3424	200	26	ds	ds	PROPN
ejpam-3424	200	27	k	k	PROPN
ejpam-3424	200	28	,	,	PUNCT
ejpam-3424	200	29	nl	nl	PROPN
ejpam-3424	200	30	m	m	PROPN
ejpam-3424	200	31	k	k	NOUN
ejpam-3424	200	32	,	,	PUNCT
ejpam-3424	200	33	h	h	NOUN
ejpam-3424	200	34	,	,	PUNCT
ejpam-3424	200	35	s.	s.	PROPN
ejpam-3424	200	36	(	(	PUNCT
ejpam-3424	200	37	34	34	NUM
ejpam-3424	200	38	)	)	PUNCT
ejpam-3424	200	39	substituting	substituting	NOUN
ejpam-3424	200	40	(	(	PUNCT
ejpam-3424	200	41	34	34	NUM
ejpam-3424	200	42	)	)	PUNCT
ejpam-3424	200	43	to	to	ADP
ejpam-3424	200	44	(	(	PUNCT
ejpam-3424	200	45	11	11	NUM
ejpam-3424	200	46	)	)	PUNCT
ejpam-3424	200	47	yields	yield	VERB
ejpam-3424	200	48	bh	bh	PROPN
ejpam-3424	200	49	,	,	PUNCT
ejpam-3424	200	50	n	n	PROPN
ejpam-3424	200	51	=	=	SYM
ejpam-3424	200	52	n∑	n∑	PROPN
ejpam-3424	200	53	m=0	m=0	PROPN
ejpam-3424	200	54	n∑	n∑	PROPN
ejpam-3424	200	55	s=0	s=0	PROPN
ejpam-3424	200	56	ds	ds	PROPN
ejpam-3424	200	57	k	k	PROPN
ejpam-3424	200	58	,	,	PUNCT
ejpam-3424	200	59	nl	nl	PROPN
ejpam-3424	200	60	m	m	PROPN
ejpam-3424	200	61	k	k	NOUN
ejpam-3424	200	62	,	,	PUNCT
ejpam-3424	200	63	h	h	NOUN
ejpam-3424	200	64	,	,	PUNCT
ejpam-3424	200	65	s	s	PART
ejpam-3424	200	66	which	which	PRON
ejpam-3424	200	67	implies	imply	VERB
ejpam-3424	200	68	bh	bh	NOUN
ejpam-3424	200	69	,	,	PUNCT
ejpam-3424	200	70	n	n	PROPN
ejpam-3424	200	71	=	=	SYM
ejpam-3424	200	72	n∑	n∑	PROPN
ejpam-3424	200	73	s=0	s=0	PROPN
ejpam-3424	200	74	{	{	PUNCT
ejpam-3424	200	75	n∑	n∑	PROPN
ejpam-3424	200	76	m=0	m=0	PROPN
ejpam-3424	200	77	lmk	lmk	PROPN
ejpam-3424	200	78	,	,	PUNCT
ejpam-3424	200	79	h	h	NOUN
ejpam-3424	200	80	,	,	PUNCT
ejpam-3424	200	81	s	s	PART
ejpam-3424	200	82	}	}	PUNCT
ejpam-3424	200	83	ds	ds	PROPN
ejpam-3424	200	84	k	k	X
ejpam-3424	200	85	,	,	PUNCT
ejpam-3424	200	86	n.	n.	PROPN
ejpam-3424	200	87	(	(	PUNCT
ejpam-3424	200	88	35	35	NUM
ejpam-3424	200	89	)	)	PUNCT
ejpam-3424	200	90	note	note	NOUN
ejpam-3424	200	91	that	that	SCONJ
ejpam-3424	200	92	(	(	PUNCT
ejpam-3424	200	93	32	32	NUM
ejpam-3424	200	94	)	)	PUNCT
ejpam-3424	200	95	is	be	AUX
ejpam-3424	200	96	analogous	analogous	ADJ
ejpam-3424	200	97	to	to	ADP
ejpam-3424	200	98	the	the	DET
ejpam-3424	200	99	qi	qi	NOUN
ejpam-3424	200	100	formula	formula	NOUN
ejpam-3424	200	101	.	.	PUNCT
ejpam-3424	201	1	for	for	ADP
ejpam-3424	201	2	h	h	NOUN
ejpam-3424	201	3	=	=	SYM
ejpam-3424	201	4	2	2	NUM
ejpam-3424	201	5	,	,	PUNCT
ejpam-3424	201	6	and	and	CCONJ
ejpam-3424	201	7	k	k	X
ejpam-3424	201	8	=	=	SYM
ejpam-3424	201	9	1	1	NUM
ejpam-3424	201	10	,	,	PUNCT
ejpam-3424	201	11	the	the	DET
ejpam-3424	201	12	first	first	ADJ
ejpam-3424	201	13	five	five	NUM
ejpam-3424	201	14	values	value	NOUN
ejpam-3424	201	15	of	of	ADP
ejpam-3424	201	16	b2,n	b2,n	PROPN
ejpam-3424	201	17	are	be	AUX
ejpam-3424	201	18	b2,0	b2,0	NOUN
ejpam-3424	201	19	=	=	SYM
ejpam-3424	201	20	1	1	NUM
ejpam-3424	201	21	b2,1	b2,1	NOUN
ejpam-3424	201	22	=	=	SYM
ejpam-3424	201	23	1	1	NUM
ejpam-3424	201	24	b2,2	b2,2	NOUN
ejpam-3424	201	25	=	=	SYM
ejpam-3424	201	26	0	0	PUNCT
ejpam-3424	202	1	b2,3	b2,3	NOUN
ejpam-3424	202	2	=	=	NOUN
ejpam-3424	202	3	−1	−1	NOUN
ejpam-3424	202	4	b2,4	b2,4	NOUN
ejpam-3424	202	5	=	=	SYM
ejpam-3424	202	6	1	1	X
ejpam-3424	202	7	.	.	PUNCT
ejpam-3424	202	8	by	by	ADP
ejpam-3424	202	9	switching	switch	VERB
ejpam-3424	202	10	the	the	DET
ejpam-3424	202	11	values	value	NOUN
ejpam-3424	202	12	of	of	ADP
ejpam-3424	202	13	k	k	PROPN
ejpam-3424	202	14	and	and	CCONJ
ejpam-3424	202	15	h	h	PROPN
ejpam-3424	202	16	(	(	PUNCT
ejpam-3424	202	17	i.e.	i.e.	X
ejpam-3424	202	18	,	,	PUNCT
ejpam-3424	202	19	k	k	PROPN
ejpam-3424	202	20	=	=	SYM
ejpam-3424	202	21	2	2	NUM
ejpam-3424	202	22	and	and	CCONJ
ejpam-3424	202	23	h	h	NOUN
ejpam-3424	203	1	=	=	NOUN
ejpam-3424	203	2	1	1	NUM
ejpam-3424	203	3	)	)	PUNCT
ejpam-3424	203	4	,	,	PUNCT
ejpam-3424	203	5	the	the	DET
ejpam-3424	203	6	explicit	explicit	ADJ
ejpam-3424	203	7	formula	formula	NOUN
ejpam-3424	203	8	for	for	ADP
ejpam-3424	203	9	generalized	generalized	ADJ
ejpam-3424	203	10	bell	bell	NOUN
ejpam-3424	203	11	numbers	number	NOUN
ejpam-3424	203	12	bh	bh	PROPN
ejpam-3424	203	13	,	,	PUNCT
ejpam-3424	203	14	n	n	PROPN
ejpam-3424	203	15	=	=	SYM
ejpam-3424	203	16	n∑	n∑	PROPN
ejpam-3424	203	17	s=0	s=0	PROPN
ejpam-3424	203	18	{	{	PUNCT
ejpam-3424	203	19	n∑	n∑	PROPN
ejpam-3424	203	20	m=0	m=0	PROPN
ejpam-3424	203	21	lmk	lmk	PROPN
ejpam-3424	203	22	,	,	PUNCT
ejpam-3424	203	23	h	h	NOUN
ejpam-3424	203	24	,	,	PUNCT
ejpam-3424	203	25	s	s	PART
ejpam-3424	203	26	}	}	PUNCT
ejpam-3424	203	27	ds	ds	PROPN
ejpam-3424	203	28	k	k	NOUN
ejpam-3424	203	29	,	,	PUNCT
ejpam-3424	203	30	n	n	PRON
ejpam-3424	203	31	generates	generate	VERB
ejpam-3424	203	32	the	the	DET
ejpam-3424	203	33	ordinary	ordinary	ADJ
ejpam-3424	203	34	bell	bell	NOUN
ejpam-3424	203	35	numbers	number	NOUN
ejpam-3424	203	36	for	for	ADP
ejpam-3424	203	37	n	n	NOUN
ejpam-3424	203	38	=	=	SYM
ejpam-3424	203	39	1	1	NUM
ejpam-3424	203	40	,	,	PUNCT
ejpam-3424	203	41	2	2	NUM
ejpam-3424	203	42	,	,	PUNCT
ejpam-3424	203	43	.	.	PUNCT
ejpam-3424	203	44	.	.	PUNCT
ejpam-3424	204	1	.	.	PUNCT
ejpam-3424	205	1	,	,	PUNCT
ejpam-3424	205	2	b1,0	b1,0	PRON
ejpam-3424	205	3	=	=	NOUN
ejpam-3424	205	4	1	1	NUM
ejpam-3424	205	5	b1,1	b1,1	NOUN
ejpam-3424	205	6	=	=	SYM
ejpam-3424	205	7	1	1	NUM
ejpam-3424	205	8	b1,2	b1,2	PROPN
ejpam-3424	205	9	=	=	SYM
ejpam-3424	205	10	2	2	NUM
ejpam-3424	205	11	b1,3	b1,3	NOUN
ejpam-3424	205	12	=	=	NOUN
ejpam-3424	205	13	5	5	NUM
ejpam-3424	205	14	b1,4	b1,4	NOUN
ejpam-3424	205	15	=	=	SYM
ejpam-3424	205	16	15	15	NUM
ejpam-3424	205	17	.	.	PUNCT
ejpam-3424	205	18	remark	remark	NOUN
ejpam-3424	205	19	3.6	3.6	NUM
ejpam-3424	205	20	.	.	PUNCT
ejpam-3424	206	1	tauber	tauber	PROPN
ejpam-3424	206	2	’s	’s	PART
ejpam-3424	206	3	generalized	generalize	VERB
ejpam-3424	206	4	bell	bell	PROPN
ejpam-3424	206	5	numbers	number	NOUN
ejpam-3424	206	6	bh	bh	PROPN
ejpam-3424	206	7	,	,	PUNCT
ejpam-3424	206	8	n	n	PRON
ejpam-3424	206	9	are	be	AUX
ejpam-3424	206	10	equal	equal	ADJ
ejpam-3424	206	11	to	to	PART
ejpam-3424	206	12	eidle	eidle	VERB
ejpam-3424	206	13	,	,	PUNCT
ejpam-3424	206	14	where	where	SCONJ
ejpam-3424	206	15	d	d	NOUN
ejpam-3424	206	16	and	and	CCONJ
ejpam-3424	206	17	l	l	NOUN
ejpam-3424	206	18	are	be	AUX
ejpam-3424	206	19	the	the	DET
ejpam-3424	206	20	generalized	generalized	ADJ
ejpam-3424	206	21	stirling	stirling	NOUN
ejpam-3424	206	22	and	and	CCONJ
ejpam-3424	206	23	lah	lah	PROPN
ejpam-3424	206	24	matrices	matrix	NOUN
ejpam-3424	206	25	,	,	PUNCT
ejpam-3424	206	26	ei	ei	X
ejpam-3424	206	27	is	be	AUX
ejpam-3424	206	28	the	the	DET
ejpam-3424	206	29	i	i	PROPN
ejpam-3424	206	30	-	-	PUNCT
ejpam-3424	206	31	th	th	PROPN
ejpam-3424	206	32	unit	unit	NOUN
ejpam-3424	206	33	vector	vector	NOUN
ejpam-3424	206	34	,	,	PUNCT
ejpam-3424	206	35	and	and	CCONJ
ejpam-3424	206	36	e	e	NOUN
ejpam-3424	206	37	is	be	AUX
ejpam-3424	206	38	the	the	DET
ejpam-3424	206	39	vector	vector	NOUN
ejpam-3424	206	40	with	with	ADP
ejpam-3424	206	41	all	all	DET
ejpam-3424	206	42	entries	entry	NOUN
ejpam-3424	206	43	equal	equal	ADJ
ejpam-3424	206	44	to	to	ADP
ejpam-3424	206	45	1	1	NUM
ejpam-3424	206	46	.	.	PUNCT
ejpam-3424	206	47	references	reference	NOUN
ejpam-3424	206	48	1081	1081	NUM
ejpam-3424	206	49	remark	remark	NOUN
ejpam-3424	206	50	3.6	3.6	NUM
ejpam-3424	206	51	is	be	AUX
ejpam-3424	206	52	equivalent	equivalent	ADJ
ejpam-3424	206	53	to	to	ADP
ejpam-3424	206	54	the	the	DET
ejpam-3424	206	55	following	follow	VERB
ejpam-3424	206	56	matrix	matrix	NOUN
ejpam-3424	206	57	relation	relation	NOUN
ejpam-3424	206	58	[	[	PUNCT
ejpam-3424	206	59	di	di	NOUN
ejpam-3424	206	60	h	h	PROPN
ejpam-3424	206	61	,	,	PUNCT
ejpam-3424	206	62	j	j	PROPN
ejpam-3424	206	63	]	]	X
ejpam-3424	207	1	n×n	n×n	PROPN
ejpam-3424	207	2	=	=	SYM
ejpam-3424	207	3	[	[	PUNCT
ejpam-3424	207	4	di	di	X
ejpam-3424	207	5	k	k	PROPN
ejpam-3424	207	6	,	,	PUNCT
ejpam-3424	207	7	j	j	PROPN
ejpam-3424	207	8	]	]	X
ejpam-3424	208	1	n×n	n×n	PROPN
ejpam-3424	208	2	[	[	PUNCT
ejpam-3424	208	3	ljk	ljk	ADJ
ejpam-3424	208	4	,	,	PUNCT
ejpam-3424	208	5	h	h	NOUN
ejpam-3424	208	6	,	,	PUNCT
ejpam-3424	208	7	i	i	PRON
ejpam-3424	208	8	]	]	PUNCT
ejpam-3424	209	1	n×n	n×n	PROPN
ejpam-3424	209	2	.	.	PUNCT
ejpam-3424	210	1	(	(	PUNCT
ejpam-3424	210	2	36	36	NUM
ejpam-3424	210	3	)	)	PUNCT
ejpam-3424	210	4	now	now	ADV
ejpam-3424	210	5	,	,	PUNCT
ejpam-3424	210	6	the	the	DET
ejpam-3424	210	7	orthogonality	orthogonality	NOUN
ejpam-3424	210	8	relation	relation	NOUN
ejpam-3424	210	9	in	in	ADP
ejpam-3424	210	10	theorem	theorem	ADJ
ejpam-3424	210	11	3.3	3.3	NUM
ejpam-3424	210	12	implies	imply	VERB
ejpam-3424	210	13	the	the	DET
ejpam-3424	210	14	following	follow	VERB
ejpam-3424	210	15	matrix	matrix	NOUN
ejpam-3424	210	16	relation	relation	NOUN
ejpam-3424	210	17	[	[	PUNCT
ejpam-3424	210	18	c	c	PROPN
ejpam-3424	211	1	j	j	PROPN
ejpam-3424	211	2	k	k	PROPN
ejpam-3424	211	3	,	,	PUNCT
ejpam-3424	211	4	i	i	PRON
ejpam-3424	211	5	]	]	PUNCT
ejpam-3424	212	1	n×n	n×n	PROPN
ejpam-3424	213	1	[	[	PUNCT
ejpam-3424	213	2	d	d	X
ejpam-3424	213	3	i	i	PRON
ejpam-3424	213	4	k	k	PROPN
ejpam-3424	213	5	,	,	PUNCT
ejpam-3424	213	6	j	j	X
ejpam-3424	213	7	]	]	X
ejpam-3424	213	8	n×n	n×n	PROPN
ejpam-3424	213	9	=	=	SYM
ejpam-3424	213	10	in	in	ADP
ejpam-3424	213	11	,	,	PUNCT
ejpam-3424	213	12	(	(	PUNCT
ejpam-3424	213	13	37	37	NUM
ejpam-3424	213	14	)	)	PUNCT
ejpam-3424	213	15	where	where	SCONJ
ejpam-3424	213	16	in	in	ADP
ejpam-3424	213	17	is	be	AUX
ejpam-3424	213	18	the	the	DET
ejpam-3424	213	19	identity	identity	NOUN
ejpam-3424	213	20	matrix	matrix	NOUN
ejpam-3424	213	21	of	of	ADP
ejpam-3424	213	22	order	order	NOUN
ejpam-3424	213	23	n.	n.	NOUN
ejpam-3424	213	24	that	that	PRON
ejpam-3424	213	25	is	be	AUX
ejpam-3424	213	26	,	,	PUNCT
ejpam-3424	213	27	[	[	PUNCT
ejpam-3424	213	28	d	d	X
ejpam-3424	213	29	i	i	PRON
ejpam-3424	213	30	k	k	PROPN
ejpam-3424	213	31	,	,	PUNCT
ejpam-3424	213	32	j	j	PROPN
ejpam-3424	213	33	]	]	X
ejpam-3424	213	34	−1	−1	NOUN
ejpam-3424	213	35	n×n	n×n	PROPN
ejpam-3424	213	36	=	=	PUNCT
ejpam-3424	214	1	[	[	PUNCT
ejpam-3424	214	2	c	c	X
ejpam-3424	214	3	j	j	PROPN
ejpam-3424	214	4	k	k	PROPN
ejpam-3424	214	5	,	,	PUNCT
ejpam-3424	214	6	i	i	PRON
ejpam-3424	214	7	]	]	PUNCT
ejpam-3424	214	8	n×n	n×n	PROPN
ejpam-3424	214	9	,	,	PUNCT
ejpam-3424	214	10	which	which	PRON
ejpam-3424	214	11	implies	imply	VERB
ejpam-3424	214	12	[	[	PUNCT
ejpam-3424	214	13	c	c	X
ejpam-3424	214	14	j	j	PROPN
ejpam-3424	214	15	k	k	PROPN
ejpam-3424	214	16	,	,	PUNCT
ejpam-3424	214	17	i	i	PRON
ejpam-3424	214	18	]	]	PUNCT
ejpam-3424	215	1	n×n	n×n	PROPN
ejpam-3424	215	2	[	[	PUNCT
ejpam-3424	215	3	d	d	X
ejpam-3424	215	4	i	i	PRON
ejpam-3424	215	5	h	h	NOUN
ejpam-3424	215	6	,	,	PUNCT
ejpam-3424	215	7	j	j	PROPN
ejpam-3424	215	8	]	]	X
ejpam-3424	216	1	n×n	n×n	PROPN
ejpam-3424	216	2	=	=	SYM
ejpam-3424	216	3	[	[	PUNCT
ejpam-3424	216	4	ljk	ljk	ADJ
ejpam-3424	216	5	,	,	PUNCT
ejpam-3424	216	6	h	h	NOUN
ejpam-3424	216	7	,	,	PUNCT
ejpam-3424	216	8	i	i	PRON
ejpam-3424	216	9	]	]	PUNCT
ejpam-3424	217	1	n×n	n×n	PROPN
ejpam-3424	217	2	.	.	PUNCT
ejpam-3424	218	1	(	(	PUNCT
ejpam-3424	218	2	38	38	NUM
ejpam-3424	218	3	)	)	PUNCT
ejpam-3424	218	4	the	the	DET
ejpam-3424	218	5	matrix	matrix	NOUN
ejpam-3424	218	6	equation	equation	NOUN
ejpam-3424	218	7	(	(	PUNCT
ejpam-3424	218	8	38	38	NUM
ejpam-3424	218	9	)	)	PUNCT
ejpam-3424	218	10	is	be	AUX
ejpam-3424	218	11	equivalent	equivalent	ADJ
ejpam-3424	218	12	to	to	ADP
ejpam-3424	218	13	equation	equation	NOUN
ejpam-3424	218	14	(	(	PUNCT
ejpam-3424	218	15	10	10	NUM
ejpam-3424	218	16	)	)	PUNCT
ejpam-3424	218	17	.	.	PUNCT
ejpam-3424	219	1	references	reference	NOUN
ejpam-3424	219	2	[	[	X
ejpam-3424	219	3	1	1	NUM
ejpam-3424	219	4	]	]	X
ejpam-3424	219	5	benoumhani	benoumhani	NOUN
ejpam-3424	219	6	,	,	PUNCT
ejpam-3424	219	7	m.	m.	NOUN
ejpam-3424	219	8	,	,	PUNCT
ejpam-3424	219	9	on	on	ADP
ejpam-3424	219	10	whitney	whitney	PROPN
ejpam-3424	219	11	numbers	number	NOUN
ejpam-3424	219	12	of	of	ADP
ejpam-3424	219	13	dowling	dowling	NOUN
ejpam-3424	219	14	lattices	lattice	NOUN
ejpam-3424	219	15	,	,	PUNCT
ejpam-3424	219	16	discrete	discrete	ADJ
ejpam-3424	219	17	math	math	NOUN
ejpam-3424	219	18	,	,	PUNCT
ejpam-3424	219	19	133	133	NUM
ejpam-3424	219	20	(	(	PUNCT
ejpam-3424	219	21	1996	1996	NUM
ejpam-3424	219	22	)	)	PUNCT
ejpam-3424	219	23	,	,	PUNCT
ejpam-3424	219	24	199–218	199–218	NUM
ejpam-3424	219	25	.	.	PUNCT
ejpam-3424	220	1	[	[	X
ejpam-3424	220	2	2	2	NUM
ejpam-3424	220	3	]	]	PUNCT
ejpam-3424	220	4	comtet	comtet	NOUN
ejpam-3424	220	5	,	,	PUNCT
ejpam-3424	220	6	l.	l.	PROPN
ejpam-3424	220	7	,	,	PUNCT
ejpam-3424	220	8	advanced	advanced	ADJ
ejpam-3424	220	9	combinatorics	combinatoric	NOUN
ejpam-3424	220	10	,	,	PUNCT
ejpam-3424	220	11	d.reidel	d.reidel	PROPN
ejpam-3424	220	12	publishing	publishing	PROPN
ejpam-3424	220	13	company	company	PROPN
ejpam-3424	220	14	inc	inc	PROPN
ejpam-3424	220	15	..	..	PROPN
ejpam-3424	220	16	dordrecht	dordrecht	PROPN
ejpam-3424	220	17	,	,	PUNCT
ejpam-3424	220	18	holland	holland	PROPN
ejpam-3424	220	19	,	,	PUNCT
ejpam-3424	220	20	1974	1974	NUM
ejpam-3424	220	21	.	.	PUNCT
ejpam-3424	221	1	[	[	X
ejpam-3424	221	2	3	3	NUM
ejpam-3424	221	3	]	]	X
ejpam-3424	221	4	daboul	daboul	PROPN
ejpam-3424	221	5	,	,	PUNCT
ejpam-3424	221	6	s.	s.	PROPN
ejpam-3424	221	7	,	,	PUNCT
ejpam-3424	221	8	mangaldan	mangaldan	PROPN
ejpam-3424	221	9	,	,	PUNCT
ejpam-3424	221	10	j.	j.	PROPN
ejpam-3424	221	11	,	,	PUNCT
ejpam-3424	221	12	spivey	spivey	PROPN
ejpam-3424	221	13	,	,	PUNCT
ejpam-3424	221	14	m.	m.	NOUN
ejpam-3424	221	15	,	,	PUNCT
ejpam-3424	221	16	&	&	CCONJ
ejpam-3424	221	17	taylor	taylor	PROPN
ejpam-3424	221	18	,	,	PUNCT
ejpam-3424	221	19	p.	p.	PROPN
ejpam-3424	221	20	,	,	PUNCT
ejpam-3424	221	21	the	the	DET
ejpam-3424	221	22	lah	lah	NOUN
ejpam-3424	221	23	numbers	number	NOUN
ejpam-3424	221	24	and	and	CCONJ
ejpam-3424	221	25	the	the	DET
ejpam-3424	221	26	nth	nth	NOUN
ejpam-3424	221	27	derivative	derivative	NOUN
ejpam-3424	221	28	of	of	ADP
ejpam-3424	221	29	e	e	PROPN
ejpam-3424	221	30	1	1	NUM
ejpam-3424	221	31	x	x	SYM
ejpam-3424	221	32	,	,	PUNCT
ejpam-3424	221	33	math	math	NOUN
ejpam-3424	221	34	.	.	PUNCT
ejpam-3424	222	1	mag	mag	PROPN
ejpam-3424	222	2	.	.	PUNCT
ejpam-3424	223	1	86(1	86(1	PROPN
ejpam-3424	223	2	)	)	PUNCT
ejpam-3424	223	3	(	(	PUNCT
ejpam-3424	223	4	2013	2013	NUM
ejpam-3424	223	5	)	)	PUNCT
ejpam-3424	223	6	,	,	PUNCT
ejpam-3424	223	7	39–47	39–47	NUM
ejpam-3424	223	8	.	.	PUNCT
ejpam-3424	224	1	[	[	X
ejpam-3424	224	2	4	4	NUM
ejpam-3424	224	3	]	]	SYM
ejpam-3424	224	4	qi	qi	PROPN
ejpam-3424	224	5	,	,	PUNCT
ejpam-3424	224	6	f.	f.	PROPN
ejpam-3424	224	7	,	,	PUNCT
ejpam-3424	224	8	an	an	DET
ejpam-3424	224	9	explicit	explicit	ADJ
ejpam-3424	224	10	formula	formula	NOUN
ejpam-3424	224	11	for	for	ADP
ejpam-3424	224	12	the	the	DET
ejpam-3424	224	13	bell	bell	NOUN
ejpam-3424	224	14	numbers	number	NOUN
ejpam-3424	224	15	in	in	ADP
ejpam-3424	224	16	terms	term	NOUN
ejpam-3424	224	17	of	of	ADP
ejpam-3424	224	18	lah	lah	NOUN
ejpam-3424	224	19	and	and	CCONJ
ejpam-3424	224	20	stirling	stirling	NOUN
ejpam-3424	224	21	numbers	number	NOUN
ejpam-3424	224	22	,	,	PUNCT
ejpam-3424	224	23	mediterr	mediterr	PROPN
ejpam-3424	224	24	.	.	PUNCT
ejpam-3424	225	1	j.	j.	PROPN
ejpam-3424	225	2	math	math	PROPN
ejpam-3424	225	3	,	,	PUNCT
ejpam-3424	225	4	13	13	NUM
ejpam-3424	225	5	(	(	PUNCT
ejpam-3424	225	6	2016	2016	NUM
ejpam-3424	225	7	)	)	PUNCT
ejpam-3424	225	8	,	,	PUNCT
ejpam-3424	225	9	2795–2800	2795–2800	NUM
ejpam-3424	225	10	.	.	PUNCT
ejpam-3424	226	1	[	[	X
ejpam-3424	226	2	5	5	NUM
ejpam-3424	226	3	]	]	X
ejpam-3424	226	4	spivey	spivey	PROPN
ejpam-3424	226	5	,	,	PUNCT
ejpam-3424	226	6	m.	m.	NOUN
ejpam-3424	226	7	,	,	PUNCT
ejpam-3424	226	8	a	a	DET
ejpam-3424	226	9	generalized	generalized	ADJ
ejpam-3424	226	10	recurrence	recurrence	NOUN
ejpam-3424	226	11	for	for	ADP
ejpam-3424	226	12	bell	bell	NOUN
ejpam-3424	226	13	numbers	number	NOUN
ejpam-3424	226	14	,	,	PUNCT
ejpam-3424	226	15	journal	journal	NOUN
ejpam-3424	226	16	of	of	ADP
ejpam-3424	226	17	integer	integer	PROPN
ejpam-3424	226	18	sequences	sequence	NOUN
ejpam-3424	226	19	,	,	PUNCT
ejpam-3424	226	20	11	11	NUM
ejpam-3424	226	21	(	(	PUNCT
ejpam-3424	226	22	2008	2008	NUM
ejpam-3424	226	23	)	)	PUNCT
ejpam-3424	226	24	.	.	PUNCT
ejpam-3424	227	1	[	[	X
ejpam-3424	227	2	6	6	NUM
ejpam-3424	227	3	]	]	SYM
ejpam-3424	227	4	tauber	tauber	PROPN
ejpam-3424	227	5	,	,	PUNCT
ejpam-3424	227	6	s.	s.	PROPN
ejpam-3424	227	7	,	,	PUNCT
ejpam-3424	227	8	on	on	ADP
ejpam-3424	227	9	generalised	generalised	ADJ
ejpam-3424	227	10	lah	lah	NOUN
ejpam-3424	227	11	-	-	PUNCT
ejpam-3424	227	12	numbers	number	NOUN
ejpam-3424	227	13	,	,	PUNCT
ejpam-3424	227	14	portland	portland	PROPN
ejpam-3424	227	15	state	state	PROPN
ejpam-3424	227	16	college	college	PROPN
ejpam-3424	227	17	,	,	PUNCT
ejpam-3424	227	18	1964	1964	NUM
ejpam-3424	227	19	.	.	PUNCT
ejpam-3424	228	1	[	[	X
ejpam-3424	228	2	7	7	NUM
ejpam-3424	228	3	]	]	SYM
ejpam-3424	228	4	tauber	tauber	PROPN
ejpam-3424	228	5	,	,	PUNCT
ejpam-3424	228	6	s.	s.	PROPN
ejpam-3424	228	7	,	,	PUNCT
ejpam-3424	228	8	lah	lah	PROPN
ejpam-3424	228	9	numbers	number	NOUN
ejpam-3424	228	10	for	for	ADP
ejpam-3424	228	11	r	r	NOUN
ejpam-3424	228	12	-	-	PUNCT
ejpam-3424	228	13	polynomials	polynomial	NOUN
ejpam-3424	228	14	,	,	PUNCT
ejpam-3424	228	15	portland	portland	PROPN
ejpam-3424	228	16	state	state	PROPN
ejpam-3424	228	17	college	college	PROPN
ejpam-3424	228	18	,	,	PUNCT
ejpam-3424	228	19	1968	1968	NUM
ejpam-3424	228	20	.	.	PUNCT
ejpam-3424	229	1	[	[	X
ejpam-3424	229	2	8	8	NUM
ejpam-3424	229	3	]	]	SYM
ejpam-3424	229	4	tauber	tauber	PROPN
ejpam-3424	229	5	,	,	PUNCT
ejpam-3424	229	6	s.	s.	PROPN
ejpam-3424	229	7	,	,	PUNCT
ejpam-3424	229	8	on	on	ADP
ejpam-3424	229	9	quasi	quasi	ADJ
ejpam-3424	229	10	-	-	ADJ
ejpam-3424	229	11	orthogonal	orthogonal	ADJ
ejpam-3424	229	12	numbers	number	NOUN
ejpam-3424	229	13	,	,	PUNCT
ejpam-3424	229	14	amer	amer	PROPN
ejpam-3424	229	15	.	.	PROPN
ejpam-3424	229	16	math	math	PROPN
ejpam-3424	229	17	.	.	PUNCT
ejpam-3424	230	1	monthly	monthly	ADV
ejpam-3424	230	2	,	,	PUNCT
ejpam-3424	230	3	69	69	NUM
ejpam-3424	230	4	(	(	PUNCT
ejpam-3424	230	5	1962	1962	NUM
ejpam-3424	230	6	)	)	PUNCT
ejpam-3424	230	7	,	,	PUNCT
ejpam-3424	230	8	365	365	NUM
ejpam-3424	230	9	–	–	PUNCT
ejpam-3424	230	10	372	372	NUM
ejpam-3424	230	11	.	.	PUNCT
ejpam-3424	231	1	[	[	X
ejpam-3424	231	2	9	9	NUM
ejpam-3424	231	3	]	]	X
ejpam-3424	231	4	zhang	zhang	PROPN
ejpam-3424	231	5	,	,	PUNCT
ejpam-3424	231	6	x	x	PROPN
ejpam-3424	231	7	-	-	PUNCT
ejpam-3424	231	8	j.	j.	PROPN
ejpam-3424	231	9	,	,	PUNCT
ejpam-3424	231	10	qi	qi	PROPN
ejpam-3424	231	11	,	,	PUNCT
ejpam-3424	231	12	f.	f.	PROPN
ejpam-3424	231	13	,	,	PUNCT
ejpam-3424	231	14	li	li	PROPN
ejpam-3424	231	15	,	,	PUNCT
ejpam-3424	231	16	&	&	CCONJ
ejpam-3424	231	17	w	w	PROPN
ejpam-3424	231	18	-	-	PUNCT
ejpam-3424	231	19	h.	h.	NOUN
ejpam-3424	231	20	,	,	PUNCT
ejpam-3424	231	21	properties	property	NOUN
ejpam-3424	231	22	of	of	ADP
ejpam-3424	231	23	three	three	NUM
ejpam-3424	231	24	functions	function	NOUN
ejpam-3424	231	25	relating	relate	VERB
ejpam-3424	231	26	to	to	ADP
ejpam-3424	231	27	the	the	DET
ejpam-3424	231	28	exponentiasl	exponentiasl	NOUN
ejpam-3424	231	29	function	function	NOUN
ejpam-3424	231	30	and	and	CCONJ
ejpam-3424	231	31	the	the	DET
ejpam-3424	231	32	existence	existence	NOUN
ejpam-3424	231	33	of	of	ADP
ejpam-3424	231	34	partitions	partition	NOUN
ejpam-3424	231	35	of	of	ADP
ejpam-3424	231	36	unity	unity	NOUN
ejpam-3424	231	37	,	,	PUNCT
ejpam-3424	231	38	int	int	NOUN
ejpam-3424	231	39	.	.	PUNCT
ejpam-3424	232	1	j.	j.	PROPN
ejpam-3424	232	2	open	open	PROPN
ejpam-3424	232	3	probl	probl	PROPN
ejpam-3424	232	4	.	.	PUNCT
ejpam-3424	233	1	comput	comput	NOUN
ejpam-3424	233	2	.	.	PUNCT
ejpam-3424	234	1	sci	sci	PROPN
ejpam-3424	234	2	.	.	PUNCT
ejpam-3424	234	3	math	math	PROPN
ejpam-3424	234	4	.	.	PUNCT
ejpam-3424	235	1	5(2	5(2	NUM
ejpam-3424	235	2	)	)	PUNCT
ejpam-3424	235	3	(	(	PUNCT
ejpam-3424	235	4	2012	2012	NUM
ejpam-3424	235	5	)	)	PUNCT
ejpam-3424	235	6	,	,	PUNCT
ejpam-3424	235	7	122–127	122–127	NUM
ejpam-3424	235	8	;	;	PUNCT
ejpam-3424	235	9	available	available	ADJ
ejpam-3424	235	10	online	online	ADV
ejpam-3424	235	11	at	at	ADP
ejpam-3424	235	12	https://doi.org/10.12816/0006128	https://doi.org/10.12816/0006128	NOUN
ejpam-3424	235	13	.	.	PUNCT