id	sid	tid	token	lemma	pos
ejpam-3494	1	1	european	european	PROPN
ejpam-3494	1	2	journal	journal	PROPN
ejpam-3494	1	3	of	of	ADP
ejpam-3494	1	4	pure	pure	ADJ
ejpam-3494	1	5	and	and	CCONJ
ejpam-3494	1	6	applied	apply	VERB
ejpam-3494	1	7	mathematics	mathematic	NOUN
ejpam-3494	1	8	vol	vol	NOUN
ejpam-3494	1	9	.	.	PROPN
ejpam-3494	2	1	12	12	NUM
ejpam-3494	2	2	,	,	PUNCT
ejpam-3494	2	3	no	no	INTJ
ejpam-3494	2	4	.	.	NOUN
ejpam-3494	2	5	3	3	NUM
ejpam-3494	2	6	,	,	PUNCT
ejpam-3494	2	7	2019	2019	NUM
ejpam-3494	2	8	,	,	PUNCT
ejpam-3494	2	9	1122	1122	NUM
ejpam-3494	2	10	-	-	SYM
ejpam-3494	2	11	1137	1137	NUM
ejpam-3494	2	12	issn	issn	PROPN
ejpam-3494	2	13	1307	1307	NUM
ejpam-3494	2	14	-	-	SYM
ejpam-3494	2	15	5543	5543	NUM
ejpam-3494	2	16	–	–	PUNCT
ejpam-3494	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3494	2	18	published	publish	VERB
ejpam-3494	2	19	by	by	ADP
ejpam-3494	2	20	new	new	PROPN
ejpam-3494	2	21	york	york	PROPN
ejpam-3494	2	22	business	business	PROPN
ejpam-3494	2	23	global	global	PROPN
ejpam-3494	2	24	the	the	DET
ejpam-3494	2	25	r	r	NOUN
ejpam-3494	2	26	-	-	PUNCT
ejpam-3494	2	27	dowling	dowle	VERB
ejpam-3494	2	28	numbers	number	NOUN
ejpam-3494	2	29	and	and	CCONJ
ejpam-3494	2	30	matrices	matrix	NOUN
ejpam-3494	2	31	containing	contain	VERB
ejpam-3494	2	32	r	r	NOUN
ejpam-3494	2	33	-	-	PUNCT
ejpam-3494	2	34	whitney	whitney	NOUN
ejpam-3494	2	35	numbers	number	NOUN
ejpam-3494	2	36	of	of	ADP
ejpam-3494	2	37	the	the	DET
ejpam-3494	2	38	second	second	ADJ
ejpam-3494	2	39	kind	kind	NOUN
ejpam-3494	2	40	and	and	CCONJ
ejpam-3494	2	41	lah	lah	PROPN
ejpam-3494	2	42	numbers	number	NOUN
ejpam-3494	2	43	roberto	roberto	PROPN
ejpam-3494	2	44	b.	b.	PROPN
ejpam-3494	2	45	corcino1,∗	corcino1,∗	PROPN
ejpam-3494	2	46	,	,	PUNCT
ejpam-3494	2	47	charles	charles	PROPN
ejpam-3494	2	48	b.	b.	PROPN
ejpam-3494	2	49	montero2	montero2	PROPN
ejpam-3494	2	50	,	,	PUNCT
ejpam-3494	2	51	maribeth	maribeth	PROPN
ejpam-3494	2	52	b.	b.	PROPN
ejpam-3494	2	53	montero2	montero2	PROPN
ejpam-3494	2	54	,	,	PUNCT
ejpam-3494	2	55	jay	jay	PROPN
ejpam-3494	2	56	m.	m.	NOUN
ejpam-3494	2	57	ontolan1	ontolan1	ADJ
ejpam-3494	2	58	1	1	NUM
ejpam-3494	2	59	research	research	NOUN
ejpam-3494	2	60	institute	institute	NOUN
ejpam-3494	2	61	for	for	ADP
ejpam-3494	2	62	computational	computational	ADJ
ejpam-3494	2	63	mathematics	mathematic	NOUN
ejpam-3494	2	64	and	and	CCONJ
ejpam-3494	2	65	physics	physics	NOUN
ejpam-3494	2	66	,	,	PUNCT
ejpam-3494	2	67	cebu	cebu	NOUN
ejpam-3494	2	68	normal	normal	ADJ
ejpam-3494	2	69	university	university	NOUN
ejpam-3494	2	70	,	,	PUNCT
ejpam-3494	2	71	6000	6000	NUM
ejpam-3494	2	72	cebu	cebu	NOUN
ejpam-3494	2	73	city	city	NOUN
ejpam-3494	2	74	,	,	PUNCT
ejpam-3494	2	75	philippines	philippines	PROPN
ejpam-3494	2	76	2	2	NUM
ejpam-3494	2	77	department	department	NOUN
ejpam-3494	2	78	of	of	ADP
ejpam-3494	2	79	mathematics	mathematic	NOUN
ejpam-3494	2	80	,	,	PUNCT
ejpam-3494	2	81	mindanao	mindanao	PROPN
ejpam-3494	2	82	state	state	PROPN
ejpam-3494	2	83	university	university	PROPN
ejpam-3494	2	84	,	,	PUNCT
ejpam-3494	2	85	9700	9700	NUM
ejpam-3494	2	86	marawi	marawi	PROPN
ejpam-3494	2	87	city	city	PROPN
ejpam-3494	2	88	,	,	PUNCT
ejpam-3494	2	89	philippines	philippine	NOUN
ejpam-3494	2	90	abstract	abstract	ADJ
ejpam-3494	2	91	.	.	PUNCT
ejpam-3494	3	1	this	this	DET
ejpam-3494	3	2	paper	paper	NOUN
ejpam-3494	3	3	derives	derive	VERB
ejpam-3494	3	4	three	three	NUM
ejpam-3494	3	5	forms	form	NOUN
ejpam-3494	3	6	of	of	ADP
ejpam-3494	3	7	explicit	explicit	ADJ
ejpam-3494	3	8	formula	formula	NOUN
ejpam-3494	3	9	for	for	ADP
ejpam-3494	3	10	r	r	NOUN
ejpam-3494	3	11	-	-	PUNCT
ejpam-3494	3	12	dowling	dowle	VERB
ejpam-3494	3	13	numbers	number	NOUN
ejpam-3494	3	14	.	.	PUNCT
ejpam-3494	4	1	one	one	NUM
ejpam-3494	4	2	of	of	ADP
ejpam-3494	4	3	these	these	PRON
ejpam-3494	4	4	is	be	AUX
ejpam-3494	4	5	expressed	express	VERB
ejpam-3494	4	6	in	in	ADP
ejpam-3494	4	7	terms	term	NOUN
ejpam-3494	4	8	of	of	ADP
ejpam-3494	4	9	exponential	exponential	ADJ
ejpam-3494	4	10	polynomial	polynomial	NOUN
ejpam-3494	4	11	.	.	PUNCT
ejpam-3494	5	1	the	the	DET
ejpam-3494	5	2	other	other	ADJ
ejpam-3494	5	3	two	two	NUM
ejpam-3494	5	4	formulas	formula	NOUN
ejpam-3494	5	5	are	be	AUX
ejpam-3494	5	6	derived	derive	VERB
ejpam-3494	5	7	using	use	VERB
ejpam-3494	5	8	an	an	DET
ejpam-3494	5	9	inverse	inverse	NOUN
ejpam-3494	5	10	relation	relation	NOUN
ejpam-3494	5	11	and	and	CCONJ
ejpam-3494	5	12	faa	faa	PROPN
ejpam-3494	5	13	di	di	PROPN
ejpam-3494	5	14	bruno	bruno	PROPN
ejpam-3494	5	15	’s	’s	PART
ejpam-3494	5	16	formula	formula	NOUN
ejpam-3494	5	17	together	together	ADV
ejpam-3494	5	18	with	with	ADP
ejpam-3494	5	19	certain	certain	ADJ
ejpam-3494	5	20	identity	identity	NOUN
ejpam-3494	5	21	of	of	ADP
ejpam-3494	5	22	bell	bell	NOUN
ejpam-3494	5	23	polynomials	polynomial	NOUN
ejpam-3494	5	24	of	of	ADP
ejpam-3494	5	25	the	the	DET
ejpam-3494	5	26	second	second	ADJ
ejpam-3494	5	27	kind	kind	NOUN
ejpam-3494	5	28	.	.	PUNCT
ejpam-3494	6	1	these	these	DET
ejpam-3494	6	2	two	two	NUM
ejpam-3494	6	3	formulas	formula	NOUN
ejpam-3494	6	4	are	be	AUX
ejpam-3494	6	5	expressed	express	VERB
ejpam-3494	6	6	in	in	ADP
ejpam-3494	6	7	terms	term	NOUN
ejpam-3494	6	8	of	of	ADP
ejpam-3494	6	9	the	the	DET
ejpam-3494	6	10	r	r	NOUN
ejpam-3494	6	11	-	-	PUNCT
ejpam-3494	6	12	whitney	whitney	NOUN
ejpam-3494	6	13	numbers	number	NOUN
ejpam-3494	6	14	of	of	ADP
ejpam-3494	6	15	the	the	DET
ejpam-3494	6	16	second	second	ADJ
ejpam-3494	6	17	kind	kind	NOUN
ejpam-3494	6	18	,	,	PUNCT
ejpam-3494	6	19	r	r	NOUN
ejpam-3494	6	20	-	-	PUNCT
ejpam-3494	6	21	whitney	whitney	NOUN
ejpam-3494	6	22	-	-	PUNCT
ejpam-3494	6	23	lah	lah	NOUN
ejpam-3494	6	24	numbers	number	NOUN
ejpam-3494	6	25	,	,	PUNCT
ejpam-3494	6	26	and	and	CCONJ
ejpam-3494	6	27	the	the	DET
ejpam-3494	6	28	ordinary	ordinary	ADJ
ejpam-3494	6	29	lah	lah	NOUN
ejpam-3494	6	30	numbers	number	NOUN
ejpam-3494	6	31	.	.	PUNCT
ejpam-3494	7	1	as	as	ADP
ejpam-3494	7	2	a	a	DET
ejpam-3494	7	3	consequence	consequence	NOUN
ejpam-3494	7	4	,	,	PUNCT
ejpam-3494	7	5	a	a	DET
ejpam-3494	7	6	relation	relation	NOUN
ejpam-3494	7	7	between	between	ADP
ejpam-3494	7	8	r	r	NOUN
ejpam-3494	7	9	-	-	PUNCT
ejpam-3494	7	10	dowling	dowle	VERB
ejpam-3494	7	11	numbers	number	NOUN
ejpam-3494	7	12	and	and	CCONJ
ejpam-3494	7	13	the	the	DET
ejpam-3494	7	14	sums	sum	NOUN
ejpam-3494	7	15	of	of	ADP
ejpam-3494	7	16	row	row	NOUN
ejpam-3494	7	17	entries	entry	NOUN
ejpam-3494	7	18	of	of	ADP
ejpam-3494	7	19	the	the	DET
ejpam-3494	7	20	product	product	NOUN
ejpam-3494	7	21	of	of	ADP
ejpam-3494	7	22	matrices	matrix	NOUN
ejpam-3494	7	23	containing	contain	VERB
ejpam-3494	7	24	the	the	DET
ejpam-3494	7	25	r	r	PROPN
ejpam-3494	7	26	-	-	PUNCT
ejpam-3494	7	27	whitney	whitney	NOUN
ejpam-3494	7	28	numbers	number	NOUN
ejpam-3494	7	29	of	of	ADP
ejpam-3494	7	30	the	the	DET
ejpam-3494	7	31	second	second	ADJ
ejpam-3494	7	32	kind	kind	NOUN
ejpam-3494	7	33	,	,	PUNCT
ejpam-3494	7	34	r	r	NOUN
ejpam-3494	7	35	-	-	PUNCT
ejpam-3494	7	36	whitney	whitney	NOUN
ejpam-3494	7	37	-	-	PUNCT
ejpam-3494	7	38	lah	lah	NOUN
ejpam-3494	7	39	numbers	number	NOUN
ejpam-3494	7	40	,	,	PUNCT
ejpam-3494	7	41	and	and	CCONJ
ejpam-3494	7	42	the	the	DET
ejpam-3494	7	43	ordinary	ordinary	ADJ
ejpam-3494	7	44	lah	lah	NOUN
ejpam-3494	7	45	numbers	number	NOUN
ejpam-3494	7	46	is	be	AUX
ejpam-3494	7	47	established	establish	VERB
ejpam-3494	7	48	.	.	PUNCT
ejpam-3494	8	1	moreover	moreover	ADV
ejpam-3494	8	2	,	,	PUNCT
ejpam-3494	8	3	a	a	DET
ejpam-3494	8	4	q	q	NOUN
ejpam-3494	8	5	-	-	PUNCT
ejpam-3494	8	6	analogue	analogue	NOUN
ejpam-3494	8	7	of	of	ADP
ejpam-3494	8	8	the	the	DET
ejpam-3494	8	9	explicit	explicit	ADJ
ejpam-3494	8	10	formula	formula	NOUN
ejpam-3494	8	11	is	be	AUX
ejpam-3494	8	12	obtained	obtain	VERB
ejpam-3494	8	13	.	.	PUNCT
ejpam-3494	9	1	2010	2010	NUM
ejpam-3494	9	2	mathematics	mathematic	NOUN
ejpam-3494	9	3	subject	subject	NOUN
ejpam-3494	9	4	classifications	classification	NOUN
ejpam-3494	9	5	:	:	PUNCT
ejpam-3494	9	6	05a15	05a15	NUM
ejpam-3494	9	7	,	,	PUNCT
ejpam-3494	9	8	11b65	11b65	NUM
ejpam-3494	9	9	,	,	PUNCT
ejpam-3494	9	10	11b73	11b73	NUM
ejpam-3494	9	11	key	key	ADJ
ejpam-3494	9	12	words	word	NOUN
ejpam-3494	9	13	and	and	CCONJ
ejpam-3494	9	14	phrases	phrase	NOUN
ejpam-3494	9	15	:	:	PUNCT
ejpam-3494	9	16	r	r	X
ejpam-3494	9	17	-	-	PUNCT
ejpam-3494	9	18	dowling	dowle	VERB
ejpam-3494	9	19	numbers	number	NOUN
ejpam-3494	9	20	,	,	PUNCT
ejpam-3494	9	21	(	(	PUNCT
ejpam-3494	9	22	r	r	NOUN
ejpam-3494	9	23	,	,	PUNCT
ejpam-3494	9	24	β)-bell	β)-bell	PUNCT
ejpam-3494	9	25	numbers	number	NOUN
ejpam-3494	9	26	,	,	PUNCT
ejpam-3494	9	27	bell	bell	NOUN
ejpam-3494	9	28	polynomials	polynomial	NOUN
ejpam-3494	9	29	,	,	PUNCT
ejpam-3494	9	30	lah	lah	NOUN
ejpam-3494	9	31	numbers	number	NOUN
ejpam-3494	9	32	,	,	PUNCT
ejpam-3494	9	33	r	r	NOUN
ejpam-3494	9	34	-	-	PUNCT
ejpam-3494	9	35	whitney	whitney	NOUN
ejpam-3494	9	36	numbers	number	NOUN
ejpam-3494	9	37	,	,	PUNCT
ejpam-3494	9	38	faa	faa	PROPN
ejpam-3494	9	39	di	di	PROPN
ejpam-3494	9	40	bruno	bruno	PROPN
ejpam-3494	9	41	’s	’s	PART
ejpam-3494	9	42	formula	formula	NOUN
ejpam-3494	9	43	,	,	PUNCT
ejpam-3494	9	44	r	r	NOUN
ejpam-3494	9	45	-	-	PUNCT
ejpam-3494	9	46	whitney	whitney	NOUN
ejpam-3494	9	47	-	-	PUNCT
ejpam-3494	9	48	lah	lah	PROPN
ejpam-3494	9	49	numbers	number	NOUN
ejpam-3494	9	50	1	1	NUM
ejpam-3494	9	51	.	.	PUNCT
ejpam-3494	10	1	introduction	introduction	NOUN
ejpam-3494	10	2	the	the	DET
ejpam-3494	10	3	bell	bell	PROPN
ejpam-3494	10	4	numbers	number	NOUN
ejpam-3494	10	5	,	,	PUNCT
ejpam-3494	10	6	denoted	denote	VERB
ejpam-3494	10	7	by	by	ADP
ejpam-3494	10	8	bn	bn	PROPN
ejpam-3494	10	9	,	,	PUNCT
ejpam-3494	10	10	were	be	AUX
ejpam-3494	10	11	defined	define	VERB
ejpam-3494	10	12	in	in	ADP
ejpam-3494	10	13	[	[	X
ejpam-3494	10	14	5	5	NUM
ejpam-3494	10	15	]	]	PUNCT
ejpam-3494	10	16	as	as	ADP
ejpam-3494	10	17	the	the	DET
ejpam-3494	10	18	sum	sum	NOUN
ejpam-3494	10	19	of	of	ADP
ejpam-3494	10	20	stirling	stirling	NOUN
ejpam-3494	10	21	numbers	number	NOUN
ejpam-3494	10	22	of	of	ADP
ejpam-3494	10	23	the	the	DET
ejpam-3494	10	24	second	second	ADJ
ejpam-3494	10	25	kind	kind	NOUN
ejpam-3494	10	26	bn	bn	INTJ
ejpam-3494	10	27	:	:	PUNCT
ejpam-3494	11	1	=	=	SYM
ejpam-3494	11	2	n∑	n∑	PROPN
ejpam-3494	11	3	k=0	k=0	PROPN
ejpam-3494	11	4	s(n	s(n	PROPN
ejpam-3494	11	5	,	,	PUNCT
ejpam-3494	11	6	k	k	NOUN
ejpam-3494	11	7	)	)	PUNCT
ejpam-3494	11	8	.	.	PUNCT
ejpam-3494	12	1	(	(	PUNCT
ejpam-3494	12	2	1	1	X
ejpam-3494	12	3	)	)	PUNCT
ejpam-3494	12	4	since	since	SCONJ
ejpam-3494	12	5	the	the	DET
ejpam-3494	12	6	numbers	number	NOUN
ejpam-3494	12	7	s(n	s(n	PROPN
ejpam-3494	12	8	,	,	PUNCT
ejpam-3494	12	9	k	k	NOUN
ejpam-3494	12	10	)	)	PUNCT
ejpam-3494	12	11	are	be	AUX
ejpam-3494	12	12	interpreted	interpret	VERB
ejpam-3494	12	13	as	as	ADP
ejpam-3494	12	14	the	the	DET
ejpam-3494	12	15	number	number	NOUN
ejpam-3494	12	16	of	of	ADP
ejpam-3494	12	17	ways	way	NOUN
ejpam-3494	12	18	to	to	PART
ejpam-3494	12	19	partition	partition	VERB
ejpam-3494	12	20	an	an	DET
ejpam-3494	12	21	n	n	ADV
ejpam-3494	12	22	-	-	PUNCT
ejpam-3494	12	23	set	set	NOUN
ejpam-3494	12	24	into	into	ADP
ejpam-3494	12	25	k	k	PROPN
ejpam-3494	12	26	nonempty	nonempty	PROPN
ejpam-3494	12	27	subsets	subset	NOUN
ejpam-3494	12	28	,	,	PUNCT
ejpam-3494	12	29	bn	bn	NOUN
ejpam-3494	12	30	can	can	AUX
ejpam-3494	12	31	then	then	ADV
ejpam-3494	12	32	be	be	AUX
ejpam-3494	12	33	interpreted	interpret	VERB
ejpam-3494	12	34	as	as	ADP
ejpam-3494	12	35	the	the	DET
ejpam-3494	12	36	total	total	ADJ
ejpam-3494	12	37	number	number	NOUN
ejpam-3494	12	38	of	of	ADP
ejpam-3494	12	39	ways	way	NOUN
ejpam-3494	12	40	to	to	PART
ejpam-3494	12	41	partition	partition	VERB
ejpam-3494	12	42	an	an	DET
ejpam-3494	12	43	n	n	ADV
ejpam-3494	12	44	-	-	PUNCT
ejpam-3494	12	45	set	set	NOUN
ejpam-3494	12	46	.	.	PUNCT
ejpam-3494	13	1	several	several	ADJ
ejpam-3494	13	2	properties	property	NOUN
ejpam-3494	13	3	and	and	CCONJ
ejpam-3494	13	4	application	application	NOUN
ejpam-3494	13	5	were	be	AUX
ejpam-3494	13	6	obtained	obtain	VERB
ejpam-3494	13	7	for	for	ADP
ejpam-3494	13	8	these	these	DET
ejpam-3494	13	9	numbers	number	NOUN
ejpam-3494	13	10	including	include	VERB
ejpam-3494	13	11	∗corresponding	∗corresponde	VERB
ejpam-3494	13	12	author	author	NOUN
ejpam-3494	13	13	.	.	PUNCT
ejpam-3494	14	1	doi	doi	NOUN
ejpam-3494	14	2	:	:	PUNCT
ejpam-3494	14	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3494	https://doi.org/10.29020/nybg.ejpam.v12i3.3494	DET
ejpam-3494	14	4	email	email	NOUN
ejpam-3494	14	5	addresses	address	VERB
ejpam-3494	14	6	:	:	PUNCT
ejpam-3494	14	7	rcorcino@yahoo.com	rcorcino@yahoo.com	PROPN
ejpam-3494	14	8	(	(	PUNCT
ejpam-3494	14	9	r.	r.	PROPN
ejpam-3494	14	10	b.	b.	PROPN
ejpam-3494	14	11	corcino	corcino	PROPN
ejpam-3494	14	12	)	)	PUNCT
ejpam-3494	14	13	,	,	PUNCT
ejpam-3494	14	14	charlesmontero@yahoo.com	charlesmontero@yahoo.com	X
ejpam-3494	14	15	(	(	PUNCT
ejpam-3494	14	16	c.	c.	PROPN
ejpam-3494	14	17	montero	montero	PROPN
ejpam-3494	14	18	)	)	PUNCT
ejpam-3494	14	19	,	,	PUNCT
ejpam-3494	14	20	bette	bette	PROPN
ejpam-3494	14	21	myb@yahoo.com	myb@yahoo.com	PROPN
ejpam-3494	14	22	(	(	PUNCT
ejpam-3494	14	23	m.	m.	PROPN
ejpam-3494	14	24	montero	montero	PROPN
ejpam-3494	14	25	)	)	PUNCT
ejpam-3494	14	26	,	,	PUNCT
ejpam-3494	14	27	ontolanjay@gmail.com	ontolanjay@gmail.com	X
ejpam-3494	14	28	(	(	PUNCT
ejpam-3494	14	29	j.	j.	PROPN
ejpam-3494	14	30	ontolan	ontolan	PROPN
ejpam-3494	14	31	)	)	PUNCT
ejpam-3494	14	32	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3494	14	33	1122	1122	NUM
ejpam-3494	15	1	c	c	X
ejpam-3494	15	2	©	©	PROPN
ejpam-3494	15	3	2019	2019	NUM
ejpam-3494	15	4	ejpam	ejpam	NOUN
ejpam-3494	15	5	all	all	DET
ejpam-3494	15	6	rights	right	NOUN
ejpam-3494	15	7	reserved	reserve	VERB
ejpam-3494	15	8	.	.	PUNCT
ejpam-3494	16	1	r.	r.	PROPN
ejpam-3494	16	2	b.	b.	PROPN
ejpam-3494	16	3	corcino	corcino	PROPN
ejpam-3494	16	4	et	et	PROPN
ejpam-3494	16	5	al	al	PROPN
ejpam-3494	16	6	.	.	PUNCT
ejpam-3494	16	7	/	/	SYM
ejpam-3494	16	8	eur	eur	PROPN
ejpam-3494	16	9	.	.	PUNCT
ejpam-3494	17	1	j.	j.	PROPN
ejpam-3494	17	2	pure	pure	PROPN
ejpam-3494	17	3	appl	appl	PROPN
ejpam-3494	17	4	.	.	PROPN
ejpam-3494	17	5	math	math	PROPN
ejpam-3494	17	6	,	,	PUNCT
ejpam-3494	17	7	12	12	NUM
ejpam-3494	17	8	(	(	PUNCT
ejpam-3494	17	9	3	3	NUM
ejpam-3494	17	10	)	)	PUNCT
ejpam-3494	17	11	(	(	PUNCT
ejpam-3494	17	12	2019	2019	NUM
ejpam-3494	17	13	)	)	PUNCT
ejpam-3494	17	14	,	,	PUNCT
ejpam-3494	17	15	1122	1122	NUM
ejpam-3494	17	16	-	-	SYM
ejpam-3494	17	17	1137	1137	NUM
ejpam-3494	17	18	1123	1123	NUM
ejpam-3494	17	19	generating	generating	NOUN
ejpam-3494	17	20	functions	function	NOUN
ejpam-3494	17	21	,	,	PUNCT
ejpam-3494	17	22	recursive	recursive	ADJ
ejpam-3494	17	23	formulas	formula	NOUN
ejpam-3494	17	24	,	,	PUNCT
ejpam-3494	17	25	explicit	explicit	ADJ
ejpam-3494	17	26	formula	formula	NOUN
ejpam-3494	17	27	,	,	PUNCT
ejpam-3494	17	28	and	and	CCONJ
ejpam-3494	17	29	expression	expression	NOUN
ejpam-3494	17	30	in	in	ADP
ejpam-3494	17	31	terms	term	NOUN
ejpam-3494	17	32	of	of	ADP
ejpam-3494	17	33	a	a	DET
ejpam-3494	17	34	moment	moment	NOUN
ejpam-3494	17	35	of	of	ADP
ejpam-3494	17	36	the	the	DET
ejpam-3494	17	37	poisson	poisson	NOUN
ejpam-3494	17	38	random	random	ADJ
ejpam-3494	17	39	variable	variable	NOUN
ejpam-3494	17	40	[	[	X
ejpam-3494	17	41	19	19	NUM
ejpam-3494	17	42	,	,	PUNCT
ejpam-3494	17	43	20	20	NUM
ejpam-3494	17	44	]	]	PUNCT
ejpam-3494	17	45	.	.	PUNCT
ejpam-3494	18	1	by	by	ADP
ejpam-3494	18	2	adding	add	VERB
ejpam-3494	18	3	one	one	NUM
ejpam-3494	18	4	parameter	parameter	NOUN
ejpam-3494	18	5	r	r	NOUN
ejpam-3494	18	6	,	,	PUNCT
ejpam-3494	18	7	a.z	a.z	PROPN
ejpam-3494	18	8	.	.	PROPN
ejpam-3494	18	9	broder	broder	NOUN
ejpam-3494	18	10	[	[	X
ejpam-3494	18	11	3	3	NUM
ejpam-3494	18	12	]	]	PUNCT
ejpam-3494	18	13	defined	define	VERB
ejpam-3494	18	14	combinatorially	combinatorially	ADV
ejpam-3494	18	15	a	a	DET
ejpam-3494	18	16	generalization	generalization	NOUN
ejpam-3494	18	17	of	of	ADP
ejpam-3494	18	18	s(n	s(n	PROPN
ejpam-3494	18	19	,	,	PUNCT
ejpam-3494	18	20	k	k	NOUN
ejpam-3494	18	21	)	)	PUNCT
ejpam-3494	18	22	,	,	PUNCT
ejpam-3494	18	23	the	the	DET
ejpam-3494	18	24	r	r	NOUN
ejpam-3494	18	25	-	-	PUNCT
ejpam-3494	18	26	stirling	stirling	NOUN
ejpam-3494	18	27	numbers	number	NOUN
ejpam-3494	18	28	of	of	ADP
ejpam-3494	18	29	the	the	DET
ejpam-3494	18	30	second	second	ADJ
ejpam-3494	18	31	kind	kind	NOUN
ejpam-3494	18	32	,	,	PUNCT
ejpam-3494	18	33	denoted	denote	VERB
ejpam-3494	18	34	by	by	ADP
ejpam-3494	18	35	{	{	PUNCT
ejpam-3494	18	36	n	n	NOUN
ejpam-3494	18	37	k	k	PROPN
ejpam-3494	18	38	}	}	PUNCT
ejpam-3494	18	39	r	r	NOUN
ejpam-3494	18	40	,	,	PUNCT
ejpam-3494	18	41	as	as	SCONJ
ejpam-3494	18	42	follows	follow	VERB
ejpam-3494	18	43	:	:	PUNCT
ejpam-3494	18	44	{	{	PUNCT
ejpam-3494	18	45	n	n	NOUN
ejpam-3494	18	46	k	k	NOUN
ejpam-3494	18	47	}	}	PUNCT
ejpam-3494	18	48	r	r	NOUN
ejpam-3494	18	49	:	:	PUNCT
ejpam-3494	18	50	=	=	NOUN
ejpam-3494	18	51	the	the	DET
ejpam-3494	18	52	number	number	NOUN
ejpam-3494	18	53	of	of	ADP
ejpam-3494	18	54	partitions	partition	NOUN
ejpam-3494	18	55	of	of	ADP
ejpam-3494	18	56	an	an	DET
ejpam-3494	18	57	n	n	ADV
ejpam-3494	18	58	-	-	PUNCT
ejpam-3494	18	59	set	set	NOUN
ejpam-3494	18	60	into	into	ADP
ejpam-3494	18	61	k	k	PROPN
ejpam-3494	18	62	nonempty	nonempty	X
ejpam-3494	18	63	subsets	subset	NOUN
ejpam-3494	18	64	such	such	ADJ
ejpam-3494	18	65	that	that	SCONJ
ejpam-3494	18	66	the	the	DET
ejpam-3494	18	67	numbers	number	NOUN
ejpam-3494	18	68	1	1	NUM
ejpam-3494	18	69	,	,	PUNCT
ejpam-3494	18	70	2	2	NUM
ejpam-3494	18	71	,	,	PUNCT
ejpam-3494	18	72	.	.	PUNCT
ejpam-3494	18	73	.	.	PUNCT
ejpam-3494	19	1	.	.	PUNCT
ejpam-3494	20	1	,	,	PUNCT
ejpam-3494	20	2	r	r	NOUN
ejpam-3494	20	3	are	be	AUX
ejpam-3494	20	4	in	in	ADP
ejpam-3494	20	5	distinct	distinct	ADJ
ejpam-3494	20	6	subsets	subset	NOUN
ejpam-3494	20	7	.	.	PUNCT
ejpam-3494	21	1	these	these	DET
ejpam-3494	21	2	numbers	number	NOUN
ejpam-3494	21	3	possessed	possess	VERB
ejpam-3494	21	4	several	several	ADJ
ejpam-3494	21	5	properties	property	NOUN
ejpam-3494	21	6	parallel	parallel	ADJ
ejpam-3494	21	7	to	to	ADP
ejpam-3494	21	8	those	those	PRON
ejpam-3494	21	9	of	of	ADP
ejpam-3494	21	10	the	the	DET
ejpam-3494	21	11	classical	classical	ADJ
ejpam-3494	21	12	stirling	stirling	NOUN
ejpam-3494	21	13	numbers	number	NOUN
ejpam-3494	21	14	of	of	ADP
ejpam-3494	21	15	the	the	DET
ejpam-3494	21	16	second	second	ADJ
ejpam-3494	21	17	kind	kind	NOUN
ejpam-3494	21	18	,	,	PUNCT
ejpam-3494	21	19	which	which	PRON
ejpam-3494	21	20	can	can	AUX
ejpam-3494	21	21	be	be	AUX
ejpam-3494	21	22	found	find	VERB
ejpam-3494	21	23	in	in	ADP
ejpam-3494	21	24	[	[	X
ejpam-3494	21	25	3	3	NUM
ejpam-3494	21	26	]	]	PUNCT
ejpam-3494	21	27	.	.	PUNCT
ejpam-3494	22	1	in	in	ADP
ejpam-3494	22	2	the	the	DET
ejpam-3494	22	3	same	same	ADJ
ejpam-3494	22	4	paper	paper	NOUN
ejpam-3494	22	5	[	[	X
ejpam-3494	22	6	3	3	X
ejpam-3494	22	7	]	]	PUNCT
ejpam-3494	22	8	,	,	PUNCT
ejpam-3494	22	9	broder	broder	PROPN
ejpam-3494	22	10	was	be	AUX
ejpam-3494	22	11	able	able	ADJ
ejpam-3494	22	12	to	to	PART
ejpam-3494	22	13	derive	derive	VERB
ejpam-3494	22	14	a	a	DET
ejpam-3494	22	15	relation	relation	NOUN
ejpam-3494	22	16	expressing	express	VERB
ejpam-3494	22	17	{	{	PUNCT
ejpam-3494	22	18	n	n	CCONJ
ejpam-3494	22	19	k	k	NOUN
ejpam-3494	22	20	}	}	PUNCT
ejpam-3494	22	21	r	r	NOUN
ejpam-3494	22	22	in	in	ADP
ejpam-3494	22	23	terms	term	NOUN
ejpam-3494	22	24	of	of	ADP
ejpam-3494	22	25	the	the	DET
ejpam-3494	22	26	classical	classical	ADJ
ejpam-3494	22	27	stirling	stirling	NOUN
ejpam-3494	22	28	numbers	number	NOUN
ejpam-3494	22	29	of	of	ADP
ejpam-3494	22	30	the	the	DET
ejpam-3494	22	31	second	second	ADJ
ejpam-3494	22	32	kind	kind	NOUN
ejpam-3494	22	33	:	:	PUNCT
ejpam-3494	22	34	{	{	PUNCT
ejpam-3494	22	35	n	n	X
ejpam-3494	22	36	k	k	ADJ
ejpam-3494	22	37	}	}	PUNCT
ejpam-3494	22	38	r	r	NOUN
ejpam-3494	22	39	=	=	SYM
ejpam-3494	22	40	n∑	n∑	PROPN
ejpam-3494	22	41	j	j	PROPN
ejpam-3494	23	1	=	=	PROPN
ejpam-3494	23	2	k	k	PROPN
ejpam-3494	23	3	(	(	PUNCT
ejpam-3494	23	4	n	n	X
ejpam-3494	23	5	j	j	PROPN
ejpam-3494	23	6	)	)	PUNCT
ejpam-3494	23	7	s(j	s(j	PROPN
ejpam-3494	23	8	,	,	PUNCT
ejpam-3494	23	9	k)rn−j	k)rn−j	X
ejpam-3494	23	10	.	.	PUNCT
ejpam-3494	24	1	(	(	PUNCT
ejpam-3494	24	2	2	2	X
ejpam-3494	24	3	)	)	PUNCT
ejpam-3494	24	4	letting	let	VERB
ejpam-3494	24	5	r	r	NOUN
ejpam-3494	24	6	=	=	SYM
ejpam-3494	24	7	0	0	NUM
ejpam-3494	24	8	,	,	PUNCT
ejpam-3494	24	9	equation	equation	NOUN
ejpam-3494	24	10	(	(	PUNCT
ejpam-3494	24	11	2	2	X
ejpam-3494	24	12	)	)	PUNCT
ejpam-3494	24	13	gives	give	VERB
ejpam-3494	24	14	{	{	PUNCT
ejpam-3494	24	15	n	n	NOUN
ejpam-3494	24	16	k	k	NOUN
ejpam-3494	24	17	}	}	PUNCT
ejpam-3494	24	18	0	0	X
ejpam-3494	25	1	=	=	SYM
ejpam-3494	25	2	s(n	s(n	PROPN
ejpam-3494	25	3	,	,	PUNCT
ejpam-3494	25	4	k	k	NOUN
ejpam-3494	25	5	)	)	PUNCT
ejpam-3494	25	6	with	with	ADP
ejpam-3494	25	7	00	00	NUM
ejpam-3494	25	8	defined	define	VERB
ejpam-3494	25	9	to	to	PART
ejpam-3494	25	10	be	be	AUX
ejpam-3494	25	11	1	1	NUM
ejpam-3494	25	12	.	.	PUNCT
ejpam-3494	25	13	parallel	parallel	ADJ
ejpam-3494	25	14	to	to	ADP
ejpam-3494	25	15	the	the	DET
ejpam-3494	25	16	definition	definition	NOUN
ejpam-3494	25	17	of	of	ADP
ejpam-3494	25	18	bell	bell	NOUN
ejpam-3494	25	19	numbers	number	NOUN
ejpam-3494	25	20	in	in	ADP
ejpam-3494	25	21	(	(	PUNCT
ejpam-3494	25	22	1	1	NUM
ejpam-3494	25	23	)	)	PUNCT
ejpam-3494	25	24	,	,	PUNCT
ejpam-3494	25	25	mezo	mezo	X
ejpam-3494	26	1	[	[	X
ejpam-3494	26	2	17	17	NUM
ejpam-3494	26	3	]	]	PUNCT
ejpam-3494	26	4	defined	define	VERB
ejpam-3494	26	5	the	the	DET
ejpam-3494	26	6	r	r	NOUN
ejpam-3494	26	7	-	-	PUNCT
ejpam-3494	26	8	bell	bell	NOUN
ejpam-3494	26	9	numbers	number	NOUN
ejpam-3494	26	10	as	as	ADP
ejpam-3494	26	11	bn	bn	NOUN
ejpam-3494	26	12	,	,	PUNCT
ejpam-3494	26	13	r	r	NOUN
ejpam-3494	26	14	=	=	SYM
ejpam-3494	26	15	n∑	n∑	NOUN
ejpam-3494	26	16	k=0	k=0	PROPN
ejpam-3494	26	17	{	{	PUNCT
ejpam-3494	27	1	n+	n+	ADP
ejpam-3494	27	2	r	r	NOUN
ejpam-3494	27	3	k	k	NOUN
ejpam-3494	28	1	+	+	CCONJ
ejpam-3494	28	2	r	r	NOUN
ejpam-3494	28	3	}	}	PUNCT
ejpam-3494	28	4	r	r	NOUN
ejpam-3494	28	5	.	.	PUNCT
ejpam-3494	29	1	(	(	PUNCT
ejpam-3494	29	2	3	3	X
ejpam-3494	29	3	)	)	PUNCT
ejpam-3494	29	4	mezo	mezo	NOUN
ejpam-3494	30	1	[	[	X
ejpam-3494	30	2	17	17	NUM
ejpam-3494	30	3	]	]	PUNCT
ejpam-3494	30	4	obtained	obtain	VERB
ejpam-3494	30	5	several	several	ADJ
ejpam-3494	30	6	interesting	interesting	ADJ
ejpam-3494	30	7	properties	property	NOUN
ejpam-3494	30	8	for	for	ADP
ejpam-3494	30	9	these	these	DET
ejpam-3494	30	10	numbers	number	NOUN
ejpam-3494	30	11	analogous	analogous	ADJ
ejpam-3494	30	12	to	to	ADP
ejpam-3494	30	13	those	those	PRON
ejpam-3494	30	14	of	of	ADP
ejpam-3494	30	15	the	the	DET
ejpam-3494	30	16	classical	classical	ADJ
ejpam-3494	30	17	bell	bell	NOUN
ejpam-3494	30	18	numbers	number	NOUN
ejpam-3494	30	19	.	.	PUNCT
ejpam-3494	31	1	it	it	PRON
ejpam-3494	31	2	is	be	AUX
ejpam-3494	31	3	worth	worth	ADJ
ejpam-3494	31	4	mentioning	mention	VERB
ejpam-3494	31	5	that	that	SCONJ
ejpam-3494	31	6	r	r	NOUN
ejpam-3494	31	7	-	-	PUNCT
ejpam-3494	31	8	bell	bell	NOUN
ejpam-3494	31	9	numbers	number	NOUN
ejpam-3494	31	10	were	be	AUX
ejpam-3494	31	11	first	first	ADV
ejpam-3494	31	12	introduced	introduce	VERB
ejpam-3494	31	13	by	by	ADP
ejpam-3494	31	14	c.b	c.b	PROPN
ejpam-3494	31	15	.	.	PROPN
ejpam-3494	31	16	corcino	corcino	PROPN
ejpam-3494	31	17	in	in	ADP
ejpam-3494	31	18	[	[	X
ejpam-3494	31	19	6	6	NUM
ejpam-3494	31	20	]	]	PUNCT
ejpam-3494	31	21	.	.	PUNCT
ejpam-3494	32	1	furthermore	furthermore	ADV
ejpam-3494	32	2	,	,	PUNCT
ejpam-3494	32	3	by	by	ADP
ejpam-3494	32	4	adding	add	VERB
ejpam-3494	32	5	one	one	NUM
ejpam-3494	32	6	more	more	ADJ
ejpam-3494	32	7	parameter	parameter	NOUN
ejpam-3494	32	8	m	m	PROPN
ejpam-3494	32	9	,	,	PUNCT
ejpam-3494	32	10	mező	mező	PROPN
ejpam-3494	32	11	[	[	X
ejpam-3494	32	12	16	16	NUM
ejpam-3494	32	13	]	]	PUNCT
ejpam-3494	32	14	defined	define	VERB
ejpam-3494	32	15	the	the	DET
ejpam-3494	32	16	r	r	PROPN
ejpam-3494	32	17	-	-	PUNCT
ejpam-3494	32	18	whitney	whitney	NOUN
ejpam-3494	32	19	numbers	number	NOUN
ejpam-3494	32	20	of	of	ADP
ejpam-3494	32	21	the	the	DET
ejpam-3494	32	22	first	first	ADJ
ejpam-3494	32	23	and	and	CCONJ
ejpam-3494	32	24	second	second	ADJ
ejpam-3494	32	25	kind	kind	NOUN
ejpam-3494	32	26	,	,	PUNCT
ejpam-3494	32	27	denoted	denote	VERB
ejpam-3494	32	28	by	by	ADP
ejpam-3494	32	29	wm	wm	PROPN
ejpam-3494	32	30	,	,	PUNCT
ejpam-3494	32	31	r(n	r(n	PROPN
ejpam-3494	32	32	,	,	PUNCT
ejpam-3494	32	33	k	k	NOUN
ejpam-3494	32	34	)	)	PUNCT
ejpam-3494	32	35	and	and	CCONJ
ejpam-3494	32	36	wm	wm	PROPN
ejpam-3494	32	37	,	,	PUNCT
ejpam-3494	32	38	r(n	r(n	PROPN
ejpam-3494	32	39	,	,	PUNCT
ejpam-3494	32	40	k	k	NOUN
ejpam-3494	32	41	)	)	PUNCT
ejpam-3494	32	42	,	,	PUNCT
ejpam-3494	32	43	as	as	ADP
ejpam-3494	32	44	coefficients	coefficient	NOUN
ejpam-3494	32	45	of	of	ADP
ejpam-3494	32	46	the	the	DET
ejpam-3494	32	47	following	follow	VERB
ejpam-3494	32	48	expansions	expansion	NOUN
ejpam-3494	32	49	mn(x)n	mn(x)n	PROPN
ejpam-3494	32	50	=	=	SYM
ejpam-3494	32	51	n∑	n∑	X
ejpam-3494	32	52	k=0	k=0	PROPN
ejpam-3494	32	53	(	(	PUNCT
ejpam-3494	32	54	−1)n−kwm	−1)n−kwm	ADJ
ejpam-3494	32	55	,	,	PUNCT
ejpam-3494	32	56	r(n	r(n	PROPN
ejpam-3494	32	57	,	,	PUNCT
ejpam-3494	32	58	k)(mx+	k)(mx+	NOUN
ejpam-3494	32	59	r)k	r)k	NOUN
ejpam-3494	32	60	,	,	PUNCT
ejpam-3494	32	61	(	(	PUNCT
ejpam-3494	32	62	4	4	NUM
ejpam-3494	32	63	)	)	PUNCT
ejpam-3494	32	64	and	and	CCONJ
ejpam-3494	32	65	(	(	PUNCT
ejpam-3494	32	66	mx+	mx+	NOUN
ejpam-3494	32	67	r)n	r)n	NOUN
ejpam-3494	33	1	=	=	SYM
ejpam-3494	33	2	n∑	n∑	PROPN
ejpam-3494	33	3	k=0	k=0	PROPN
ejpam-3494	33	4	w	w	PROPN
ejpam-3494	33	5	(	(	PUNCT
ejpam-3494	33	6	n	n	X
ejpam-3494	33	7	,	,	PUNCT
ejpam-3494	33	8	k)mk(x)k	k)mk(x)k	PROPN
ejpam-3494	33	9	,	,	PUNCT
ejpam-3494	33	10	(	(	PUNCT
ejpam-3494	33	11	5	5	NUM
ejpam-3494	33	12	)	)	PUNCT
ejpam-3494	33	13	where	where	SCONJ
ejpam-3494	33	14	(	(	PUNCT
ejpam-3494	33	15	x)k	x)k	NOUN
ejpam-3494	33	16	=	=	SYM
ejpam-3494	33	17	x(x−	x(x−	PROPN
ejpam-3494	33	18	1	1	NUM
ejpam-3494	33	19	)	)	PUNCT
ejpam-3494	33	20	.	.	PUNCT
ejpam-3494	33	21	.	.	PUNCT
ejpam-3494	33	22	.	.	PUNCT
ejpam-3494	34	1	(	(	PUNCT
ejpam-3494	34	2	x−	x−	PROPN
ejpam-3494	34	3	k	k	PROPN
ejpam-3494	35	1	+	+	PROPN
ejpam-3494	35	2	1	1	X
ejpam-3494	35	3	)	)	PUNCT
ejpam-3494	35	4	if	if	SCONJ
ejpam-3494	35	5	k	k	PROPN
ejpam-3494	35	6	≥	≥	PROPN
ejpam-3494	35	7	1	1	NUM
ejpam-3494	35	8	,	,	PUNCT
ejpam-3494	35	9	with	with	ADP
ejpam-3494	35	10	(	(	PUNCT
ejpam-3494	35	11	x)0	x)0	X
ejpam-3494	35	12	=	=	SYM
ejpam-3494	35	13	1	1	X
ejpam-3494	35	14	.	.	PUNCT
ejpam-3494	35	15	below	below	ADV
ejpam-3494	35	16	are	be	AUX
ejpam-3494	35	17	the	the	DET
ejpam-3494	35	18	few	few	ADJ
ejpam-3494	35	19	values	value	NOUN
ejpam-3494	35	20	of	of	ADP
ejpam-3494	35	21	wm	wm	PROPN
ejpam-3494	35	22	,	,	PUNCT
ejpam-3494	35	23	r(n	r(n	PROPN
ejpam-3494	35	24	,	,	PUNCT
ejpam-3494	35	25	k	k	NOUN
ejpam-3494	35	26	)	)	PUNCT
ejpam-3494	35	27	and	and	CCONJ
ejpam-3494	35	28	wm	wm	PROPN
ejpam-3494	35	29	,	,	PUNCT
ejpam-3494	35	30	r(n	r(n	PROPN
ejpam-3494	35	31	,	,	PUNCT
ejpam-3494	35	32	k	k	NOUN
ejpam-3494	35	33	)	)	PUNCT
ejpam-3494	35	34	with	with	ADP
ejpam-3494	35	35	m	m	PROPN
ejpam-3494	35	36	=	=	SYM
ejpam-3494	35	37	r	r	NOUN
ejpam-3494	35	38	=	=	SYM
ejpam-3494	35	39	2	2	NUM
ejpam-3494	35	40	:	:	PUNCT
ejpam-3494	35	41	n	n	CCONJ
ejpam-3494	36	1	/	/	SYM
ejpam-3494	36	2	k	k	NOUN
ejpam-3494	36	3	0	0	NUM
ejpam-3494	36	4	1	1	NUM
ejpam-3494	36	5	2	2	NUM
ejpam-3494	36	6	3	3	NUM
ejpam-3494	36	7	4	4	NUM
ejpam-3494	36	8	n	n	CCONJ
ejpam-3494	36	9	/	/	SYM
ejpam-3494	36	10	k	k	NOUN
ejpam-3494	36	11	0	0	NUM
ejpam-3494	36	12	1	1	NUM
ejpam-3494	36	13	2	2	NUM
ejpam-3494	36	14	3	3	NUM
ejpam-3494	36	15	4	4	NUM
ejpam-3494	36	16	0	0	NUM
ejpam-3494	36	17	1	1	NUM
ejpam-3494	36	18	0	0	NUM
ejpam-3494	36	19	1	1	NUM
ejpam-3494	36	20	1	1	NUM
ejpam-3494	36	21	2	2	NUM
ejpam-3494	36	22	1	1	NUM
ejpam-3494	36	23	1	1	NUM
ejpam-3494	36	24	2	2	NUM
ejpam-3494	36	25	1	1	NUM
ejpam-3494	36	26	2	2	NUM
ejpam-3494	36	27	8	8	NUM
ejpam-3494	36	28	6	6	NUM
ejpam-3494	36	29	1	1	NUM
ejpam-3494	36	30	2	2	NUM
ejpam-3494	36	31	4	4	NUM
ejpam-3494	36	32	6	6	NUM
ejpam-3494	36	33	1	1	NUM
ejpam-3494	36	34	3	3	NUM
ejpam-3494	36	35	48	48	NUM
ejpam-3494	36	36	44	44	NUM
ejpam-3494	36	37	12	12	NUM
ejpam-3494	36	38	1	1	NUM
ejpam-3494	36	39	3	3	NUM
ejpam-3494	36	40	8	8	NUM
ejpam-3494	36	41	28	28	NUM
ejpam-3494	36	42	12	12	NUM
ejpam-3494	36	43	1	1	NUM
ejpam-3494	36	44	4	4	NUM
ejpam-3494	36	45	384	384	NUM
ejpam-3494	36	46	400	400	NUM
ejpam-3494	36	47	140	140	NUM
ejpam-3494	36	48	20	20	NUM
ejpam-3494	36	49	1	1	NUM
ejpam-3494	36	50	4	4	NUM
ejpam-3494	36	51	16	16	NUM
ejpam-3494	36	52	120	120	NUM
ejpam-3494	36	53	100	100	NUM
ejpam-3494	36	54	20	20	NUM
ejpam-3494	36	55	1	1	NUM
ejpam-3494	36	56	r.	r.	PROPN
ejpam-3494	36	57	b.	b.	PROPN
ejpam-3494	36	58	corcino	corcino	PROPN
ejpam-3494	36	59	et	et	PROPN
ejpam-3494	36	60	al	al	PROPN
ejpam-3494	36	61	.	.	PUNCT
ejpam-3494	36	62	/	/	SYM
ejpam-3494	36	63	eur	eur	PROPN
ejpam-3494	36	64	.	.	PUNCT
ejpam-3494	37	1	j.	j.	PROPN
ejpam-3494	37	2	pure	pure	PROPN
ejpam-3494	37	3	appl	appl	PROPN
ejpam-3494	37	4	.	.	PROPN
ejpam-3494	37	5	math	math	PROPN
ejpam-3494	37	6	,	,	PUNCT
ejpam-3494	37	7	12	12	NUM
ejpam-3494	37	8	(	(	PUNCT
ejpam-3494	37	9	3	3	NUM
ejpam-3494	37	10	)	)	PUNCT
ejpam-3494	37	11	(	(	PUNCT
ejpam-3494	37	12	2019	2019	NUM
ejpam-3494	37	13	)	)	PUNCT
ejpam-3494	37	14	,	,	PUNCT
ejpam-3494	37	15	1122	1122	NUM
ejpam-3494	37	16	-	-	SYM
ejpam-3494	37	17	1137	1137	NUM
ejpam-3494	37	18	1124	1124	NUM
ejpam-3494	37	19	table	table	NOUN
ejpam-3494	37	20	1	1	NUM
ejpam-3494	37	21	:	:	PUNCT
ejpam-3494	37	22	few	few	ADJ
ejpam-3494	37	23	values	value	NOUN
ejpam-3494	37	24	of	of	ADP
ejpam-3494	37	25	w2,2(n	w2,2(n	PROPN
ejpam-3494	37	26	,	,	PUNCT
ejpam-3494	37	27	k	k	NOUN
ejpam-3494	37	28	)	)	PUNCT
ejpam-3494	37	29	table	table	NOUN
ejpam-3494	38	1	2	2	NUM
ejpam-3494	38	2	:	:	PUNCT
ejpam-3494	38	3	few	few	ADJ
ejpam-3494	38	4	values	value	NOUN
ejpam-3494	38	5	of	of	ADP
ejpam-3494	38	6	w2,2(n	w2,2(n	PROPN
ejpam-3494	38	7	,	,	PUNCT
ejpam-3494	38	8	k	k	NOUN
ejpam-3494	38	9	)	)	PUNCT
ejpam-3494	38	10	it	it	PRON
ejpam-3494	38	11	would	would	AUX
ejpam-3494	38	12	be	be	AUX
ejpam-3494	38	13	interesting	interesting	ADJ
ejpam-3494	38	14	to	to	PART
ejpam-3494	38	15	note	note	VERB
ejpam-3494	38	16	that	that	SCONJ
ejpam-3494	38	17	the	the	DET
ejpam-3494	38	18	numbers	number	NOUN
ejpam-3494	38	19	wm	wm	PROPN
ejpam-3494	38	20	,	,	PUNCT
ejpam-3494	38	21	r(n	r(n	PROPN
ejpam-3494	38	22	,	,	PUNCT
ejpam-3494	38	23	k	k	NOUN
ejpam-3494	38	24	)	)	PUNCT
ejpam-3494	38	25	are	be	AUX
ejpam-3494	38	26	equivalent	equivalent	ADJ
ejpam-3494	38	27	to	to	ADP
ejpam-3494	38	28	the	the	DET
ejpam-3494	38	29	(	(	PUNCT
ejpam-3494	38	30	r	r	NOUN
ejpam-3494	38	31	,	,	PUNCT
ejpam-3494	38	32	β)stirling	β)stirle	VERB
ejpam-3494	38	33	numbers	number	NOUN
ejpam-3494	38	34	[	[	X
ejpam-3494	38	35	7	7	X
ejpam-3494	38	36	]	]	PUNCT
ejpam-3494	38	37	and	and	CCONJ
ejpam-3494	38	38	the	the	DET
ejpam-3494	38	39	numbers	number	NOUN
ejpam-3494	38	40	wm	wm	PROPN
ejpam-3494	38	41	,	,	PUNCT
ejpam-3494	38	42	r(n	r(n	PROPN
ejpam-3494	38	43	,	,	PUNCT
ejpam-3494	38	44	k	k	NOUN
ejpam-3494	38	45	)	)	PUNCT
ejpam-3494	38	46	are	be	AUX
ejpam-3494	38	47	equivalent	equivalent	ADJ
ejpam-3494	38	48	to	to	ADP
ejpam-3494	38	49	the	the	DET
ejpam-3494	38	50	numbers	number	NOUN
ejpam-3494	38	51	that	that	PRON
ejpam-3494	38	52	appeared	appear	VERB
ejpam-3494	38	53	in	in	ADP
ejpam-3494	38	54	[	[	X
ejpam-3494	38	55	10	10	NUM
ejpam-3494	38	56	]	]	PUNCT
ejpam-3494	38	57	.	.	PUNCT
ejpam-3494	39	1	one	one	PRON
ejpam-3494	39	2	can	can	AUX
ejpam-3494	39	3	easily	easily	ADV
ejpam-3494	39	4	verify	verify	VERB
ejpam-3494	39	5	that	that	SCONJ
ejpam-3494	39	6	these	these	DET
ejpam-3494	39	7	numbers	number	NOUN
ejpam-3494	39	8	satisfy	satisfy	VERB
ejpam-3494	39	9	the	the	DET
ejpam-3494	39	10	following	follow	VERB
ejpam-3494	39	11	inverse	inverse	NOUN
ejpam-3494	39	12	relation	relation	NOUN
ejpam-3494	39	13	fn	fn	PROPN
ejpam-3494	40	1	=	=	SYM
ejpam-3494	40	2	n∑	n∑	PROPN
ejpam-3494	40	3	j=0	j=0	PROPN
ejpam-3494	40	4	(	(	PUNCT
ejpam-3494	40	5	−1)n−jwβ	−1)n−jwβ	PROPN
ejpam-3494	40	6	,	,	PUNCT
ejpam-3494	40	7	r(n	r(n	PROPN
ejpam-3494	40	8	,	,	PUNCT
ejpam-3494	40	9	j)gj	j)gj	PROPN
ejpam-3494	40	10	⇐	⇐	ADJ
ejpam-3494	40	11	⇒	⇒	PROPN
ejpam-3494	40	12	gn	gn	PROPN
ejpam-3494	40	13	=	=	SYM
ejpam-3494	40	14	n∑	n∑	PROPN
ejpam-3494	40	15	j=0	j=0	PROPN
ejpam-3494	40	16	wβ	wβ	ADP
ejpam-3494	40	17	,	,	PUNCT
ejpam-3494	40	18	r(n	r(n	PROPN
ejpam-3494	40	19	,	,	PUNCT
ejpam-3494	40	20	j)fj	j)fj	PROPN
ejpam-3494	40	21	.	.	PUNCT
ejpam-3494	41	1	(	(	PUNCT
ejpam-3494	41	2	6	6	X
ejpam-3494	41	3	)	)	PUNCT
ejpam-3494	41	4	analogous	analogous	ADJ
ejpam-3494	41	5	to	to	ADP
ejpam-3494	41	6	(	(	PUNCT
ejpam-3494	41	7	2	2	NUM
ejpam-3494	41	8	)	)	PUNCT
ejpam-3494	41	9	,	,	PUNCT
ejpam-3494	41	10	cheon	cheon	NOUN
ejpam-3494	41	11	and	and	CCONJ
ejpam-3494	41	12	jung	jung	PROPN
ejpam-3494	42	1	[	[	X
ejpam-3494	42	2	4	4	X
ejpam-3494	42	3	]	]	PUNCT
ejpam-3494	42	4	expressed	express	VERB
ejpam-3494	42	5	the	the	DET
ejpam-3494	42	6	r	r	PROPN
ejpam-3494	42	7	-	-	PUNCT
ejpam-3494	42	8	whitney	whitney	NOUN
ejpam-3494	42	9	numbers	number	NOUN
ejpam-3494	42	10	of	of	ADP
ejpam-3494	42	11	the	the	DET
ejpam-3494	42	12	second	second	ADJ
ejpam-3494	42	13	kind	kind	NOUN
ejpam-3494	42	14	wm	wm	PROPN
ejpam-3494	42	15	,	,	PUNCT
ejpam-3494	42	16	r(n	r(n	PROPN
ejpam-3494	42	17	,	,	PUNCT
ejpam-3494	42	18	k	k	NOUN
ejpam-3494	42	19	)	)	PUNCT
ejpam-3494	42	20	in	in	ADP
ejpam-3494	42	21	terms	term	NOUN
ejpam-3494	42	22	of	of	ADP
ejpam-3494	42	23	the	the	DET
ejpam-3494	42	24	classical	classical	ADJ
ejpam-3494	42	25	stirling	stirling	NOUN
ejpam-3494	42	26	numbers	number	NOUN
ejpam-3494	42	27	of	of	ADP
ejpam-3494	42	28	the	the	DET
ejpam-3494	42	29	second	second	ADJ
ejpam-3494	42	30	kind	kind	NOUN
ejpam-3494	42	31	s(n	s(n	PROPN
ejpam-3494	42	32	,	,	PUNCT
ejpam-3494	42	33	k	k	NOUN
ejpam-3494	42	34	)	)	PUNCT
ejpam-3494	42	35	as	as	ADP
ejpam-3494	42	36	wm	wm	PROPN
ejpam-3494	42	37	,	,	PUNCT
ejpam-3494	42	38	r(n	r(n	PROPN
ejpam-3494	42	39	,	,	PUNCT
ejpam-3494	42	40	k	k	NOUN
ejpam-3494	42	41	)	)	PUNCT
ejpam-3494	43	1	=	=	SYM
ejpam-3494	43	2	n∑	n∑	NOUN
ejpam-3494	44	1	i	i	PRON
ejpam-3494	44	2	=	=	PROPN
ejpam-3494	44	3	k	k	PROPN
ejpam-3494	44	4	(	(	PUNCT
ejpam-3494	44	5	n	n	NOUN
ejpam-3494	44	6	i	i	PROPN
ejpam-3494	44	7	)	)	PUNCT
ejpam-3494	44	8	mi−krn−is(i	mi−krn−is(i	PROPN
ejpam-3494	44	9	,	,	PUNCT
ejpam-3494	44	10	k	k	NOUN
ejpam-3494	44	11	)	)	PUNCT
ejpam-3494	44	12	.	.	PUNCT
ejpam-3494	45	1	(	(	PUNCT
ejpam-3494	45	2	7	7	X
ejpam-3494	45	3	)	)	PUNCT
ejpam-3494	45	4	replacing	replace	VERB
ejpam-3494	45	5	m	m	PRON
ejpam-3494	45	6	by	by	ADP
ejpam-3494	45	7	β	β	X
ejpam-3494	45	8	,	,	PUNCT
ejpam-3494	45	9	k	k	PROPN
ejpam-3494	45	10	by	by	ADP
ejpam-3494	45	11	j	j	PROPN
ejpam-3494	45	12	and	and	CCONJ
ejpam-3494	45	13	r	r	PROPN
ejpam-3494	45	14	by	by	ADP
ejpam-3494	45	15	−r	−r	PROPN
ejpam-3494	45	16	in	in	ADP
ejpam-3494	45	17	equation	equation	NOUN
ejpam-3494	45	18	(	(	PUNCT
ejpam-3494	45	19	7	7	NUM
ejpam-3494	45	20	)	)	PUNCT
ejpam-3494	45	21	,	,	PUNCT
ejpam-3494	45	22	yield	yield	VERB
ejpam-3494	45	23	wβ,−r(n	wβ,−r(n	PROPN
ejpam-3494	45	24	,	,	PUNCT
ejpam-3494	45	25	j	j	NOUN
ejpam-3494	45	26	)	)	PUNCT
ejpam-3494	46	1	=	=	SYM
ejpam-3494	46	2	n∑	n∑	NOUN
ejpam-3494	47	1	k	k	PROPN
ejpam-3494	47	2	=	=	ADJ
ejpam-3494	47	3	j	j	X
ejpam-3494	47	4	(	(	PUNCT
ejpam-3494	47	5	n	n	NOUN
ejpam-3494	47	6	k	k	NOUN
ejpam-3494	47	7	)	)	PUNCT
ejpam-3494	47	8	βk−j(−r)n−ks(k	βk−j(−r)n−ks(k	PROPN
ejpam-3494	47	9	,	,	PUNCT
ejpam-3494	47	10	j	j	NOUN
ejpam-3494	47	11	)	)	PUNCT
ejpam-3494	47	12	.	.	PUNCT
ejpam-3494	48	1	(	(	PUNCT
ejpam-3494	48	2	8)	8)	NUM
ejpam-3494	48	3	moreover	moreover	ADV
ejpam-3494	48	4	,	,	PUNCT
ejpam-3494	48	5	cheon	cheon	PROPN
ejpam-3494	48	6	and	and	CCONJ
ejpam-3494	48	7	jung	jung	PROPN
ejpam-3494	49	1	[	[	X
ejpam-3494	49	2	4	4	X
ejpam-3494	49	3	]	]	PUNCT
ejpam-3494	49	4	defined	define	VERB
ejpam-3494	49	5	the	the	DET
ejpam-3494	49	6	r	r	NOUN
ejpam-3494	49	7	-	-	PUNCT
ejpam-3494	49	8	dowling	dowle	VERB
ejpam-3494	49	9	polynomials	polynomial	NOUN
ejpam-3494	49	10	,	,	PUNCT
ejpam-3494	49	11	denoted	denote	VERB
ejpam-3494	49	12	by	by	ADP
ejpam-3494	49	13	dm	dm	PROPN
ejpam-3494	49	14	,	,	PUNCT
ejpam-3494	49	15	r(n	r(n	PROPN
ejpam-3494	49	16	,	,	PUNCT
ejpam-3494	49	17	x	x	NOUN
ejpam-3494	49	18	)	)	PUNCT
ejpam-3494	49	19	,	,	PUNCT
ejpam-3494	49	20	as	as	SCONJ
ejpam-3494	49	21	follows	follow	VERB
ejpam-3494	49	22	dm	dm	NOUN
ejpam-3494	49	23	,	,	PUNCT
ejpam-3494	49	24	r(n	r(n	PROPN
ejpam-3494	49	25	,	,	PUNCT
ejpam-3494	49	26	x	x	NOUN
ejpam-3494	49	27	)	)	PUNCT
ejpam-3494	49	28	=	=	SYM
ejpam-3494	49	29	n∑	n∑	PROPN
ejpam-3494	49	30	k=0	k=0	PROPN
ejpam-3494	49	31	wm	wm	PROPN
ejpam-3494	49	32	,	,	PUNCT
ejpam-3494	49	33	r(n	r(n	PROPN
ejpam-3494	49	34	,	,	PUNCT
ejpam-3494	49	35	k)xk	k)xk	PROPN
ejpam-3494	49	36	.	.	PROPN
ejpam-3494	50	1	(	(	PUNCT
ejpam-3494	50	2	9	9	X
ejpam-3494	50	3	)	)	PUNCT
ejpam-3494	50	4	taking	take	VERB
ejpam-3494	50	5	x	x	PUNCT
ejpam-3494	50	6	=	=	SYM
ejpam-3494	50	7	1	1	NUM
ejpam-3494	50	8	,	,	PUNCT
ejpam-3494	50	9	equation	equation	NOUN
ejpam-3494	50	10	(	(	PUNCT
ejpam-3494	50	11	9	9	NUM
ejpam-3494	50	12	)	)	PUNCT
ejpam-3494	50	13	reduces	reduce	VERB
ejpam-3494	50	14	to	to	ADP
ejpam-3494	50	15	dm	dm	NOUN
ejpam-3494	50	16	,	,	PUNCT
ejpam-3494	50	17	r(n	r(n	PROPN
ejpam-3494	50	18	,	,	PUNCT
ejpam-3494	50	19	1	1	NUM
ejpam-3494	50	20	)	)	PUNCT
ejpam-3494	50	21	=	=	SYM
ejpam-3494	50	22	n∑	n∑	PROPN
ejpam-3494	50	23	k=0	k=0	PROPN
ejpam-3494	50	24	wm	wm	PROPN
ejpam-3494	50	25	,	,	PUNCT
ejpam-3494	50	26	r(n	r(n	PROPN
ejpam-3494	50	27	,	,	PUNCT
ejpam-3494	50	28	k	k	NOUN
ejpam-3494	50	29	)	)	PUNCT
ejpam-3494	50	30	,	,	PUNCT
ejpam-3494	50	31	the	the	DET
ejpam-3494	50	32	r	r	NOUN
ejpam-3494	50	33	-	-	PUNCT
ejpam-3494	50	34	dowling	dowle	VERB
ejpam-3494	50	35	numbers	number	NOUN
ejpam-3494	50	36	.	.	PUNCT
ejpam-3494	51	1	these	these	DET
ejpam-3494	51	2	numbers	number	NOUN
ejpam-3494	51	3	are	be	AUX
ejpam-3494	51	4	equivalent	equivalent	ADJ
ejpam-3494	51	5	to	to	ADP
ejpam-3494	51	6	the	the	DET
ejpam-3494	51	7	(	(	PUNCT
ejpam-3494	51	8	r	r	NOUN
ejpam-3494	51	9	,	,	PUNCT
ejpam-3494	51	10	β)-bell	β)-bell	PUNCT
ejpam-3494	51	11	numbers	number	NOUN
ejpam-3494	51	12	in	in	ADP
ejpam-3494	51	13	[	[	X
ejpam-3494	51	14	8	8	NUM
ejpam-3494	51	15	]	]	PUNCT
ejpam-3494	51	16	,	,	PUNCT
ejpam-3494	51	17	denoted	denote	VERB
ejpam-3494	51	18	by	by	ADP
ejpam-3494	51	19	gn	gn	PROPN
ejpam-3494	51	20	,	,	PUNCT
ejpam-3494	51	21	β	β	X
ejpam-3494	51	22	,	,	PUNCT
ejpam-3494	51	23	r	r	NOUN
ejpam-3494	51	24	,	,	PUNCT
ejpam-3494	51	25	and	and	CCONJ
ejpam-3494	51	26	have	have	AUX
ejpam-3494	51	27	also	also	ADV
ejpam-3494	51	28	been	be	AUX
ejpam-3494	51	29	considered	consider	VERB
ejpam-3494	51	30	in	in	ADP
ejpam-3494	51	31	the	the	DET
ejpam-3494	51	32	paper	paper	NOUN
ejpam-3494	52	1	[	[	X
ejpam-3494	52	2	12	12	NUM
ejpam-3494	52	3	]	]	PUNCT
ejpam-3494	52	4	using	use	VERB
ejpam-3494	52	5	the	the	DET
ejpam-3494	52	6	same	same	ADJ
ejpam-3494	52	7	notation	notation	NOUN
ejpam-3494	52	8	gn	gn	PROPN
ejpam-3494	52	9	,	,	PUNCT
ejpam-3494	52	10	β	β	PROPN
ejpam-3494	52	11	,	,	PUNCT
ejpam-3494	52	12	r.	r.	PROPN
ejpam-3494	52	13	throughout	throughout	ADP
ejpam-3494	52	14	this	this	DET
ejpam-3494	52	15	paper	paper	NOUN
ejpam-3494	52	16	,	,	PUNCT
ejpam-3494	52	17	we	we	PRON
ejpam-3494	52	18	use	use	VERB
ejpam-3494	52	19	gn	gn	PROPN
ejpam-3494	52	20	,	,	PUNCT
ejpam-3494	52	21	β	β	X
ejpam-3494	52	22	,	,	PUNCT
ejpam-3494	52	23	r	r	NOUN
ejpam-3494	52	24	to	to	PART
ejpam-3494	52	25	denote	denote	VERB
ejpam-3494	52	26	the	the	DET
ejpam-3494	52	27	r	r	NOUN
ejpam-3494	52	28	-	-	PUNCT
ejpam-3494	52	29	dowling	dowle	VERB
ejpam-3494	52	30	numbers	number	NOUN
ejpam-3494	52	31	.	.	PUNCT
ejpam-3494	53	1	it	it	PRON
ejpam-3494	53	2	is	be	AUX
ejpam-3494	53	3	worth	worth	ADJ
ejpam-3494	53	4	mentioning	mention	VERB
ejpam-3494	53	5	that	that	SCONJ
ejpam-3494	53	6	gn	gn	PROPN
ejpam-3494	53	7	,	,	PUNCT
ejpam-3494	53	8	β	β	PROPN
ejpam-3494	53	9	,	,	PUNCT
ejpam-3494	53	10	r	r	NOUN
ejpam-3494	53	11	satisfy	satisfy	VERB
ejpam-3494	53	12	the	the	DET
ejpam-3494	53	13	following	follow	VERB
ejpam-3494	53	14	generating	generate	VERB
ejpam-3494	53	15	function∑	function∑	NOUN
ejpam-3494	53	16	n≥0	n≥0	ADJ
ejpam-3494	53	17	gn	gn	PROPN
ejpam-3494	53	18	,	,	PUNCT
ejpam-3494	53	19	β	β	X
ejpam-3494	53	20	,	,	PUNCT
ejpam-3494	53	21	r	r	NOUN
ejpam-3494	53	22	tn	tn	NOUN
ejpam-3494	53	23	n	n	ADV
ejpam-3494	53	24	!	!	PUNCT
ejpam-3494	54	1	=	=	PUNCT
ejpam-3494	54	2	erte	erte	NOUN
ejpam-3494	54	3	1	1	NUM
ejpam-3494	54	4	β	β	X
ejpam-3494	54	5	(	(	PUNCT
ejpam-3494	54	6	eβt−1	eβt−1	PROPN
ejpam-3494	54	7	)	)	PUNCT
ejpam-3494	54	8	.	.	PUNCT
ejpam-3494	55	1	(	(	PUNCT
ejpam-3494	55	2	10	10	NUM
ejpam-3494	55	3	)	)	PUNCT
ejpam-3494	55	4	the	the	DET
ejpam-3494	55	5	lah	lah	PROPN
ejpam-3494	55	6	numbers	number	NOUN
ejpam-3494	55	7	,	,	PUNCT
ejpam-3494	55	8	denoted	denote	VERB
ejpam-3494	55	9	by	by	ADP
ejpam-3494	55	10	l(n	l(n	PROPN
ejpam-3494	55	11	,	,	PUNCT
ejpam-3494	55	12	k	k	PROPN
ejpam-3494	55	13	)	)	PUNCT
ejpam-3494	55	14	,	,	PUNCT
ejpam-3494	55	15	were	be	AUX
ejpam-3494	55	16	defined	define	VERB
ejpam-3494	55	17	in	in	ADP
ejpam-3494	55	18	[	[	X
ejpam-3494	55	19	5	5	NUM
ejpam-3494	55	20	]	]	PUNCT
ejpam-3494	55	21	,	,	PUNCT
ejpam-3494	55	22	combinatorially	combinatorially	ADV
ejpam-3494	55	23	,	,	PUNCT
ejpam-3494	55	24	as	as	ADP
ejpam-3494	55	25	the	the	DET
ejpam-3494	55	26	number	number	NOUN
ejpam-3494	55	27	of	of	ADP
ejpam-3494	55	28	ways	way	NOUN
ejpam-3494	55	29	to	to	PART
ejpam-3494	55	30	partition	partition	VERB
ejpam-3494	55	31	an	an	DET
ejpam-3494	55	32	n	n	ADV
ejpam-3494	55	33	-	-	PUNCT
ejpam-3494	55	34	set	set	NOUN
ejpam-3494	55	35	into	into	ADP
ejpam-3494	55	36	k	k	PROPN
ejpam-3494	55	37	nonempty	nonempty	X
ejpam-3494	55	38	linearly	linearly	ADV
ejpam-3494	55	39	ordered	order	VERB
ejpam-3494	55	40	subsets	subset	NOUN
ejpam-3494	55	41	.	.	PUNCT
ejpam-3494	56	1	these	these	DET
ejpam-3494	56	2	numbers	number	NOUN
ejpam-3494	56	3	have	have	AUX
ejpam-3494	56	4	been	be	AUX
ejpam-3494	56	5	shown	show	VERB
ejpam-3494	56	6	to	to	PART
ejpam-3494	56	7	satisfy	satisfy	VERB
ejpam-3494	56	8	the	the	DET
ejpam-3494	56	9	following	follow	VERB
ejpam-3494	56	10	relations	relation	NOUN
ejpam-3494	56	11	l(n	l(n	PROPN
ejpam-3494	56	12	,	,	PUNCT
ejpam-3494	56	13	k	k	NOUN
ejpam-3494	56	14	)	)	PUNCT
ejpam-3494	56	15	=	=	SYM
ejpam-3494	57	1	(	(	PUNCT
ejpam-3494	57	2	n−	n−	NOUN
ejpam-3494	57	3	1	1	NUM
ejpam-3494	57	4	k	k	NOUN
ejpam-3494	57	5	−	−	PROPN
ejpam-3494	57	6	1	1	NUM
ejpam-3494	57	7	)	)	PUNCT
ejpam-3494	57	8	n	n	CCONJ
ejpam-3494	57	9	!	!	PUNCT
ejpam-3494	58	1	k	k	X
ejpam-3494	58	2	!	!	PUNCT
ejpam-3494	59	1	(	(	PUNCT
ejpam-3494	59	2	11	11	NUM
ejpam-3494	59	3	)	)	PUNCT
ejpam-3494	59	4	r.	r.	PROPN
ejpam-3494	59	5	b.	b.	PROPN
ejpam-3494	59	6	corcino	corcino	PROPN
ejpam-3494	59	7	et	et	PROPN
ejpam-3494	59	8	al	al	PROPN
ejpam-3494	59	9	.	.	PUNCT
ejpam-3494	59	10	/	/	SYM
ejpam-3494	59	11	eur	eur	PROPN
ejpam-3494	59	12	.	.	PUNCT
ejpam-3494	60	1	j.	j.	PROPN
ejpam-3494	60	2	pure	pure	PROPN
ejpam-3494	60	3	appl	appl	PROPN
ejpam-3494	60	4	.	.	PROPN
ejpam-3494	60	5	math	math	PROPN
ejpam-3494	60	6	,	,	PUNCT
ejpam-3494	60	7	12	12	NUM
ejpam-3494	60	8	(	(	PUNCT
ejpam-3494	60	9	3	3	NUM
ejpam-3494	60	10	)	)	PUNCT
ejpam-3494	60	11	(	(	PUNCT
ejpam-3494	60	12	2019	2019	NUM
ejpam-3494	60	13	)	)	PUNCT
ejpam-3494	60	14	,	,	PUNCT
ejpam-3494	60	15	1122	1122	NUM
ejpam-3494	60	16	-	-	SYM
ejpam-3494	60	17	1137	1137	NUM
ejpam-3494	60	18	1125	1125	NUM
ejpam-3494	60	19	l(n	l(n	PROPN
ejpam-3494	60	20	,	,	PUNCT
ejpam-3494	60	21	k	k	NOUN
ejpam-3494	60	22	)	)	PUNCT
ejpam-3494	60	23	=	=	SYM
ejpam-3494	61	1	n∑	n∑	PROPN
ejpam-3494	61	2	j	j	PROPN
ejpam-3494	61	3	=	=	PROPN
ejpam-3494	61	4	k	k	PROPN
ejpam-3494	61	5	s(n	s(n	PROPN
ejpam-3494	61	6	,	,	PUNCT
ejpam-3494	61	7	j)s(j	j)s(j	PROPN
ejpam-3494	61	8	,	,	PUNCT
ejpam-3494	61	9	k	k	NOUN
ejpam-3494	61	10	)	)	PUNCT
ejpam-3494	61	11	.	.	PUNCT
ejpam-3494	62	1	(	(	PUNCT
ejpam-3494	62	2	12	12	NUM
ejpam-3494	62	3	)	)	PUNCT
ejpam-3494	62	4	on	on	ADP
ejpam-3494	62	5	the	the	DET
ejpam-3494	62	6	other	other	ADJ
ejpam-3494	62	7	hand	hand	NOUN
ejpam-3494	62	8	,	,	PUNCT
ejpam-3494	62	9	the	the	DET
ejpam-3494	62	10	r	r	PROPN
ejpam-3494	62	11	-	-	PUNCT
ejpam-3494	62	12	whitney	whitney	NOUN
ejpam-3494	62	13	-	-	PUNCT
ejpam-3494	62	14	lah	lah	PROPN
ejpam-3494	62	15	numbers	number	NOUN
ejpam-3494	62	16	,	,	PUNCT
ejpam-3494	62	17	denoted	denote	VERB
ejpam-3494	62	18	by	by	ADP
ejpam-3494	62	19	lm	lm	NOUN
ejpam-3494	62	20	,	,	PUNCT
ejpam-3494	62	21	r(n	r(n	PROPN
ejpam-3494	62	22	,	,	PUNCT
ejpam-3494	62	23	k	k	NOUN
ejpam-3494	62	24	)	)	PUNCT
ejpam-3494	62	25	,	,	PUNCT
ejpam-3494	62	26	were	be	AUX
ejpam-3494	62	27	defined	define	VERB
ejpam-3494	62	28	by	by	ADP
ejpam-3494	62	29	cheon	cheon	PROPN
ejpam-3494	62	30	and	and	CCONJ
ejpam-3494	62	31	jung	jung	PROPN
ejpam-3494	63	1	[	[	X
ejpam-3494	63	2	4	4	NUM
ejpam-3494	63	3	]	]	PUNCT
ejpam-3494	63	4	parallel	parallel	NOUN
ejpam-3494	63	5	to	to	ADP
ejpam-3494	63	6	(	(	PUNCT
ejpam-3494	63	7	12	12	NUM
ejpam-3494	63	8	)	)	PUNCT
ejpam-3494	63	9	as	as	SCONJ
ejpam-3494	63	10	follows	follow	VERB
ejpam-3494	63	11	lm	lm	PROPN
ejpam-3494	63	12	,	,	PUNCT
ejpam-3494	63	13	r(n	r(n	PROPN
ejpam-3494	63	14	,	,	PUNCT
ejpam-3494	63	15	k	k	NOUN
ejpam-3494	63	16	)	)	PUNCT
ejpam-3494	63	17	=	=	SYM
ejpam-3494	64	1	n∑	n∑	PROPN
ejpam-3494	64	2	j	j	PROPN
ejpam-3494	64	3	=	=	PROPN
ejpam-3494	64	4	k	k	PROPN
ejpam-3494	64	5	wm	wm	PROPN
ejpam-3494	64	6	,	,	PUNCT
ejpam-3494	64	7	r(n	r(n	PROPN
ejpam-3494	64	8	,	,	PUNCT
ejpam-3494	64	9	j)wm	j)wm	PROPN
ejpam-3494	64	10	,	,	PUNCT
ejpam-3494	64	11	r(j	r(j	PROPN
ejpam-3494	64	12	,	,	PUNCT
ejpam-3494	64	13	k	k	NOUN
ejpam-3494	64	14	)	)	PUNCT
ejpam-3494	64	15	.	.	PUNCT
ejpam-3494	65	1	(	(	PUNCT
ejpam-3494	65	2	13	13	NUM
ejpam-3494	65	3	)	)	PUNCT
ejpam-3494	65	4	several	several	ADJ
ejpam-3494	65	5	properties	property	NOUN
ejpam-3494	65	6	of	of	ADP
ejpam-3494	65	7	lm	lm	NOUN
ejpam-3494	65	8	,	,	PUNCT
ejpam-3494	65	9	r(n	r(n	PROPN
ejpam-3494	65	10	,	,	PUNCT
ejpam-3494	65	11	k	k	NOUN
ejpam-3494	65	12	)	)	PUNCT
ejpam-3494	65	13	have	have	AUX
ejpam-3494	65	14	been	be	AUX
ejpam-3494	65	15	derived	derive	VERB
ejpam-3494	65	16	through	through	ADP
ejpam-3494	65	17	factorization	factorization	NOUN
ejpam-3494	65	18	of	of	ADP
ejpam-3494	65	19	the	the	DET
ejpam-3494	65	20	r	r	PROPN
ejpam-3494	65	21	-	-	PUNCT
ejpam-3494	65	22	whitneylah	whitneylah	NOUN
ejpam-3494	65	23	matrix	matrix	NOUN
ejpam-3494	65	24	[	[	X
ejpam-3494	65	25	lm	lm	INTJ
ejpam-3494	65	26	,	,	PUNCT
ejpam-3494	65	27	r(n	r(n	PROPN
ejpam-3494	65	28	,	,	PUNCT
ejpam-3494	65	29	k)]n	k)]n	PROPN
ejpam-3494	65	30	,	,	PUNCT
ejpam-3494	65	31	k≥0	k≥0	PROPN
ejpam-3494	65	32	(	(	PUNCT
ejpam-3494	65	33	see	see	VERB
ejpam-3494	65	34	[	[	X
ejpam-3494	65	35	4	4	NUM
ejpam-3494	65	36	]	]	PUNCT
ejpam-3494	65	37	)	)	PUNCT
ejpam-3494	65	38	including	include	VERB
ejpam-3494	65	39	the	the	DET
ejpam-3494	65	40	triangular	triangular	NOUN
ejpam-3494	65	41	relation	relation	NOUN
ejpam-3494	65	42	lm	lm	PROPN
ejpam-3494	65	43	,	,	PUNCT
ejpam-3494	65	44	r(n	r(n	PROPN
ejpam-3494	65	45	,	,	PUNCT
ejpam-3494	65	46	k	k	NOUN
ejpam-3494	65	47	)	)	PUNCT
ejpam-3494	66	1	=	=	SYM
ejpam-3494	66	2	lm	lm	PROPN
ejpam-3494	66	3	,	,	PUNCT
ejpam-3494	66	4	r(n−	r(n−	NOUN
ejpam-3494	66	5	1	1	NUM
ejpam-3494	66	6	,	,	PUNCT
ejpam-3494	66	7	k	k	PROPN
ejpam-3494	66	8	−	−	PROPN
ejpam-3494	66	9	1	1	NUM
ejpam-3494	66	10	)	)	PUNCT
ejpam-3494	66	11	+	+	CCONJ
ejpam-3494	66	12	(	(	PUNCT
ejpam-3494	66	13	2r	2r	NUM
ejpam-3494	66	14	+	+	CCONJ
ejpam-3494	66	15	(	(	PUNCT
ejpam-3494	66	16	n+	n+	NUM
ejpam-3494	66	17	k	k	NOUN
ejpam-3494	66	18	−	−	PROPN
ejpam-3494	67	1	1)m)lm	1)m)lm	NUM
ejpam-3494	67	2	,	,	PUNCT
ejpam-3494	67	3	r(n−	r(n−	NOUN
ejpam-3494	67	4	1	1	NUM
ejpam-3494	67	5	,	,	PUNCT
ejpam-3494	67	6	k	k	NOUN
ejpam-3494	67	7	)	)	PUNCT
ejpam-3494	67	8	below	below	ADV
ejpam-3494	67	9	is	be	AUX
ejpam-3494	67	10	a	a	DET
ejpam-3494	67	11	triangular	triangular	NOUN
ejpam-3494	67	12	array	array	NOUN
ejpam-3494	67	13	of	of	ADP
ejpam-3494	67	14	values	value	NOUN
ejpam-3494	67	15	for	for	ADP
ejpam-3494	67	16	lm	lm	PROPN
ejpam-3494	67	17	,	,	PUNCT
ejpam-3494	67	18	r(n	r(n	PROPN
ejpam-3494	67	19	,	,	PUNCT
ejpam-3494	67	20	k	k	NOUN
ejpam-3494	67	21	)	)	PUNCT
ejpam-3494	67	22	with	with	ADP
ejpam-3494	67	23	m	m	PROPN
ejpam-3494	67	24	=	=	SYM
ejpam-3494	67	25	r	r	NOUN
ejpam-3494	67	26	=	=	SYM
ejpam-3494	67	27	2	2	NUM
ejpam-3494	67	28	:	:	PUNCT
ejpam-3494	67	29	n	n	CCONJ
ejpam-3494	67	30	/	/	SYM
ejpam-3494	67	31	k	k	NOUN
ejpam-3494	67	32	0	0	NUM
ejpam-3494	67	33	1	1	NUM
ejpam-3494	67	34	2	2	NUM
ejpam-3494	67	35	3	3	NUM
ejpam-3494	67	36	4	4	NUM
ejpam-3494	67	37	0	0	NUM
ejpam-3494	67	38	1	1	NUM
ejpam-3494	67	39	1	1	NUM
ejpam-3494	67	40	4	4	NUM
ejpam-3494	67	41	1	1	NUM
ejpam-3494	67	42	2	2	NUM
ejpam-3494	67	43	24	24	NUM
ejpam-3494	67	44	12	12	NUM
ejpam-3494	67	45	1	1	NUM
ejpam-3494	67	46	3	3	NUM
ejpam-3494	67	47	192	192	NUM
ejpam-3494	67	48	144	144	NUM
ejpam-3494	67	49	24	24	NUM
ejpam-3494	67	50	1	1	NUM
ejpam-3494	67	51	4	4	NUM
ejpam-3494	67	52	1920	1920	NUM
ejpam-3494	67	53	1920	1920	NUM
ejpam-3494	67	54	480	480	NUM
ejpam-3494	67	55	40	40	NUM
ejpam-3494	67	56	1	1	NUM
ejpam-3494	67	57	table	table	NOUN
ejpam-3494	67	58	3	3	NUM
ejpam-3494	67	59	:	:	PUNCT
ejpam-3494	67	60	few	few	ADJ
ejpam-3494	67	61	values	value	NOUN
ejpam-3494	67	62	of	of	ADP
ejpam-3494	67	63	l2,2(n	l2,2(n	PROPN
ejpam-3494	67	64	,	,	PUNCT
ejpam-3494	67	65	k	k	NOUN
ejpam-3494	67	66	)	)	PUNCT
ejpam-3494	67	67	.	.	PUNCT
ejpam-3494	68	1	in	in	ADP
ejpam-3494	68	2	this	this	DET
ejpam-3494	68	3	paper	paper	NOUN
ejpam-3494	68	4	,	,	PUNCT
ejpam-3494	68	5	two	two	NUM
ejpam-3494	68	6	explicit	explicit	ADJ
ejpam-3494	68	7	formulas	formula	NOUN
ejpam-3494	68	8	for	for	ADP
ejpam-3494	68	9	gn	gn	PROPN
ejpam-3494	68	10	,	,	PUNCT
ejpam-3494	68	11	β	β	PROPN
ejpam-3494	68	12	,	,	PUNCT
ejpam-3494	68	13	r	r	NOUN
ejpam-3494	68	14	are	be	AUX
ejpam-3494	68	15	derived	derive	VERB
ejpam-3494	68	16	using	use	VERB
ejpam-3494	68	17	the	the	DET
ejpam-3494	68	18	two	two	NUM
ejpam-3494	68	19	methods	method	NOUN
ejpam-3494	68	20	applied	apply	VERB
ejpam-3494	68	21	by	by	ADP
ejpam-3494	68	22	feng	feng	PROPN
ejpam-3494	68	23	qi	qi	PROPN
ejpam-3494	69	1	[	[	X
ejpam-3494	69	2	21	21	NUM
ejpam-3494	69	3	]	]	PUNCT
ejpam-3494	69	4	in	in	ADP
ejpam-3494	69	5	expressing	express	VERB
ejpam-3494	69	6	the	the	DET
ejpam-3494	69	7	bell	bell	NOUN
ejpam-3494	69	8	numbers	number	NOUN
ejpam-3494	69	9	in	in	ADP
ejpam-3494	69	10	terms	term	NOUN
ejpam-3494	69	11	of	of	ADP
ejpam-3494	69	12	stirling	stirling	NOUN
ejpam-3494	69	13	numbers	number	NOUN
ejpam-3494	69	14	of	of	ADP
ejpam-3494	69	15	the	the	DET
ejpam-3494	69	16	second	second	ADJ
ejpam-3494	69	17	kind	kind	NOUN
ejpam-3494	69	18	and	and	CCONJ
ejpam-3494	69	19	lah	lah	NOUN
ejpam-3494	69	20	numbers	number	NOUN
ejpam-3494	69	21	.	.	PUNCT
ejpam-3494	70	1	the	the	DET
ejpam-3494	70	2	two	two	NUM
ejpam-3494	70	3	methods	method	NOUN
ejpam-3494	70	4	yield	yield	VERB
ejpam-3494	70	5	exactly	exactly	ADV
ejpam-3494	70	6	the	the	DET
ejpam-3494	70	7	same	same	ADJ
ejpam-3494	70	8	explicit	explicit	ADJ
ejpam-3494	70	9	formula	formula	NOUN
ejpam-3494	70	10	when	when	SCONJ
ejpam-3494	70	11	they	they	PRON
ejpam-3494	70	12	are	be	AUX
ejpam-3494	70	13	applied	apply	VERB
ejpam-3494	70	14	by	by	ADP
ejpam-3494	70	15	feng	feng	PROPN
ejpam-3494	70	16	qi	qi	PROPN
ejpam-3494	70	17	to	to	ADP
ejpam-3494	70	18	bell	bell	NOUN
ejpam-3494	70	19	numbers	number	NOUN
ejpam-3494	70	20	.	.	PUNCT
ejpam-3494	71	1	however	however	ADV
ejpam-3494	71	2	,	,	PUNCT
ejpam-3494	71	3	when	when	SCONJ
ejpam-3494	71	4	these	these	DET
ejpam-3494	71	5	methods	method	NOUN
ejpam-3494	71	6	are	be	AUX
ejpam-3494	71	7	applied	apply	VERB
ejpam-3494	71	8	here	here	ADV
ejpam-3494	71	9	to	to	ADP
ejpam-3494	71	10	gn	gn	PROPN
ejpam-3494	71	11	,	,	PUNCT
ejpam-3494	71	12	β	β	X
ejpam-3494	71	13	,	,	PUNCT
ejpam-3494	71	14	r	r	NOUN
ejpam-3494	71	15	,	,	PUNCT
ejpam-3494	71	16	they	they	PRON
ejpam-3494	71	17	give	give	VERB
ejpam-3494	71	18	two	two	NUM
ejpam-3494	71	19	equivalent	equivalent	ADJ
ejpam-3494	71	20	formulas	formula	NOUN
ejpam-3494	71	21	of	of	ADP
ejpam-3494	71	22	different	different	ADJ
ejpam-3494	71	23	forms	form	NOUN
ejpam-3494	71	24	.	.	PUNCT
ejpam-3494	72	1	these	these	DET
ejpam-3494	72	2	formulas	formula	NOUN
ejpam-3494	72	3	imply	imply	VERB
ejpam-3494	72	4	two	two	NUM
ejpam-3494	72	5	matrix	matrix	NOUN
ejpam-3494	72	6	relations	relation	NOUN
ejpam-3494	72	7	involving	involve	VERB
ejpam-3494	72	8	r	r	NOUN
ejpam-3494	72	9	-	-	PUNCT
ejpam-3494	72	10	dowling	dowle	VERB
ejpam-3494	72	11	numbers	number	NOUN
ejpam-3494	72	12	,	,	PUNCT
ejpam-3494	72	13	r	r	NOUN
ejpam-3494	72	14	-	-	PUNCT
ejpam-3494	72	15	whitney	whitney	NOUN
ejpam-3494	72	16	numbers	number	NOUN
ejpam-3494	72	17	of	of	ADP
ejpam-3494	72	18	the	the	DET
ejpam-3494	72	19	second	second	ADJ
ejpam-3494	72	20	,	,	PUNCT
ejpam-3494	72	21	r	r	NOUN
ejpam-3494	72	22	-	-	PUNCT
ejpam-3494	72	23	whitney	whitney	NOUN
ejpam-3494	72	24	-	-	PUNCT
ejpam-3494	72	25	lah	lah	NOUN
ejpam-3494	72	26	numbers	number	NOUN
ejpam-3494	72	27	and	and	CCONJ
ejpam-3494	72	28	lah	lah	NOUN
ejpam-3494	72	29	numbers	number	NOUN
ejpam-3494	72	30	.	.	PUNCT
ejpam-3494	73	1	2	2	X
ejpam-3494	73	2	.	.	X
ejpam-3494	73	3	expression	expression	NOUN
ejpam-3494	73	4	in	in	ADP
ejpam-3494	73	5	terms	term	NOUN
ejpam-3494	73	6	of	of	ADP
ejpam-3494	73	7	exponential	exponential	ADJ
ejpam-3494	73	8	polynomials	polynomial	NOUN
ejpam-3494	73	9	the	the	DET
ejpam-3494	73	10	exponential	exponential	ADJ
ejpam-3494	73	11	polynomial	polynomial	NOUN
ejpam-3494	73	12	[	[	X
ejpam-3494	73	13	2	2	NUM
ejpam-3494	73	14	]	]	PUNCT
ejpam-3494	73	15	,	,	PUNCT
ejpam-3494	73	16	denoted	denote	VERB
ejpam-3494	73	17	by	by	ADP
ejpam-3494	73	18	φn(x	φn(x	NOUN
ejpam-3494	73	19	)	)	PUNCT
ejpam-3494	73	20	,	,	PUNCT
ejpam-3494	73	21	appeared	appear	VERB
ejpam-3494	73	22	in	in	ADP
ejpam-3494	73	23	the	the	DET
ejpam-3494	73	24	resulting	result	VERB
ejpam-3494	73	25	expression	expression	NOUN
ejpam-3494	73	26	in	in	ADP
ejpam-3494	73	27	applying	apply	VERB
ejpam-3494	73	28	mellin	mellin	PROPN
ejpam-3494	73	29	derivative	derivative	NOUN
ejpam-3494	73	30	(	(	PUNCT
ejpam-3494	73	31	x	x	PUNCT
ejpam-3494	73	32	d	d	NOUN
ejpam-3494	73	33	dx	dx	PROPN
ejpam-3494	73	34	)	)	PUNCT
ejpam-3494	73	35	n	n	CCONJ
ejpam-3494	73	36	to	to	ADP
ejpam-3494	73	37	the	the	DET
ejpam-3494	73	38	function	function	NOUN
ejpam-3494	73	39	ex	ex	PROPN
ejpam-3494	73	40	.	.	PUNCT
ejpam-3494	74	1	the	the	DET
ejpam-3494	74	2	notation	notation	NOUN
ejpam-3494	74	3	for	for	ADP
ejpam-3494	74	4	mellin	mellin	PROPN
ejpam-3494	74	5	derivative	derivative	NOUN
ejpam-3494	74	6	would	would	AUX
ejpam-3494	74	7	mean	mean	VERB
ejpam-3494	74	8	that	that	SCONJ
ejpam-3494	74	9	the	the	DET
ejpam-3494	74	10	differential	differential	ADJ
ejpam-3494	74	11	operator	operator	NOUN
ejpam-3494	74	12	x	x	PUNCT
ejpam-3494	75	1	d	d	X
ejpam-3494	75	2	dx	dx	PROPN
ejpam-3494	75	3	is	be	AUX
ejpam-3494	75	4	applied	apply	VERB
ejpam-3494	75	5	n	n	DET
ejpam-3494	75	6	times	time	NOUN
ejpam-3494	75	7	to	to	ADP
ejpam-3494	75	8	ex	ex	PRON
ejpam-3494	75	9	.	.	PUNCT
ejpam-3494	76	1	the	the	DET
ejpam-3494	76	2	first	first	ADJ
ejpam-3494	76	3	two	two	NUM
ejpam-3494	76	4	applications	application	NOUN
ejpam-3494	76	5	of	of	ADP
ejpam-3494	76	6	the	the	DET
ejpam-3494	76	7	operator	operator	NOUN
ejpam-3494	76	8	give	give	VERB
ejpam-3494	76	9	x	x	PUNCT
ejpam-3494	77	1	d	d	X
ejpam-3494	77	2	dx	dx	PROPN
ejpam-3494	77	3	ex	ex	X
ejpam-3494	78	1	=	=	PROPN
ejpam-3494	78	2	xex	xex	PROPN
ejpam-3494	78	3	(	(	PUNCT
ejpam-3494	78	4	x	x	PROPN
ejpam-3494	78	5	d	d	NOUN
ejpam-3494	78	6	dx	dx	PROPN
ejpam-3494	78	7	)	)	PUNCT
ejpam-3494	78	8	2	2	NUM
ejpam-3494	78	9	ex	ex	NOUN
ejpam-3494	78	10	=	=	NOUN
ejpam-3494	78	11	(	(	PUNCT
ejpam-3494	78	12	x	x	PUNCT
ejpam-3494	78	13	d	d	NOUN
ejpam-3494	78	14	dx	dx	PROPN
ejpam-3494	78	15	)	)	PUNCT
ejpam-3494	78	16	(	(	PUNCT
ejpam-3494	78	17	x	x	PUNCT
ejpam-3494	78	18	d	d	X
ejpam-3494	78	19	dx	dx	PROPN
ejpam-3494	78	20	ex	ex	X
ejpam-3494	78	21	)	)	PUNCT
ejpam-3494	78	22	r.	r.	PROPN
ejpam-3494	78	23	b.	b.	PROPN
ejpam-3494	78	24	corcino	corcino	PROPN
ejpam-3494	78	25	et	et	PROPN
ejpam-3494	78	26	al	al	PROPN
ejpam-3494	78	27	.	.	PUNCT
ejpam-3494	78	28	/	/	SYM
ejpam-3494	78	29	eur	eur	PROPN
ejpam-3494	78	30	.	.	PUNCT
ejpam-3494	79	1	j.	j.	PROPN
ejpam-3494	79	2	pure	pure	PROPN
ejpam-3494	79	3	appl	appl	PROPN
ejpam-3494	79	4	.	.	PROPN
ejpam-3494	79	5	math	math	PROPN
ejpam-3494	79	6	,	,	PUNCT
ejpam-3494	79	7	12	12	NUM
ejpam-3494	79	8	(	(	PUNCT
ejpam-3494	79	9	3	3	NUM
ejpam-3494	79	10	)	)	PUNCT
ejpam-3494	79	11	(	(	PUNCT
ejpam-3494	79	12	2019	2019	NUM
ejpam-3494	79	13	)	)	PUNCT
ejpam-3494	79	14	,	,	PUNCT
ejpam-3494	79	15	1122	1122	NUM
ejpam-3494	79	16	-	-	SYM
ejpam-3494	79	17	1137	1137	NUM
ejpam-3494	79	18	1126	1126	NUM
ejpam-3494	79	19	=	=	PUNCT
ejpam-3494	80	1	x	x	PUNCT
ejpam-3494	80	2	d	d	X
ejpam-3494	80	3	dx	dx	PROPN
ejpam-3494	80	4	(	(	PUNCT
ejpam-3494	80	5	xex	xex	PROPN
ejpam-3494	80	6	)	)	PUNCT
ejpam-3494	80	7	=	=	PRON
ejpam-3494	81	1	(	(	PUNCT
ejpam-3494	81	2	x2	x2	PROPN
ejpam-3494	81	3	+	+	CCONJ
ejpam-3494	81	4	x	x	X
ejpam-3494	81	5	)	)	PUNCT
ejpam-3494	81	6	ex	ex	NOUN
ejpam-3494	81	7	.	.	PUNCT
ejpam-3494	81	8	continuing	continue	VERB
ejpam-3494	81	9	in	in	ADP
ejpam-3494	81	10	this	this	DET
ejpam-3494	81	11	manner	manner	NOUN
ejpam-3494	81	12	yields	yield	NOUN
ejpam-3494	81	13	(	(	PUNCT
ejpam-3494	81	14	x	x	SYM
ejpam-3494	81	15	d	d	NOUN
ejpam-3494	81	16	dx	dx	PROPN
ejpam-3494	81	17	)	)	PUNCT
ejpam-3494	81	18	n	n	PRON
ejpam-3494	81	19	ex	ex	ADJ
ejpam-3494	81	20	=	=	NOUN
ejpam-3494	81	21	φn(x)ex	φn(x)ex	NOUN
ejpam-3494	81	22	.	.	PUNCT
ejpam-3494	82	1	the	the	DET
ejpam-3494	82	2	exponential	exponential	ADJ
ejpam-3494	82	3	polynomial	polynomial	ADJ
ejpam-3494	82	4	satisfies	satisfie	NOUN
ejpam-3494	82	5	the	the	DET
ejpam-3494	82	6	following	follow	VERB
ejpam-3494	82	7	generating	generate	VERB
ejpam-3494	82	8	function	function	NOUN
ejpam-3494	82	9	ex(e	ex(e	ADJ
ejpam-3494	82	10	t−1	t−1	NOUN
ejpam-3494	82	11	)	)	PUNCT
ejpam-3494	82	12	=	=	PUNCT
ejpam-3494	83	1	∞∑	∞∑	NUM
ejpam-3494	83	2	n=0	n=0	NUM
ejpam-3494	83	3	φn(x	φn(x	NUM
ejpam-3494	83	4	)	)	PUNCT
ejpam-3494	83	5	tn	tn	NOUN
ejpam-3494	83	6	n	n	CCONJ
ejpam-3494	83	7	!	!	PROPN
ejpam-3494	83	8	,	,	PUNCT
ejpam-3494	83	9	(	(	PUNCT
ejpam-3494	83	10	14	14	NUM
ejpam-3494	83	11	)	)	PUNCT
ejpam-3494	83	12	which	which	PRON
ejpam-3494	83	13	can	can	AUX
ejpam-3494	83	14	be	be	AUX
ejpam-3494	83	15	expressed	express	VERB
ejpam-3494	83	16	in	in	ADP
ejpam-3494	83	17	polynomial	polynomial	ADJ
ejpam-3494	83	18	form	form	NOUN
ejpam-3494	83	19	as	as	ADP
ejpam-3494	83	20	φn(x	φn(x	NOUN
ejpam-3494	83	21	)	)	PUNCT
ejpam-3494	83	22	=	=	SYM
ejpam-3494	83	23	n∑	n∑	X
ejpam-3494	83	24	k=0	k=0	PROPN
ejpam-3494	83	25	s(n	s(n	PROPN
ejpam-3494	83	26	,	,	PUNCT
ejpam-3494	83	27	k)xk	k)xk	PROPN
ejpam-3494	83	28	,	,	PUNCT
ejpam-3494	83	29	(	(	PUNCT
ejpam-3494	83	30	15	15	NUM
ejpam-3494	83	31	)	)	PUNCT
ejpam-3494	83	32	whose	whose	DET
ejpam-3494	83	33	coefficients	coefficient	NOUN
ejpam-3494	83	34	are	be	AUX
ejpam-3494	83	35	the	the	DET
ejpam-3494	83	36	stirling	stirling	NOUN
ejpam-3494	83	37	numbers	number	NOUN
ejpam-3494	83	38	of	of	ADP
ejpam-3494	83	39	the	the	DET
ejpam-3494	83	40	second	second	ADJ
ejpam-3494	83	41	kind	kind	NOUN
ejpam-3494	83	42	.	.	PUNCT
ejpam-3494	84	1	note	note	VERB
ejpam-3494	84	2	that	that	SCONJ
ejpam-3494	84	3	,	,	PUNCT
ejpam-3494	84	4	when	when	SCONJ
ejpam-3494	84	5	x	x	SYM
ejpam-3494	84	6	=	=	SYM
ejpam-3494	84	7	1	1	NUM
ejpam-3494	84	8	/	/	SYM
ejpam-3494	84	9	β	β	X
ejpam-3494	84	10	and	and	CCONJ
ejpam-3494	84	11	t	t	NOUN
ejpam-3494	84	12	=	=	SYM
ejpam-3494	84	13	βt	βt	PROPN
ejpam-3494	84	14	,	,	PUNCT
ejpam-3494	84	15	(	(	PUNCT
ejpam-3494	84	16	16	16	NUM
ejpam-3494	84	17	)	)	PUNCT
ejpam-3494	84	18	reduces	reduce	VERB
ejpam-3494	84	19	to	to	ADP
ejpam-3494	84	20	e	e	PROPN
ejpam-3494	84	21	1	1	NUM
ejpam-3494	84	22	β	β	X
ejpam-3494	84	23	(	(	PUNCT
ejpam-3494	84	24	et−1	et−1	NOUN
ejpam-3494	84	25	)	)	PUNCT
ejpam-3494	84	26	=	=	PUNCT
ejpam-3494	85	1	∞∑	∞∑	PRON
ejpam-3494	85	2	n=0	n=0	NUM
ejpam-3494	85	3	φn	φn	NOUN
ejpam-3494	85	4	(	(	PUNCT
ejpam-3494	85	5	1	1	NUM
ejpam-3494	85	6	/	/	SYM
ejpam-3494	85	7	β	β	NOUN
ejpam-3494	85	8	)	)	PUNCT
ejpam-3494	85	9	(	(	PUNCT
ejpam-3494	85	10	βt)n	βt)n	PROPN
ejpam-3494	85	11	n	n	CCONJ
ejpam-3494	85	12	!	!	PUNCT
ejpam-3494	85	13	,	,	PUNCT
ejpam-3494	85	14	β	β	PROPN
ejpam-3494	85	15	6=	6=	ADP
ejpam-3494	85	16	0	0	NUM
ejpam-3494	85	17	.	.	PUNCT
ejpam-3494	86	1	(	(	PUNCT
ejpam-3494	86	2	16	16	NUM
ejpam-3494	86	3	)	)	PUNCT
ejpam-3494	86	4	hence	hence	ADV
ejpam-3494	86	5	,	,	PUNCT
ejpam-3494	86	6	the	the	DET
ejpam-3494	86	7	exponential	exponential	ADJ
ejpam-3494	86	8	generating	generating	NOUN
ejpam-3494	86	9	function	function	NOUN
ejpam-3494	86	10	in	in	ADP
ejpam-3494	86	11	(	(	PUNCT
ejpam-3494	86	12	10	10	NUM
ejpam-3494	86	13	)	)	PUNCT
ejpam-3494	86	14	can	can	AUX
ejpam-3494	86	15	be	be	AUX
ejpam-3494	86	16	written	write	VERB
ejpam-3494	86	17	as	as	ADP
ejpam-3494	86	18	∑	∑	PUNCT
ejpam-3494	86	19	n≥0	n≥0	PROPN
ejpam-3494	86	20	gn	gn	PROPN
ejpam-3494	86	21	,	,	PUNCT
ejpam-3494	86	22	β	β	X
ejpam-3494	86	23	,	,	PUNCT
ejpam-3494	86	24	r	r	NOUN
ejpam-3494	86	25	tn	tn	NOUN
ejpam-3494	86	26	n	n	CCONJ
ejpam-3494	86	27	!	!	PUNCT
ejpam-3494	87	1	=	=	PUNCT
ejpam-3494	88	1	∑	∑	NOUN
ejpam-3494	88	2	n≥0	n≥0	PROPN
ejpam-3494	88	3	(	(	PUNCT
ejpam-3494	88	4	rt)n	rt)n	PROPN
ejpam-3494	88	5	n	n	X
ejpam-3494	88	6	!	!	PUNCT
ejpam-3494	88	7	∑	∑	PROPN
ejpam-3494	89	1	n≥0	n≥0	ADJ
ejpam-3494	89	2	φn	φn	X
ejpam-3494	89	3	(	(	PUNCT
ejpam-3494	89	4	1	1	NUM
ejpam-3494	89	5	/	/	SYM
ejpam-3494	89	6	β	β	NOUN
ejpam-3494	89	7	)	)	PUNCT
ejpam-3494	89	8	(	(	PUNCT
ejpam-3494	89	9	βt)n	βt)n	NUM
ejpam-3494	89	10	n	n	CCONJ
ejpam-3494	89	11	!	!	PUNCT
ejpam-3494	90	1			PROPN
ejpam-3494	90	2	=	=	PUNCT
ejpam-3494	91	1	∑	∑	PUNCT
ejpam-3494	91	2	n≥0	n≥0	PROPN
ejpam-3494	91	3	{	{	PUNCT
ejpam-3494	91	4	n∑	n∑	NOUN
ejpam-3494	91	5	k=0	k=0	PROPN
ejpam-3494	91	6	φk	φk	ADP
ejpam-3494	91	7	(	(	PUNCT
ejpam-3494	91	8	1	1	NUM
ejpam-3494	91	9	/	/	SYM
ejpam-3494	91	10	β	β	NOUN
ejpam-3494	91	11	)	)	PUNCT
ejpam-3494	91	12	(	(	PUNCT
ejpam-3494	91	13	βt)k	βt)k	PROPN
ejpam-3494	91	14	k	k	X
ejpam-3494	91	15	!	!	PUNCT
ejpam-3494	92	1	(	(	PUNCT
ejpam-3494	92	2	rt)n−k	rt)n−k	NOUN
ejpam-3494	92	3	(	(	PUNCT
ejpam-3494	92	4	n−	n−	NOUN
ejpam-3494	92	5	k	k	NOUN
ejpam-3494	92	6	)	)	PUNCT
ejpam-3494	92	7	!	!	PUNCT
ejpam-3494	92	8	}	}	PUNCT
ejpam-3494	93	1	=	=	PUNCT
ejpam-3494	93	2	∑	∑	PUNCT
ejpam-3494	93	3	n≥0	n≥0	PROPN
ejpam-3494	93	4	{	{	PUNCT
ejpam-3494	93	5	n∑	n∑	NOUN
ejpam-3494	93	6	k=0	k=0	PROPN
ejpam-3494	93	7	(	(	PUNCT
ejpam-3494	93	8	n	n	X
ejpam-3494	93	9	k	k	NOUN
ejpam-3494	93	10	)	)	PUNCT
ejpam-3494	93	11	φk	φk	ADP
ejpam-3494	93	12	(	(	PUNCT
ejpam-3494	93	13	1	1	NUM
ejpam-3494	93	14	/	/	SYM
ejpam-3494	93	15	β)βkrn−k	β)βkrn−k	NOUN
ejpam-3494	93	16	}	}	PUNCT
ejpam-3494	93	17	tn	tn	PROPN
ejpam-3494	93	18	n	n	X
ejpam-3494	93	19	!	!	PUNCT
ejpam-3494	93	20	.	.	PUNCT
ejpam-3494	94	1	comparing	compare	VERB
ejpam-3494	94	2	the	the	DET
ejpam-3494	94	3	coefficients	coefficient	NOUN
ejpam-3494	94	4	of	of	ADP
ejpam-3494	94	5	tn	tn	NOUN
ejpam-3494	94	6	n	n	X
ejpam-3494	94	7	!	!	PUNCT
ejpam-3494	95	1	yields	yield	VERB
ejpam-3494	95	2	the	the	DET
ejpam-3494	95	3	following	follow	VERB
ejpam-3494	95	4	explicit	explicit	ADJ
ejpam-3494	95	5	formula	formula	NOUN
ejpam-3494	95	6	.	.	PUNCT
ejpam-3494	96	1	theorem	theorem	VERB
ejpam-3494	96	2	2.1	2.1	NUM
ejpam-3494	96	3	.	.	PUNCT
ejpam-3494	97	1	the	the	DET
ejpam-3494	97	2	r	r	NOUN
ejpam-3494	97	3	-	-	PUNCT
ejpam-3494	97	4	dowling	dowle	VERB
ejpam-3494	97	5	numbers	number	NOUN
ejpam-3494	97	6	can	can	AUX
ejpam-3494	97	7	be	be	AUX
ejpam-3494	97	8	expressed	express	VERB
ejpam-3494	97	9	as	as	ADP
ejpam-3494	97	10	gn	gn	PROPN
ejpam-3494	97	11	,	,	PUNCT
ejpam-3494	97	12	β	β	X
ejpam-3494	97	13	,	,	PUNCT
ejpam-3494	97	14	r	r	NOUN
ejpam-3494	97	15	=	=	SYM
ejpam-3494	97	16	n∑	n∑	NOUN
ejpam-3494	98	1	k=0	k=0	PROPN
ejpam-3494	98	2	(	(	PUNCT
ejpam-3494	98	3	n	n	X
ejpam-3494	98	4	k	k	NOUN
ejpam-3494	98	5	)	)	PUNCT
ejpam-3494	98	6	φk	φk	ADP
ejpam-3494	98	7	(	(	PUNCT
ejpam-3494	98	8	1	1	NUM
ejpam-3494	98	9	/	/	SYM
ejpam-3494	98	10	β)βkrn−k	β)βkrn−k	NOUN
ejpam-3494	98	11	,	,	PUNCT
ejpam-3494	98	12	(	(	PUNCT
ejpam-3494	98	13	17	17	NUM
ejpam-3494	98	14	)	)	PUNCT
ejpam-3494	98	15	which	which	PRON
ejpam-3494	98	16	is	be	AUX
ejpam-3494	98	17	a	a	DET
ejpam-3494	98	18	kind	kind	NOUN
ejpam-3494	98	19	of	of	ADP
ejpam-3494	98	20	binomial	binomial	ADJ
ejpam-3494	98	21	combination	combination	NOUN
ejpam-3494	98	22	of	of	ADP
ejpam-3494	98	23	φk(1	φk(1	PROPN
ejpam-3494	98	24	/	/	SYM
ejpam-3494	98	25	β	β	NOUN
ejpam-3494	98	26	)	)	PUNCT
ejpam-3494	98	27	.	.	PUNCT
ejpam-3494	99	1	r.	r.	PROPN
ejpam-3494	99	2	b.	b.	PROPN
ejpam-3494	99	3	corcino	corcino	PROPN
ejpam-3494	99	4	et	et	PROPN
ejpam-3494	99	5	al	al	PROPN
ejpam-3494	99	6	.	.	PUNCT
ejpam-3494	99	7	/	/	SYM
ejpam-3494	99	8	eur	eur	PROPN
ejpam-3494	99	9	.	.	PUNCT
ejpam-3494	100	1	j.	j.	PROPN
ejpam-3494	100	2	pure	pure	PROPN
ejpam-3494	100	3	appl	appl	PROPN
ejpam-3494	100	4	.	.	PROPN
ejpam-3494	100	5	math	math	PROPN
ejpam-3494	100	6	,	,	PUNCT
ejpam-3494	100	7	12	12	NUM
ejpam-3494	100	8	(	(	PUNCT
ejpam-3494	100	9	3	3	NUM
ejpam-3494	100	10	)	)	PUNCT
ejpam-3494	100	11	(	(	PUNCT
ejpam-3494	100	12	2019	2019	NUM
ejpam-3494	100	13	)	)	PUNCT
ejpam-3494	100	14	,	,	PUNCT
ejpam-3494	100	15	1122	1122	NUM
ejpam-3494	100	16	-	-	SYM
ejpam-3494	100	17	1137	1137	NUM
ejpam-3494	100	18	1127	1127	NUM
ejpam-3494	100	19	using	use	VERB
ejpam-3494	100	20	(	(	PUNCT
ejpam-3494	100	21	15	15	NUM
ejpam-3494	100	22	)	)	PUNCT
ejpam-3494	100	23	,	,	PUNCT
ejpam-3494	100	24	the	the	DET
ejpam-3494	100	25	explicit	explicit	ADJ
ejpam-3494	100	26	formula	formula	NOUN
ejpam-3494	100	27	in	in	ADP
ejpam-3494	100	28	(	(	PUNCT
ejpam-3494	100	29	17	17	NUM
ejpam-3494	100	30	)	)	PUNCT
ejpam-3494	100	31	can	can	AUX
ejpam-3494	100	32	further	far	ADV
ejpam-3494	100	33	be	be	AUX
ejpam-3494	100	34	written	write	VERB
ejpam-3494	100	35	as	as	ADP
ejpam-3494	100	36	gn	gn	PROPN
ejpam-3494	100	37	,	,	PUNCT
ejpam-3494	100	38	β	β	X
ejpam-3494	100	39	,	,	PUNCT
ejpam-3494	100	40	r	r	NOUN
ejpam-3494	100	41	=	=	SYM
ejpam-3494	100	42	n∑	n∑	PROPN
ejpam-3494	100	43	k=0	k=0	PROPN
ejpam-3494	100	44			PUNCT
ejpam-3494	100	45	k∑	k∑	PROPN
ejpam-3494	100	46	j=0	j=0	VERB
ejpam-3494	100	47	s(k	s(k	ADV
ejpam-3494	100	48	,	,	PUNCT
ejpam-3494	100	49	j)(1	j)(1	NOUN
ejpam-3494	100	50	/	/	SYM
ejpam-3494	100	51	β)j	β)j	X
ejpam-3494	100	52			X
ejpam-3494	100	53	(	(	PUNCT
ejpam-3494	100	54	n	n	X
ejpam-3494	100	55	k	k	PROPN
ejpam-3494	100	56	)	)	PUNCT
ejpam-3494	100	57	βkrn−k	βkrn−k	PROPN
ejpam-3494	100	58	.	.	PUNCT
ejpam-3494	101	1	(	(	PUNCT
ejpam-3494	101	2	18	18	NUM
ejpam-3494	101	3	)	)	PUNCT
ejpam-3494	101	4	this	this	PRON
ejpam-3494	101	5	gives	give	VERB
ejpam-3494	101	6	the	the	DET
ejpam-3494	101	7	following	follow	VERB
ejpam-3494	101	8	matrix	matrix	NOUN
ejpam-3494	101	9	relation	relation	NOUN
ejpam-3494	101	10	.	.	PUNCT
ejpam-3494	102	1	theorem	theorem	VERB
ejpam-3494	102	2	2.2	2.2	NUM
ejpam-3494	102	3	.	.	PUNCT
ejpam-3494	103	1	for	for	ADP
ejpam-3494	103	2	n	n	PRON
ejpam-3494	103	3	∈	∈	PROPN
ejpam-3494	103	4	n	n	CCONJ
ejpam-3494	103	5	,	,	PUNCT
ejpam-3494	103	6	the	the	DET
ejpam-3494	103	7	r	r	NOUN
ejpam-3494	103	8	-	-	PUNCT
ejpam-3494	103	9	dowling	dowle	VERB
ejpam-3494	103	10	numbers	number	NOUN
ejpam-3494	103	11	gi	gi	ADP
ejpam-3494	103	12	,	,	PUNCT
ejpam-3494	103	13	β	β	X
ejpam-3494	103	14	,	,	PUNCT
ejpam-3494	103	15	r	r	NOUN
ejpam-3494	103	16	equal	equal	ADJ
ejpam-3494	103	17	to	to	ADP
ejpam-3494	103	18	the	the	DET
ejpam-3494	103	19	sum	sum	NOUN
ejpam-3494	103	20	of	of	ADP
ejpam-3494	103	21	the	the	DET
ejpam-3494	103	22	entries	entry	NOUN
ejpam-3494	103	23	of	of	ADP
ejpam-3494	103	24	the	the	DET
ejpam-3494	103	25	ith	ith	PROPN
ejpam-3494	103	26	row	row	NOUN
ejpam-3494	103	27	of	of	ADP
ejpam-3494	103	28	the	the	DET
ejpam-3494	103	29	product	product	NOUN
ejpam-3494	103	30	of	of	ADP
ejpam-3494	103	31	two	two	NUM
ejpam-3494	103	32	matrices	matrix	NOUN
ejpam-3494	103	33	[	[	X
ejpam-3494	103	34	(	(	PUNCT
ejpam-3494	103	35	i	i	PRON
ejpam-3494	103	36	j	j	PROPN
ejpam-3494	103	37	)	)	PUNCT
ejpam-3494	104	1	βjri−j	βjri−j	PROPN
ejpam-3494	104	2	]	]	PUNCT
ejpam-3494	104	3	(	(	PUNCT
ejpam-3494	104	4	n+1)×(n+1	n+1)×(n+1	NOUN
ejpam-3494	104	5	)	)	PUNCT
ejpam-3494	104	6	[	[	PUNCT
ejpam-3494	104	7	s(i	s(i	PROPN
ejpam-3494	104	8	,	,	PUNCT
ejpam-3494	104	9	j)(1	j)(1	NOUN
ejpam-3494	104	10	/	/	SYM
ejpam-3494	104	11	β)j	β)j	X
ejpam-3494	104	12	]	]	PUNCT
ejpam-3494	104	13	(	(	PUNCT
ejpam-3494	104	14	n+1)×(n+1	n+1)×(n+1	NOUN
ejpam-3494	104	15	)	)	PUNCT
ejpam-3494	104	16	.	.	PUNCT
ejpam-3494	105	1	(	(	PUNCT
ejpam-3494	105	2	19	19	NUM
ejpam-3494	105	3	)	)	PUNCT
ejpam-3494	105	4	3	3	NUM
ejpam-3494	105	5	.	.	X
ejpam-3494	106	1	r	r	X
ejpam-3494	106	2	-	-	PUNCT
ejpam-3494	106	3	whitney	whitney	NOUN
ejpam-3494	106	4	numbers	number	NOUN
ejpam-3494	106	5	of	of	ADP
ejpam-3494	106	6	the	the	DET
ejpam-3494	106	7	second	second	ADJ
ejpam-3494	106	8	kind	kind	NOUN
ejpam-3494	106	9	and	and	CCONJ
ejpam-3494	106	10	r	r	NOUN
ejpam-3494	106	11	-	-	PUNCT
ejpam-3494	106	12	whitney	whitney	NOUN
ejpam-3494	106	13	-	-	PUNCT
ejpam-3494	106	14	lah	lah	PROPN
ejpam-3494	106	15	numbers	number	NOUN
ejpam-3494	106	16	in	in	ADP
ejpam-3494	106	17	this	this	DET
ejpam-3494	106	18	section	section	NOUN
ejpam-3494	106	19	,	,	PUNCT
ejpam-3494	106	20	a	a	DET
ejpam-3494	106	21	new	new	ADJ
ejpam-3494	106	22	explicit	explicit	ADJ
ejpam-3494	106	23	formula	formula	NOUN
ejpam-3494	106	24	for	for	ADP
ejpam-3494	106	25	r	r	NOUN
ejpam-3494	106	26	-	-	PUNCT
ejpam-3494	106	27	dowling	dowle	VERB
ejpam-3494	106	28	numbers	number	NOUN
ejpam-3494	106	29	expressed	express	VERB
ejpam-3494	106	30	in	in	ADP
ejpam-3494	106	31	terms	term	NOUN
ejpam-3494	106	32	of	of	ADP
ejpam-3494	106	33	r	r	NOUN
ejpam-3494	106	34	-	-	PUNCT
ejpam-3494	106	35	whitney	whitney	NOUN
ejpam-3494	106	36	lah	lah	PROPN
ejpam-3494	106	37	numbers	number	NOUN
ejpam-3494	106	38	and	and	CCONJ
ejpam-3494	106	39	r	r	NOUN
ejpam-3494	106	40	-	-	PUNCT
ejpam-3494	106	41	whitney	whitney	NOUN
ejpam-3494	106	42	numbers	number	NOUN
ejpam-3494	106	43	of	of	ADP
ejpam-3494	106	44	the	the	DET
ejpam-3494	106	45	second	second	ADJ
ejpam-3494	106	46	kind	kind	NOUN
ejpam-3494	106	47	is	be	AUX
ejpam-3494	106	48	established	establish	VERB
ejpam-3494	106	49	.	.	PUNCT
ejpam-3494	107	1	as	as	ADP
ejpam-3494	107	2	a	a	DET
ejpam-3494	107	3	consequence	consequence	NOUN
ejpam-3494	107	4	,	,	PUNCT
ejpam-3494	107	5	a	a	DET
ejpam-3494	107	6	relation	relation	NOUN
ejpam-3494	107	7	in	in	ADP
ejpam-3494	107	8	terms	term	NOUN
ejpam-3494	107	9	of	of	ADP
ejpam-3494	107	10	matrices	matrix	NOUN
ejpam-3494	107	11	involving	involve	VERB
ejpam-3494	107	12	the	the	DET
ejpam-3494	107	13	r	r	NOUN
ejpam-3494	107	14	-	-	PUNCT
ejpam-3494	107	15	dowling	dowle	VERB
ejpam-3494	107	16	numbers	number	NOUN
ejpam-3494	107	17	,	,	PUNCT
ejpam-3494	107	18	the	the	DET
ejpam-3494	107	19	rwhitney	rwhitney	NOUN
ejpam-3494	107	20	-	-	PUNCT
ejpam-3494	107	21	lah	lah	NOUN
ejpam-3494	107	22	numbers	number	NOUN
ejpam-3494	107	23	and	and	CCONJ
ejpam-3494	107	24	the	the	DET
ejpam-3494	107	25	r	r	NOUN
ejpam-3494	107	26	-	-	PUNCT
ejpam-3494	107	27	whitney	whitney	NOUN
ejpam-3494	107	28	numbers	number	NOUN
ejpam-3494	107	29	of	of	ADP
ejpam-3494	107	30	the	the	DET
ejpam-3494	107	31	second	second	ADJ
ejpam-3494	107	32	kind	kind	NOUN
ejpam-3494	107	33	is	be	AUX
ejpam-3494	107	34	obtained	obtain	VERB
ejpam-3494	107	35	.	.	PUNCT
ejpam-3494	108	1	note	note	VERB
ejpam-3494	108	2	that	that	SCONJ
ejpam-3494	108	3	equation	equation	NOUN
ejpam-3494	108	4	(	(	PUNCT
ejpam-3494	108	5	13	13	NUM
ejpam-3494	108	6	)	)	PUNCT
ejpam-3494	108	7	can	can	AUX
ejpam-3494	108	8	be	be	AUX
ejpam-3494	108	9	rewritten	rewrite	VERB
ejpam-3494	108	10	as	as	SCONJ
ejpam-3494	108	11	follows	follow	VERB
ejpam-3494	108	12	(	(	PUNCT
ejpam-3494	108	13	−1)nlβ	−1)nlβ	PROPN
ejpam-3494	108	14	,	,	PUNCT
ejpam-3494	108	15	r(n	r(n	PROPN
ejpam-3494	108	16	,	,	PUNCT
ejpam-3494	108	17	k	k	NOUN
ejpam-3494	108	18	)	)	PUNCT
ejpam-3494	109	1	=	=	SYM
ejpam-3494	109	2	n∑	n∑	NOUN
ejpam-3494	109	3	j=0	j=0	PROPN
ejpam-3494	109	4	wβ	wβ	ADP
ejpam-3494	109	5	,	,	PUNCT
ejpam-3494	109	6	r(n	r(n	PROPN
ejpam-3494	109	7	,	,	PUNCT
ejpam-3494	109	8	j)wβ	j)wβ	PROPN
ejpam-3494	109	9	,	,	PUNCT
ejpam-3494	109	10	r(j	r(j	PROPN
ejpam-3494	109	11	,	,	PUNCT
ejpam-3494	109	12	k	k	NOUN
ejpam-3494	109	13	)	)	PUNCT
ejpam-3494	109	14	.	.	PUNCT
ejpam-3494	110	1	(	(	PUNCT
ejpam-3494	110	2	20	20	NUM
ejpam-3494	110	3	)	)	PUNCT
ejpam-3494	110	4	using	use	VERB
ejpam-3494	110	5	the	the	DET
ejpam-3494	110	6	inverse	inverse	NOUN
ejpam-3494	110	7	relation	relation	NOUN
ejpam-3494	110	8	of	of	ADP
ejpam-3494	110	9	r	r	NOUN
ejpam-3494	110	10	-	-	PUNCT
ejpam-3494	110	11	whitney	whitney	NOUN
ejpam-3494	110	12	numbers	number	NOUN
ejpam-3494	110	13	in	in	ADP
ejpam-3494	110	14	(	(	PUNCT
ejpam-3494	110	15	6	6	NUM
ejpam-3494	110	16	)	)	PUNCT
ejpam-3494	110	17	with	with	ADP
ejpam-3494	110	18	fn	fn	NOUN
ejpam-3494	110	19	=	=	SYM
ejpam-3494	110	20	(	(	PUNCT
ejpam-3494	110	21	−1)nlβ	−1)nlβ	PROPN
ejpam-3494	110	22	,	,	PUNCT
ejpam-3494	110	23	r(n	r(n	PROPN
ejpam-3494	110	24	,	,	PUNCT
ejpam-3494	110	25	k	k	NOUN
ejpam-3494	110	26	)	)	PUNCT
ejpam-3494	110	27	and	and	CCONJ
ejpam-3494	110	28	gj	gj	NOUN
ejpam-3494	110	29	=	=	SYM
ejpam-3494	110	30	(	(	PUNCT
ejpam-3494	110	31	−1)jwβ	−1)jwβ	PROPN
ejpam-3494	110	32	,	,	PUNCT
ejpam-3494	110	33	r(j	r(j	PROPN
ejpam-3494	110	34	,	,	PUNCT
ejpam-3494	110	35	k	k	NOUN
ejpam-3494	110	36	)	)	PUNCT
ejpam-3494	110	37	,	,	PUNCT
ejpam-3494	110	38	equation	equation	NOUN
ejpam-3494	110	39	(	(	PUNCT
ejpam-3494	110	40	20	20	NUM
ejpam-3494	110	41	)	)	PUNCT
ejpam-3494	110	42	yields	yield	NOUN
ejpam-3494	110	43	(	(	PUNCT
ejpam-3494	110	44	−1)nwβ	−1)nwβ	PROPN
ejpam-3494	110	45	,	,	PUNCT
ejpam-3494	110	46	r(n	r(n	PROPN
ejpam-3494	110	47	,	,	PUNCT
ejpam-3494	110	48	k	k	NOUN
ejpam-3494	110	49	)	)	PUNCT
ejpam-3494	110	50	=	=	SYM
ejpam-3494	110	51	n∑	n∑	NOUN
ejpam-3494	110	52	j=0	j=0	PROPN
ejpam-3494	110	53	wβ	wβ	ADP
ejpam-3494	110	54	,	,	PUNCT
ejpam-3494	110	55	r(n	r(n	PROPN
ejpam-3494	110	56	,	,	PUNCT
ejpam-3494	110	57	j)(−1)jlβ	j)(−1)jlβ	PROPN
ejpam-3494	110	58	,	,	PUNCT
ejpam-3494	110	59	r(j	r(j	PROPN
ejpam-3494	110	60	,	,	PUNCT
ejpam-3494	110	61	k	k	PROPN
ejpam-3494	110	62	)	)	PUNCT
ejpam-3494	110	63	;	;	PUNCT
ejpam-3494	110	64	that	that	PRON
ejpam-3494	110	65	is	be	AUX
ejpam-3494	110	66	,	,	PUNCT
ejpam-3494	110	67	s(n	s(n	PROPN
ejpam-3494	110	68	,	,	PUNCT
ejpam-3494	110	69	k;β	k;β	PROPN
ejpam-3494	110	70	,	,	PUNCT
ejpam-3494	110	71	r	r	NOUN
ejpam-3494	110	72	)	)	PUNCT
ejpam-3494	110	73	=	=	SYM
ejpam-3494	110	74	wβ	wβ	ADP
ejpam-3494	110	75	,	,	PUNCT
ejpam-3494	110	76	r(n	r(n	PROPN
ejpam-3494	110	77	,	,	PUNCT
ejpam-3494	110	78	k	k	NOUN
ejpam-3494	110	79	)	)	PUNCT
ejpam-3494	110	80	=	=	SYM
ejpam-3494	110	81	n∑	n∑	X
ejpam-3494	110	82	j=0	j=0	PROPN
ejpam-3494	110	83	(	(	PUNCT
ejpam-3494	110	84	−1)n−jwβ	−1)n−jwβ	PROPN
ejpam-3494	110	85	,	,	PUNCT
ejpam-3494	110	86	r(n	r(n	PROPN
ejpam-3494	110	87	,	,	PUNCT
ejpam-3494	110	88	j)lβ	j)lβ	PROPN
ejpam-3494	110	89	,	,	PUNCT
ejpam-3494	110	90	r(j	r(j	PROPN
ejpam-3494	110	91	,	,	PUNCT
ejpam-3494	110	92	k	k	NOUN
ejpam-3494	110	93	)	)	PUNCT
ejpam-3494	110	94	.	.	PUNCT
ejpam-3494	111	1	summing	sum	VERB
ejpam-3494	111	2	up	up	ADP
ejpam-3494	111	3	both	both	DET
ejpam-3494	111	4	sides	side	NOUN
ejpam-3494	111	5	over	over	ADP
ejpam-3494	111	6	k	k	PROPN
ejpam-3494	111	7	from	from	ADP
ejpam-3494	111	8	0	0	NUM
ejpam-3494	111	9	to	to	ADP
ejpam-3494	111	10	n	n	CCONJ
ejpam-3494	111	11	,	,	PUNCT
ejpam-3494	111	12	gives	give	VERB
ejpam-3494	111	13	the	the	DET
ejpam-3494	111	14	following	follow	VERB
ejpam-3494	111	15	theorem	theorem	VERB
ejpam-3494	111	16	.	.	PUNCT
ejpam-3494	111	17	theorem	theorem	PROPN
ejpam-3494	111	18	3.1	3.1	NUM
ejpam-3494	111	19	.	.	PUNCT
ejpam-3494	112	1	the	the	DET
ejpam-3494	112	2	explicit	explicit	ADJ
ejpam-3494	112	3	formula	formula	NOUN
ejpam-3494	112	4	for	for	ADP
ejpam-3494	112	5	r	r	NOUN
ejpam-3494	112	6	-	-	PUNCT
ejpam-3494	112	7	dowling	dowle	VERB
ejpam-3494	112	8	numbers	number	NOUN
ejpam-3494	112	9	is	be	AUX
ejpam-3494	112	10	given	give	VERB
ejpam-3494	112	11	by	by	ADP
ejpam-3494	112	12	gn	gn	PROPN
ejpam-3494	112	13	,	,	PUNCT
ejpam-3494	112	14	β	β	X
ejpam-3494	112	15	,	,	PUNCT
ejpam-3494	112	16	r	r	NOUN
ejpam-3494	112	17	=	=	SYM
ejpam-3494	112	18	n∑	n∑	NOUN
ejpam-3494	112	19	j=0	j=0	PROPN
ejpam-3494	112	20	(	(	PUNCT
ejpam-3494	112	21	−1)n−j	−1)n−j	X
ejpam-3494	112	22	{	{	PUNCT
ejpam-3494	112	23	j∑	j∑	PROPN
ejpam-3494	112	24	k=0	k=0	PROPN
ejpam-3494	112	25	lβ	lβ	PROPN
ejpam-3494	112	26	,	,	PUNCT
ejpam-3494	112	27	r(j	r(j	PROPN
ejpam-3494	112	28	,	,	PUNCT
ejpam-3494	112	29	k	k	NOUN
ejpam-3494	112	30	)	)	PUNCT
ejpam-3494	112	31	}	}	PUNCT
ejpam-3494	112	32	wβ	wβ	ADP
ejpam-3494	112	33	,	,	PUNCT
ejpam-3494	112	34	r(n	r(n	PROPN
ejpam-3494	112	35	,	,	PUNCT
ejpam-3494	112	36	j	j	NOUN
ejpam-3494	112	37	)	)	PUNCT
ejpam-3494	112	38	.	.	PUNCT
ejpam-3494	113	1	(	(	PUNCT
ejpam-3494	113	2	21	21	NUM
ejpam-3494	113	3	)	)	PUNCT
ejpam-3494	113	4	r.	r.	PROPN
ejpam-3494	113	5	b.	b.	PROPN
ejpam-3494	113	6	corcino	corcino	PROPN
ejpam-3494	113	7	et	et	PROPN
ejpam-3494	113	8	al	al	PROPN
ejpam-3494	113	9	.	.	PUNCT
ejpam-3494	113	10	/	/	SYM
ejpam-3494	113	11	eur	eur	PROPN
ejpam-3494	113	12	.	.	PUNCT
ejpam-3494	114	1	j.	j.	PROPN
ejpam-3494	114	2	pure	pure	PROPN
ejpam-3494	114	3	appl	appl	PROPN
ejpam-3494	114	4	.	.	PROPN
ejpam-3494	114	5	math	math	PROPN
ejpam-3494	114	6	,	,	PUNCT
ejpam-3494	114	7	12	12	NUM
ejpam-3494	114	8	(	(	PUNCT
ejpam-3494	114	9	3	3	NUM
ejpam-3494	114	10	)	)	PUNCT
ejpam-3494	114	11	(	(	PUNCT
ejpam-3494	114	12	2019	2019	NUM
ejpam-3494	114	13	)	)	PUNCT
ejpam-3494	114	14	,	,	PUNCT
ejpam-3494	114	15	1122	1122	NUM
ejpam-3494	114	16	-	-	SYM
ejpam-3494	114	17	1137	1137	NUM
ejpam-3494	114	18	1128	1128	NUM
ejpam-3494	114	19	for	for	ADP
ejpam-3494	114	20	instance	instance	NOUN
ejpam-3494	114	21	,	,	PUNCT
ejpam-3494	114	22	when	when	SCONJ
ejpam-3494	114	23	β	β	X
ejpam-3494	114	24	=	=	SYM
ejpam-3494	114	25	r	r	NOUN
ejpam-3494	114	26	=	=	SYM
ejpam-3494	114	27	2	2	NUM
ejpam-3494	114	28	and	and	CCONJ
ejpam-3494	114	29	n	n	NOUN
ejpam-3494	114	30	=	=	SYM
ejpam-3494	114	31	4	4	NUM
ejpam-3494	114	32	,	,	PUNCT
ejpam-3494	114	33	we	we	PRON
ejpam-3494	114	34	get	get	VERB
ejpam-3494	114	35	g4,2,2	g4,2,2	PROPN
ejpam-3494	114	36	=	=	SYM
ejpam-3494	114	37	4∑	4∑	PROPN
ejpam-3494	114	38	j=0	j=0	PROPN
ejpam-3494	114	39	(	(	PUNCT
ejpam-3494	114	40	−1)4−j	−1)4−j	VERB
ejpam-3494	114	41	{	{	PUNCT
ejpam-3494	114	42	j∑	j∑	PROPN
ejpam-3494	114	43	k=0	k=0	PROPN
ejpam-3494	114	44	l2,2(j	l2,2(j	PROPN
ejpam-3494	114	45	,	,	PUNCT
ejpam-3494	114	46	k	k	NOUN
ejpam-3494	114	47	)	)	PUNCT
ejpam-3494	114	48	}	}	PUNCT
ejpam-3494	114	49	w2,2(4	w2,2(4	PROPN
ejpam-3494	114	50	,	,	PUNCT
ejpam-3494	114	51	j	j	NOUN
ejpam-3494	114	52	)	)	PUNCT
ejpam-3494	114	53	=	=	PUNCT
ejpam-3494	115	1	(	(	PUNCT
ejpam-3494	115	2	1)(16)−	1)(16)−	NUM
ejpam-3494	115	3	(	(	PUNCT
ejpam-3494	115	4	5)(120	5)(120	NOUN
ejpam-3494	115	5	)	)	PUNCT
ejpam-3494	116	1	+	+	CCONJ
ejpam-3494	116	2	(	(	PUNCT
ejpam-3494	116	3	37)(100)−	37)(100)−	NUM
ejpam-3494	116	4	(	(	PUNCT
ejpam-3494	116	5	361)(20	361)(20	PROPN
ejpam-3494	116	6	)	)	PUNCT
ejpam-3494	116	7	+	+	CCONJ
ejpam-3494	116	8	(	(	PUNCT
ejpam-3494	116	9	461)(1	461)(1	NOUN
ejpam-3494	116	10	)	)	PUNCT
ejpam-3494	116	11	=	=	PUNCT
ejpam-3494	117	1	257	257	X
ejpam-3494	117	2	.	.	PUNCT
ejpam-3494	118	1	now	now	ADV
ejpam-3494	118	2	,	,	PUNCT
ejpam-3494	118	3	we	we	PRON
ejpam-3494	118	4	can	can	AUX
ejpam-3494	118	5	rewrite	rewrite	VERB
ejpam-3494	118	6	the	the	DET
ejpam-3494	118	7	sum	sum	NOUN
ejpam-3494	118	8	in	in	ADP
ejpam-3494	118	9	(	(	PUNCT
ejpam-3494	118	10	21	21	NUM
ejpam-3494	118	11	)	)	PUNCT
ejpam-3494	118	12	as	as	ADP
ejpam-3494	118	13	gn	gn	PROPN
ejpam-3494	118	14	,	,	PUNCT
ejpam-3494	118	15	β	β	X
ejpam-3494	118	16	,	,	PUNCT
ejpam-3494	118	17	r	r	NOUN
ejpam-3494	118	18	=	=	SYM
ejpam-3494	118	19	s0	s0	PROPN
ejpam-3494	118	20	+	+	CCONJ
ejpam-3494	118	21	s1	s1	PROPN
ejpam-3494	118	22	+	+	CCONJ
ejpam-3494	118	23	s2	s2	NOUN
ejpam-3494	118	24	+	+	X
ejpam-3494	118	25	.	.	PUNCT
ejpam-3494	118	26	.	.	PUNCT
ejpam-3494	119	1	.+	.+	NOUN
ejpam-3494	119	2	sn	sn	INTJ
ejpam-3494	119	3	where	where	SCONJ
ejpam-3494	119	4	sj	sj	PROPN
ejpam-3494	119	5	=	=	NOUN
ejpam-3494	119	6	n∑	n∑	PROPN
ejpam-3494	119	7	k=0	k=0	PROPN
ejpam-3494	119	8	(	(	PUNCT
ejpam-3494	119	9	−1)n−kwβ	−1)n−kwβ	X
ejpam-3494	119	10	,	,	PUNCT
ejpam-3494	119	11	r(n	r(n	PROPN
ejpam-3494	119	12	,	,	PUNCT
ejpam-3494	119	13	k)lβ	k)lβ	PROPN
ejpam-3494	119	14	,	,	PUNCT
ejpam-3494	119	15	r(k	r(k	PROPN
ejpam-3494	119	16	,	,	PUNCT
ejpam-3494	119	17	j	j	PROPN
ejpam-3494	119	18	)	)	PUNCT
ejpam-3494	119	19	.	.	PUNCT
ejpam-3494	120	1	as	as	ADP
ejpam-3494	120	2	a	a	DET
ejpam-3494	120	3	consequence	consequence	NOUN
ejpam-3494	120	4	,	,	PUNCT
ejpam-3494	120	5	we	we	PRON
ejpam-3494	120	6	have	have	VERB
ejpam-3494	120	7	the	the	DET
ejpam-3494	120	8	following	follow	VERB
ejpam-3494	120	9	theorem	theorem	VERB
ejpam-3494	120	10	.	.	PUNCT
ejpam-3494	120	11	theorem	theorem	PROPN
ejpam-3494	120	12	3.2	3.2	NUM
ejpam-3494	120	13	.	.	PUNCT
ejpam-3494	121	1	for	for	ADP
ejpam-3494	121	2	n	n	PRON
ejpam-3494	121	3	∈	∈	PROPN
ejpam-3494	121	4	n	n	CCONJ
ejpam-3494	121	5	,	,	PUNCT
ejpam-3494	121	6	the	the	DET
ejpam-3494	121	7	r	r	NOUN
ejpam-3494	121	8	-	-	PUNCT
ejpam-3494	121	9	dowling	dowle	VERB
ejpam-3494	121	10	numbers	number	NOUN
ejpam-3494	121	11	gi	gi	ADP
ejpam-3494	121	12	,	,	PUNCT
ejpam-3494	121	13	β	β	X
ejpam-3494	121	14	,	,	PUNCT
ejpam-3494	121	15	r	r	NOUN
ejpam-3494	121	16	equal	equal	ADJ
ejpam-3494	121	17	to	to	ADP
ejpam-3494	121	18	the	the	DET
ejpam-3494	121	19	sum	sum	NOUN
ejpam-3494	121	20	of	of	ADP
ejpam-3494	121	21	the	the	DET
ejpam-3494	121	22	entries	entry	NOUN
ejpam-3494	121	23	of	of	ADP
ejpam-3494	121	24	the	the	DET
ejpam-3494	121	25	ith	ith	PROPN
ejpam-3494	121	26	row	row	NOUN
ejpam-3494	121	27	of	of	ADP
ejpam-3494	121	28	the	the	DET
ejpam-3494	121	29	product	product	NOUN
ejpam-3494	121	30	of	of	ADP
ejpam-3494	121	31	two	two	NUM
ejpam-3494	121	32	matrices	matrix	NOUN
ejpam-3494	121	33	[	[	PUNCT
ejpam-3494	121	34	(	(	PUNCT
ejpam-3494	121	35	−1)i−jwβ	−1)i−jwβ	ADP
ejpam-3494	121	36	,	,	PUNCT
ejpam-3494	121	37	r(i	r(i	PROPN
ejpam-3494	121	38	,	,	PUNCT
ejpam-3494	121	39	j	j	PROPN
ejpam-3494	121	40	)	)	PUNCT
ejpam-3494	121	41	]	]	PUNCT
ejpam-3494	121	42	(	(	PUNCT
ejpam-3494	121	43	n+1)×(n+1	n+1)×(n+1	NOUN
ejpam-3494	121	44	)	)	PUNCT
ejpam-3494	121	45	[	[	X
ejpam-3494	121	46	lβ	lβ	ADP
ejpam-3494	121	47	,	,	PUNCT
ejpam-3494	121	48	r(i	r(i	X
ejpam-3494	121	49	,	,	PUNCT
ejpam-3494	121	50	j)](n+1)×(n+1	j)](n+1)×(n+1	NOUN
ejpam-3494	121	51	)	)	PUNCT
ejpam-3494	121	52	,	,	PUNCT
ejpam-3494	121	53	(	(	PUNCT
ejpam-3494	121	54	22	22	X
ejpam-3494	121	55	)	)	PUNCT
ejpam-3494	121	56	whose	whose	DET
ejpam-3494	121	57	entries	entry	NOUN
ejpam-3494	121	58	are	be	AUX
ejpam-3494	121	59	respectively	respectively	ADV
ejpam-3494	121	60	the	the	DET
ejpam-3494	121	61	r	r	NOUN
ejpam-3494	121	62	-	-	PUNCT
ejpam-3494	121	63	whitney	whitney	NOUN
ejpam-3494	121	64	numbers	number	NOUN
ejpam-3494	121	65	of	of	ADP
ejpam-3494	121	66	the	the	DET
ejpam-3494	121	67	second	second	ADJ
ejpam-3494	121	68	kind	kind	NOUN
ejpam-3494	121	69	and	and	CCONJ
ejpam-3494	121	70	the	the	DET
ejpam-3494	121	71	r	r	PROPN
ejpam-3494	121	72	-	-	PUNCT
ejpam-3494	121	73	whitney	whitney	PROPN
ejpam-3494	121	74	lah	lah	PROPN
ejpam-3494	121	75	numbers	number	NOUN
ejpam-3494	121	76	.	.	PUNCT
ejpam-3494	122	1	for	for	ADP
ejpam-3494	122	2	instance	instance	NOUN
ejpam-3494	122	3	,	,	PUNCT
ejpam-3494	122	4	when	when	SCONJ
ejpam-3494	122	5	β	β	X
ejpam-3494	122	6	=	=	SYM
ejpam-3494	122	7	r	r	NOUN
ejpam-3494	122	8	=	=	SYM
ejpam-3494	122	9	2	2	NUM
ejpam-3494	122	10	and	and	CCONJ
ejpam-3494	122	11	n	n	NOUN
ejpam-3494	122	12	=	=	SYM
ejpam-3494	122	13	3	3	NUM
ejpam-3494	122	14	,	,	PUNCT
ejpam-3494	122	15	we	we	PRON
ejpam-3494	122	16	get	get	VERB
ejpam-3494	122	17	[	[	PUNCT
ejpam-3494	122	18	(	(	PUNCT
ejpam-3494	122	19	−1)i−jw2,2(i	−1)i−jw2,2(i	NOUN
ejpam-3494	122	20	,	,	PUNCT
ejpam-3494	122	21	j	j	PROPN
ejpam-3494	122	22	)	)	PUNCT
ejpam-3494	122	23	]	]	PUNCT
ejpam-3494	123	1	4×4	4×4	NUM
ejpam-3494	124	1	[	[	X
ejpam-3494	124	2	lβ	lβ	ADP
ejpam-3494	124	3	,	,	PUNCT
ejpam-3494	124	4	r(i	r(i	PROPN
ejpam-3494	124	5	,	,	PUNCT
ejpam-3494	124	6	j)]4×4	j)]4×4	PROPN
ejpam-3494	124	7	=	=	SYM
ejpam-3494	124	8			NOUN
ejpam-3494	124	9	1	1	NUM
ejpam-3494	124	10	0	0	NUM
ejpam-3494	124	11	0	0	NUM
ejpam-3494	124	12	0	0	NUM
ejpam-3494	124	13	−2	−2	NOUN
ejpam-3494	124	14	1	1	NUM
ejpam-3494	124	15	0	0	NUM
ejpam-3494	124	16	0	0	NUM
ejpam-3494	124	17	4	4	NUM
ejpam-3494	124	18	−6	−6	NOUN
ejpam-3494	124	19	1	1	NUM
ejpam-3494	124	20	0	0	NUM
ejpam-3494	124	21	−8	−8	SYM
ejpam-3494	125	1	28	28	NUM
ejpam-3494	125	2	−12	−12	NUM
ejpam-3494	125	3	1	1	NUM
ejpam-3494	125	4			NOUN
ejpam-3494	125	5			NOUN
ejpam-3494	125	6	1	1	NUM
ejpam-3494	125	7	0	0	NUM
ejpam-3494	125	8	0	0	NUM
ejpam-3494	125	9	0	0	NUM
ejpam-3494	125	10	4	4	NUM
ejpam-3494	125	11	1	1	NUM
ejpam-3494	125	12	0	0	NUM
ejpam-3494	125	13	0	0	NUM
ejpam-3494	125	14	24	24	NUM
ejpam-3494	125	15	12	12	NUM
ejpam-3494	125	16	1	1	NUM
ejpam-3494	125	17	0	0	NUM
ejpam-3494	125	18	192	192	NUM
ejpam-3494	125	19	144	144	NUM
ejpam-3494	125	20	24	24	NUM
ejpam-3494	125	21	1	1	NUM
ejpam-3494	125	22			NOUN
ejpam-3494	125	23	=	=	PUNCT
ejpam-3494	125	24			NOUN
ejpam-3494	125	25	1	1	NUM
ejpam-3494	125	26	0	0	NUM
ejpam-3494	125	27	0	0	NUM
ejpam-3494	125	28	0	0	NUM
ejpam-3494	125	29	2	2	NUM
ejpam-3494	125	30	1	1	NUM
ejpam-3494	125	31	0	0	NUM
ejpam-3494	125	32	0	0	NUM
ejpam-3494	125	33	4	4	NUM
ejpam-3494	125	34	6	6	NUM
ejpam-3494	125	35	1	1	NUM
ejpam-3494	125	36	0	0	NUM
ejpam-3494	125	37	8	8	NUM
ejpam-3494	125	38	28	28	NUM
ejpam-3494	125	39	12	12	NUM
ejpam-3494	125	40	1	1	NUM
ejpam-3494	125	41			NOUN
ejpam-3494	125	42	summing	sum	VERB
ejpam-3494	125	43	up	up	ADP
ejpam-3494	125	44	the	the	DET
ejpam-3494	125	45	entries	entry	NOUN
ejpam-3494	125	46	of	of	ADP
ejpam-3494	125	47	each	each	DET
ejpam-3494	125	48	row	row	NOUN
ejpam-3494	125	49	of	of	ADP
ejpam-3494	125	50	the	the	DET
ejpam-3494	125	51	above	above	ADJ
ejpam-3494	125	52	matrix	matrix	NOUN
ejpam-3494	125	53	product	product	NOUN
ejpam-3494	125	54	,	,	PUNCT
ejpam-3494	125	55	we	we	PRON
ejpam-3494	125	56	obtain	obtain	VERB
ejpam-3494	125	57	the	the	DET
ejpam-3494	125	58	column	column	NOUN
ejpam-3494	125	59	vector	vector	NOUN
ejpam-3494	125	60	whose	whose	DET
ejpam-3494	125	61	entries	entry	NOUN
ejpam-3494	125	62	are	be	AUX
ejpam-3494	125	63	the	the	DET
ejpam-3494	125	64	r	r	NOUN
ejpam-3494	125	65	-	-	PUNCT
ejpam-3494	125	66	dowling	dowle	VERB
ejpam-3494	125	67	numbers	numbers	ADV
ejpam-3494	125	68	1	1	NUM
ejpam-3494	125	69	2	2	NUM
ejpam-3494	125	70	+	+	CCONJ
ejpam-3494	125	71	1	1	NUM
ejpam-3494	125	72	4	4	NUM
ejpam-3494	125	73	+	+	NUM
ejpam-3494	125	74	6	6	NUM
ejpam-3494	125	75	+	+	SYM
ejpam-3494	125	76	1	1	NUM
ejpam-3494	125	77	8	8	NUM
ejpam-3494	125	78	+	+	NUM
ejpam-3494	125	79	28	28	NUM
ejpam-3494	125	80	+	+	CCONJ
ejpam-3494	125	81	12	12	NUM
ejpam-3494	125	82	+	+	SYM
ejpam-3494	125	83	1	1	NUM
ejpam-3494	125	84			NOUN
ejpam-3494	125	85	=	=	SYM
ejpam-3494	125	86			NOUN
ejpam-3494	125	87	1	1	NUM
ejpam-3494	125	88	3	3	NUM
ejpam-3494	125	89	11	11	NUM
ejpam-3494	125	90	49	49	NUM
ejpam-3494	125	91			NOUN
ejpam-3494	125	92	=	=	SYM
ejpam-3494	125	93			NOUN
ejpam-3494	125	94	g0,2,2	g0,2,2	NOUN
ejpam-3494	125	95	g1,2,2	g1,2,2	PROPN
ejpam-3494	125	96	g2,2,2	g2,2,2	PROPN
ejpam-3494	125	97	g3,2,2	g3,2,2	PROPN
ejpam-3494	125	98			PROPN
ejpam-3494	125	99	.	.	PUNCT
ejpam-3494	126	1	r.	r.	PROPN
ejpam-3494	126	2	b.	b.	PROPN
ejpam-3494	126	3	corcino	corcino	PROPN
ejpam-3494	126	4	et	et	PROPN
ejpam-3494	126	5	al	al	PROPN
ejpam-3494	126	6	.	.	PUNCT
ejpam-3494	126	7	/	/	SYM
ejpam-3494	126	8	eur	eur	PROPN
ejpam-3494	126	9	.	.	PUNCT
ejpam-3494	127	1	j.	j.	PROPN
ejpam-3494	127	2	pure	pure	PROPN
ejpam-3494	127	3	appl	appl	PROPN
ejpam-3494	127	4	.	.	PROPN
ejpam-3494	127	5	math	math	PROPN
ejpam-3494	127	6	,	,	PUNCT
ejpam-3494	127	7	12	12	NUM
ejpam-3494	127	8	(	(	PUNCT
ejpam-3494	127	9	3	3	NUM
ejpam-3494	127	10	)	)	PUNCT
ejpam-3494	127	11	(	(	PUNCT
ejpam-3494	127	12	2019	2019	NUM
ejpam-3494	127	13	)	)	PUNCT
ejpam-3494	127	14	,	,	PUNCT
ejpam-3494	127	15	1122	1122	NUM
ejpam-3494	127	16	-	-	SYM
ejpam-3494	127	17	1137	1137	NUM
ejpam-3494	127	18	1129	1129	NUM
ejpam-3494	127	19	corollary	corollary	ADJ
ejpam-3494	127	20	3.3	3.3	NUM
ejpam-3494	127	21	.	.	PUNCT
ejpam-3494	128	1	for	for	ADP
ejpam-3494	128	2	0	0	NUM
ejpam-3494	128	3	≤	≤	NOUN
ejpam-3494	128	4	i	i	PRON
ejpam-3494	128	5	,	,	PUNCT
ejpam-3494	128	6	l	l	PROPN
ejpam-3494	128	7	≤	≤	NOUN
ejpam-3494	128	8	n	n	CCONJ
ejpam-3494	128	9	,	,	PUNCT
ejpam-3494	128	10	the	the	DET
ejpam-3494	128	11	r	r	NOUN
ejpam-3494	128	12	-	-	PUNCT
ejpam-3494	128	13	whitney	whitney	NOUN
ejpam-3494	128	14	numbers	number	NOUN
ejpam-3494	128	15	of	of	ADP
ejpam-3494	128	16	the	the	DET
ejpam-3494	128	17	second	second	ADJ
ejpam-3494	128	18	kind	kind	NOUN
ejpam-3494	128	19	satisfy	satisfy	VERB
ejpam-3494	128	20	the	the	DET
ejpam-3494	128	21	following	follow	VERB
ejpam-3494	128	22	explicit	explicit	ADJ
ejpam-3494	128	23	formula	formula	NOUN
ejpam-3494	128	24	wβ	wβ	ADP
ejpam-3494	128	25	,	,	PUNCT
ejpam-3494	128	26	r(i	r(i	X
ejpam-3494	128	27	,	,	PUNCT
ejpam-3494	128	28	l	l	NOUN
ejpam-3494	128	29	)	)	PUNCT
ejpam-3494	128	30	=	=	SYM
ejpam-3494	129	1	i∑	i∑	PROPN
ejpam-3494	129	2	j=0	j=0	PROPN
ejpam-3494	129	3	(	(	PUNCT
ejpam-3494	129	4	−1)i−jwβ	−1)i−jwβ	ADP
ejpam-3494	129	5	,	,	PUNCT
ejpam-3494	129	6	r(i	r(i	X
ejpam-3494	129	7	,	,	PUNCT
ejpam-3494	129	8	j)lβ	j)lβ	PROPN
ejpam-3494	129	9	,	,	PUNCT
ejpam-3494	129	10	r(j	r(j	PROPN
ejpam-3494	129	11	,	,	PUNCT
ejpam-3494	129	12	l	l	PROPN
ejpam-3494	129	13	)	)	PUNCT
ejpam-3494	129	14	;	;	PUNCT
ejpam-3494	129	15	that	that	PRON
ejpam-3494	129	16	is	be	AUX
ejpam-3494	129	17	,	,	PUNCT
ejpam-3494	129	18	[	[	X
ejpam-3494	129	19	wβ	wβ	ADP
ejpam-3494	129	20	,	,	PUNCT
ejpam-3494	129	21	r(i	r(i	X
ejpam-3494	129	22	,	,	PUNCT
ejpam-3494	129	23	j)]n+1×n+1	j)]n+1×n+1	PROPN
ejpam-3494	129	24	=	=	PUNCT
ejpam-3494	130	1	[	[	PUNCT
ejpam-3494	130	2	(	(	PUNCT
ejpam-3494	130	3	−1)i−jwβ	−1)i−jwβ	ADP
ejpam-3494	130	4	,	,	PUNCT
ejpam-3494	130	5	r(i	r(i	PROPN
ejpam-3494	130	6	,	,	PUNCT
ejpam-3494	130	7	j	j	NOUN
ejpam-3494	130	8	)	)	PUNCT
ejpam-3494	130	9	]	]	PUNCT
ejpam-3494	131	1	n+1×n+1	n+1×n+1	NOUN
ejpam-3494	131	2	[	[	X
ejpam-3494	131	3	lβ	lβ	ADP
ejpam-3494	131	4	,	,	PUNCT
ejpam-3494	131	5	r(i	r(i	X
ejpam-3494	131	6	,	,	PUNCT
ejpam-3494	131	7	j)]n+1×n+1	j)]n+1×n+1	PROPN
ejpam-3494	131	8	.	.	PUNCT
ejpam-3494	132	1	it	it	PRON
ejpam-3494	132	2	can	can	AUX
ejpam-3494	132	3	easily	easily	ADV
ejpam-3494	132	4	be	be	AUX
ejpam-3494	132	5	shown	show	VERB
ejpam-3494	132	6	that	that	SCONJ
ejpam-3494	132	7	n∑	n∑	PROPN
ejpam-3494	132	8	j	j	PROPN
ejpam-3494	133	1	=	=	VERB
ejpam-3494	133	2	i	i	PROPN
ejpam-3494	133	3	(	(	PUNCT
ejpam-3494	133	4	−1)n−jwβ	−1)n−jwβ	PROPN
ejpam-3494	133	5	,	,	PUNCT
ejpam-3494	133	6	r(n	r(n	PROPN
ejpam-3494	133	7	,	,	PUNCT
ejpam-3494	133	8	j)wβ	j)wβ	PROPN
ejpam-3494	133	9	,	,	PUNCT
ejpam-3494	133	10	r(j	r(j	PROPN
ejpam-3494	133	11	,	,	PUNCT
ejpam-3494	133	12	i	i	NOUN
ejpam-3494	133	13	)	)	PUNCT
ejpam-3494	133	14	=	=	PUNCT
ejpam-3494	133	15	n∑	n∑	PROPN
ejpam-3494	133	16	j	j	PROPN
ejpam-3494	134	1	=	=	NOUN
ejpam-3494	134	2	i	i	NOUN
ejpam-3494	134	3	wβ	wβ	ADP
ejpam-3494	134	4	,	,	PUNCT
ejpam-3494	134	5	r(n	r(n	PROPN
ejpam-3494	134	6	,	,	PUNCT
ejpam-3494	134	7	j)(−1)j−iwβ	j)(−1)j−iwβ	NOUN
ejpam-3494	134	8	,	,	PUNCT
ejpam-3494	134	9	r(j	r(j	PROPN
ejpam-3494	134	10	,	,	PUNCT
ejpam-3494	134	11	i	i	NOUN
ejpam-3494	134	12	)	)	PUNCT
ejpam-3494	134	13	=	=	SYM
ejpam-3494	134	14	δni	δni	PROPN
ejpam-3494	134	15	,	,	PUNCT
ejpam-3494	134	16	(	(	PUNCT
ejpam-3494	134	17	23	23	NUM
ejpam-3494	134	18	)	)	PUNCT
ejpam-3494	134	19	where	where	SCONJ
ejpam-3494	134	20	δni	δni	PROPN
ejpam-3494	134	21	is	be	AUX
ejpam-3494	134	22	the	the	DET
ejpam-3494	134	23	kronecker	kronecker	NOUN
ejpam-3494	134	24	delta	delta	NOUN
ejpam-3494	134	25	.	.	PUNCT
ejpam-3494	135	1	this	this	DET
ejpam-3494	135	2	relation	relation	NOUN
ejpam-3494	135	3	implies	imply	VERB
ejpam-3494	135	4	that	that	SCONJ
ejpam-3494	136	1	[	[	X
ejpam-3494	136	2	wβ	wβ	ADP
ejpam-3494	136	3	,	,	PUNCT
ejpam-3494	136	4	r(i	r(i	PROPN
ejpam-3494	136	5	,	,	PUNCT
ejpam-3494	136	6	j	j	PROPN
ejpam-3494	136	7	)	)	PUNCT
ejpam-3494	136	8	]	]	PUNCT
ejpam-3494	136	9	−1	−1	NOUN
ejpam-3494	136	10	n+1×n+1	n+1×n+1	NOUN
ejpam-3494	136	11	=	=	PUNCT
ejpam-3494	136	12	[	[	PUNCT
ejpam-3494	136	13	(	(	PUNCT
ejpam-3494	136	14	−1)i−jwβ	−1)i−jwβ	ADP
ejpam-3494	136	15	,	,	PUNCT
ejpam-3494	136	16	r(i	r(i	PROPN
ejpam-3494	136	17	,	,	PUNCT
ejpam-3494	136	18	j	j	NOUN
ejpam-3494	136	19	)	)	PUNCT
ejpam-3494	136	20	]	]	PUNCT
ejpam-3494	136	21	n+1×n+1	n+1×n+1	NOUN
ejpam-3494	136	22	.	.	PUNCT
ejpam-3494	137	1	(	(	PUNCT
ejpam-3494	137	2	24	24	NUM
ejpam-3494	137	3	)	)	PUNCT
ejpam-3494	137	4	thus	thus	ADV
ejpam-3494	137	5	,	,	PUNCT
ejpam-3494	137	6	we	we	PRON
ejpam-3494	137	7	have	have	VERB
ejpam-3494	137	8	[	[	PUNCT
ejpam-3494	137	9	(	(	PUNCT
ejpam-3494	137	10	−1)i−jwβ	−1)i−jwβ	ADP
ejpam-3494	137	11	,	,	PUNCT
ejpam-3494	137	12	r(i	r(i	PROPN
ejpam-3494	137	13	,	,	PUNCT
ejpam-3494	137	14	j	j	NOUN
ejpam-3494	137	15	)	)	PUNCT
ejpam-3494	137	16	]	]	PUNCT
ejpam-3494	138	1	n+1×n+1	n+1×n+1	NOUN
ejpam-3494	138	2	[	[	PUNCT
ejpam-3494	138	3	(	(	PUNCT
ejpam-3494	138	4	−1)i−jwβ	−1)i−jwβ	ADP
ejpam-3494	138	5	,	,	PUNCT
ejpam-3494	138	6	r(i	r(i	PROPN
ejpam-3494	138	7	,	,	PUNCT
ejpam-3494	138	8	j	j	NOUN
ejpam-3494	138	9	)	)	PUNCT
ejpam-3494	138	10	]	]	PUNCT
ejpam-3494	139	1	n+1×n+1	n+1×n+1	NOUN
ejpam-3494	139	2	[	[	X
ejpam-3494	139	3	lβ	lβ	ADP
ejpam-3494	139	4	,	,	PUNCT
ejpam-3494	139	5	r(i	r(i	X
ejpam-3494	139	6	,	,	PUNCT
ejpam-3494	139	7	j)]n+1×n+1	j)]n+1×n+1	PROPN
ejpam-3494	139	8	=	=	SYM
ejpam-3494	139	9	in+1	in+1	PROPN
ejpam-3494	139	10	.	.	NOUN
ejpam-3494	140	1	4	4	NUM
ejpam-3494	140	2	.	.	X
ejpam-3494	140	3	r	r	X
ejpam-3494	140	4	-	-	PUNCT
ejpam-3494	140	5	whitney	whitney	NOUN
ejpam-3494	140	6	numbers	number	NOUN
ejpam-3494	140	7	of	of	ADP
ejpam-3494	140	8	the	the	DET
ejpam-3494	140	9	second	second	ADJ
ejpam-3494	140	10	kind	kind	NOUN
ejpam-3494	140	11	and	and	CCONJ
ejpam-3494	140	12	lah	lah	NOUN
ejpam-3494	140	13	numbers	number	NOUN
ejpam-3494	140	14	in	in	ADP
ejpam-3494	140	15	this	this	DET
ejpam-3494	140	16	section	section	NOUN
ejpam-3494	140	17	,	,	PUNCT
ejpam-3494	140	18	we	we	PRON
ejpam-3494	140	19	will	will	AUX
ejpam-3494	140	20	find	find	VERB
ejpam-3494	140	21	a	a	DET
ejpam-3494	140	22	new	new	ADJ
ejpam-3494	140	23	explicit	explicit	ADJ
ejpam-3494	140	24	formula	formula	NOUN
ejpam-3494	140	25	for	for	ADP
ejpam-3494	140	26	computing	compute	VERB
ejpam-3494	140	27	r	r	NOUN
ejpam-3494	140	28	-	-	PUNCT
ejpam-3494	140	29	dowling	dowle	VERB
ejpam-3494	140	30	numbers	number	NOUN
ejpam-3494	140	31	gn	gn	PROPN
ejpam-3494	140	32	,	,	PUNCT
ejpam-3494	140	33	β	β	X
ejpam-3494	140	34	,	,	PUNCT
ejpam-3494	140	35	r	r	NOUN
ejpam-3494	140	36	in	in	ADP
ejpam-3494	140	37	terms	term	NOUN
ejpam-3494	140	38	of	of	ADP
ejpam-3494	140	39	r	r	NOUN
ejpam-3494	140	40	-	-	PUNCT
ejpam-3494	140	41	whitney	whitney	NOUN
ejpam-3494	140	42	numbers	number	NOUN
ejpam-3494	140	43	of	of	ADP
ejpam-3494	140	44	the	the	DET
ejpam-3494	140	45	second	second	ADJ
ejpam-3494	140	46	kind	kind	NOUN
ejpam-3494	140	47	and	and	CCONJ
ejpam-3494	140	48	the	the	DET
ejpam-3494	140	49	ordinary	ordinary	ADJ
ejpam-3494	140	50	lah	lah	NOUN
ejpam-3494	140	51	numbers	number	NOUN
ejpam-3494	140	52	using	use	VERB
ejpam-3494	140	53	the	the	DET
ejpam-3494	140	54	faa	faa	PROPN
ejpam-3494	140	55	di	di	PROPN
ejpam-3494	140	56	bruno	bruno	PROPN
ejpam-3494	140	57	’s	’s	PART
ejpam-3494	140	58	formula	formula	NOUN
ejpam-3494	140	59	and	and	CCONJ
ejpam-3494	140	60	certain	certain	ADJ
ejpam-3494	140	61	identity	identity	NOUN
ejpam-3494	140	62	of	of	ADP
ejpam-3494	140	63	bell	bell	NOUN
ejpam-3494	140	64	polynomials	polynomial	NOUN
ejpam-3494	140	65	of	of	ADP
ejpam-3494	140	66	the	the	DET
ejpam-3494	140	67	second	second	ADJ
ejpam-3494	140	68	kind	kind	NOUN
ejpam-3494	140	69	.	.	PUNCT
ejpam-3494	141	1	the	the	DET
ejpam-3494	141	2	following	follow	VERB
ejpam-3494	141	3	theorem	theorem	NOUN
ejpam-3494	141	4	contains	contain	VERB
ejpam-3494	141	5	the	the	DET
ejpam-3494	141	6	desired	desire	VERB
ejpam-3494	141	7	formula	formula	NOUN
ejpam-3494	141	8	.	.	PUNCT
ejpam-3494	142	1	theorem	theorem	VERB
ejpam-3494	142	2	4.1	4.1	NUM
ejpam-3494	142	3	.	.	PUNCT
ejpam-3494	143	1	for	for	ADP
ejpam-3494	143	2	n	n	PRON
ejpam-3494	143	3	∈	∈	PROPN
ejpam-3494	143	4	n	n	CCONJ
ejpam-3494	143	5	,	,	PUNCT
ejpam-3494	143	6	the	the	DET
ejpam-3494	143	7	r	r	NOUN
ejpam-3494	143	8	-	-	PUNCT
ejpam-3494	143	9	dowling	dowle	VERB
ejpam-3494	143	10	numbers	number	NOUN
ejpam-3494	143	11	gn	gn	PROPN
ejpam-3494	143	12	,	,	PUNCT
ejpam-3494	143	13	r	r	PROPN
ejpam-3494	143	14	,	,	PUNCT
ejpam-3494	143	15	β	β	X
ejpam-3494	143	16	equal	equal	ADJ
ejpam-3494	143	17	gn	gn	PROPN
ejpam-3494	143	18	,	,	PUNCT
ejpam-3494	143	19	r	r	NOUN
ejpam-3494	143	20	,	,	PUNCT
ejpam-3494	143	21	β	β	X
ejpam-3494	143	22	=	=	SYM
ejpam-3494	143	23	n∑	n∑	X
ejpam-3494	143	24	j=0	j=0	PROPN
ejpam-3494	143	25	(	(	PUNCT
ejpam-3494	143	26	−1)n−jwβ,−r(n	−1)n−jwβ,−r(n	PROPN
ejpam-3494	143	27	,	,	PUNCT
ejpam-3494	143	28	j	j	PROPN
ejpam-3494	143	29	)	)	PUNCT
ejpam-3494	143	30	j∑	j∑	PROPN
ejpam-3494	143	31	i=0	i=0	PROPN
ejpam-3494	143	32	βj−il(j	βj−il(j	PROPN
ejpam-3494	143	33	,	,	PUNCT
ejpam-3494	143	34	i	i	PROPN
ejpam-3494	143	35	)	)	PUNCT
ejpam-3494	143	36	.	.	PUNCT
ejpam-3494	144	1	(	(	PUNCT
ejpam-3494	144	2	25	25	NUM
ejpam-3494	144	3	)	)	PUNCT
ejpam-3494	144	4	proof	proof	NOUN
ejpam-3494	144	5	.	.	PUNCT
ejpam-3494	145	1	let	let	VERB
ejpam-3494	145	2	us	we	PRON
ejpam-3494	145	3	recall	recall	VERB
ejpam-3494	145	4	the	the	DET
ejpam-3494	145	5	following	follow	VERB
ejpam-3494	145	6	identity	identity	NOUN
ejpam-3494	145	7	from	from	ADP
ejpam-3494	145	8	[	[	X
ejpam-3494	145	9	1	1	NUM
ejpam-3494	145	10	,	,	PUNCT
ejpam-3494	145	11	13	13	NUM
ejpam-3494	145	12	]	]	PUNCT
ejpam-3494	145	13	on	on	ADP
ejpam-3494	145	14	the	the	DET
ejpam-3494	145	15	nth	nth	NOUN
ejpam-3494	145	16	derivative	derivative	NOUN
ejpam-3494	145	17	of	of	ADP
ejpam-3494	145	18	the	the	DET
ejpam-3494	145	19	exponential	exponential	ADJ
ejpam-3494	145	20	function	function	NOUN
ejpam-3494	145	21	e±	e±	PROPN
ejpam-3494	145	22	1	1	NUM
ejpam-3494	145	23	t	t	NOUN
ejpam-3494	145	24	expressed	express	VERB
ejpam-3494	145	25	in	in	ADP
ejpam-3494	145	26	terms	term	NOUN
ejpam-3494	145	27	of	of	ADP
ejpam-3494	145	28	the	the	DET
ejpam-3494	145	29	lah	lah	PROPN
ejpam-3494	145	30	numbers	number	NOUN
ejpam-3494	145	31	(	(	PUNCT
ejpam-3494	145	32	e±	e±	PROPN
ejpam-3494	145	33	1	1	NUM
ejpam-3494	145	34	t	t	NOUN
ejpam-3494	145	35	)	)	PUNCT
ejpam-3494	145	36	(	(	PUNCT
ejpam-3494	145	37	n	n	CCONJ
ejpam-3494	145	38	)	)	PUNCT
ejpam-3494	145	39	=	=	SYM
ejpam-3494	146	1	(	(	PUNCT
ejpam-3494	146	2	−1)ne±	−1)ne±	NUM
ejpam-3494	146	3	1	1	NUM
ejpam-3494	146	4	t	t	NOUN
ejpam-3494	146	5	n∑	n∑	INTJ
ejpam-3494	146	6	k=1	k=1	X
ejpam-3494	146	7	(	(	PUNCT
ejpam-3494	146	8	±1)kl(n	±1)kl(n	PROPN
ejpam-3494	146	9	,	,	PUNCT
ejpam-3494	146	10	k	k	NOUN
ejpam-3494	146	11	)	)	PUNCT
ejpam-3494	146	12	1	1	NUM
ejpam-3494	146	13	tn+k	tn+k	PROPN
ejpam-3494	146	14	,	,	PUNCT
ejpam-3494	146	15	(	(	PUNCT
ejpam-3494	146	16	26	26	NUM
ejpam-3494	146	17	)	)	PUNCT
ejpam-3494	146	18	the	the	DET
ejpam-3494	146	19	identity	identity	NOUN
ejpam-3494	146	20	from	from	ADP
ejpam-3494	146	21	[	[	X
ejpam-3494	146	22	5	5	NUM
ejpam-3494	146	23	]	]	PUNCT
ejpam-3494	146	24	on	on	ADP
ejpam-3494	146	25	bell	bell	NOUN
ejpam-3494	146	26	polynomials	polynomial	NOUN
ejpam-3494	146	27	of	of	ADP
ejpam-3494	146	28	the	the	DET
ejpam-3494	146	29	second	second	ADJ
ejpam-3494	146	30	kind	kind	NOUN
ejpam-3494	146	31	bn	bn	NOUN
ejpam-3494	146	32	,	,	PUNCT
ejpam-3494	146	33	k(abx1	k(abx1	PROPN
ejpam-3494	146	34	,	,	PUNCT
ejpam-3494	146	35	ab	ab	PROPN
ejpam-3494	146	36	2x2	2x2	NUM
ejpam-3494	146	37	,	,	PUNCT
ejpam-3494	146	38	.	.	PUNCT
ejpam-3494	146	39	.	.	PUNCT
ejpam-3494	146	40	.	.	PUNCT
ejpam-3494	147	1	,	,	PUNCT
ejpam-3494	147	2	ab	ab	PROPN
ejpam-3494	147	3	n−k+1xn−k+1	n−k+1xn−k+1	PROPN
ejpam-3494	147	4	)	)	PUNCT
ejpam-3494	147	5	=	=	SYM
ejpam-3494	147	6	akbnbn	akbnbn	NOUN
ejpam-3494	147	7	,	,	PUNCT
ejpam-3494	147	8	k(x1	k(x1	NOUN
ejpam-3494	147	9	,	,	PUNCT
ejpam-3494	147	10	x2	x2	PROPN
ejpam-3494	147	11	,	,	PUNCT
ejpam-3494	147	12	.	.	PUNCT
ejpam-3494	147	13	.	.	PUNCT
ejpam-3494	147	14	.	.	PUNCT
ejpam-3494	148	1	,	,	PUNCT
ejpam-3494	148	2	xn−k+1	xn−k+1	PROPN
ejpam-3494	148	3	)	)	PUNCT
ejpam-3494	148	4	,	,	PUNCT
ejpam-3494	148	5	(	(	PUNCT
ejpam-3494	148	6	27	27	NUM
ejpam-3494	148	7	)	)	PUNCT
ejpam-3494	148	8	r.	r.	PROPN
ejpam-3494	148	9	b.	b.	PROPN
ejpam-3494	148	10	corcino	corcino	PROPN
ejpam-3494	148	11	et	et	PROPN
ejpam-3494	148	12	al	al	PROPN
ejpam-3494	148	13	.	.	PUNCT
ejpam-3494	148	14	/	/	SYM
ejpam-3494	148	15	eur	eur	PROPN
ejpam-3494	148	16	.	.	PUNCT
ejpam-3494	149	1	j.	j.	PROPN
ejpam-3494	149	2	pure	pure	PROPN
ejpam-3494	149	3	appl	appl	PROPN
ejpam-3494	149	4	.	.	PROPN
ejpam-3494	149	5	math	math	PROPN
ejpam-3494	149	6	,	,	PUNCT
ejpam-3494	149	7	12	12	NUM
ejpam-3494	149	8	(	(	PUNCT
ejpam-3494	149	9	3	3	NUM
ejpam-3494	149	10	)	)	PUNCT
ejpam-3494	149	11	(	(	PUNCT
ejpam-3494	149	12	2019	2019	NUM
ejpam-3494	149	13	)	)	PUNCT
ejpam-3494	149	14	,	,	PUNCT
ejpam-3494	149	15	1122	1122	NUM
ejpam-3494	149	16	-	-	SYM
ejpam-3494	149	17	1137	1137	NUM
ejpam-3494	149	18	1130	1130	NUM
ejpam-3494	149	19	and	and	CCONJ
ejpam-3494	149	20	the	the	DET
ejpam-3494	149	21	famous	famous	ADJ
ejpam-3494	149	22	identity	identity	NOUN
ejpam-3494	149	23	from	from	ADP
ejpam-3494	149	24	[	[	X
ejpam-3494	149	25	5	5	NUM
ejpam-3494	149	26	]	]	PUNCT
ejpam-3494	149	27	on	on	ADP
ejpam-3494	149	28	faá	faá	PROPN
ejpam-3494	149	29	di	di	PROPN
ejpam-3494	149	30	bruno	bruno	PROPN
ejpam-3494	149	31	formula	formula	NOUN
ejpam-3494	149	32	described	describe	VERB
ejpam-3494	149	33	in	in	ADP
ejpam-3494	149	34	terms	term	NOUN
ejpam-3494	149	35	of	of	ADP
ejpam-3494	149	36	the	the	DET
ejpam-3494	149	37	bell	bell	NOUN
ejpam-3494	149	38	polynomials	polynomial	NOUN
ejpam-3494	149	39	of	of	ADP
ejpam-3494	149	40	the	the	DET
ejpam-3494	149	41	second	second	ADJ
ejpam-3494	149	42	kind	kind	NOUN
ejpam-3494	149	43	dn	dn	PROPN
ejpam-3494	149	44	dtn	dtn	PROPN
ejpam-3494	149	45	f	f	PROPN
ejpam-3494	149	46	◦	◦	VERB
ejpam-3494	149	47	h(t	h(t	NUM
ejpam-3494	149	48	)	)	PUNCT
ejpam-3494	150	1	=	=	SYM
ejpam-3494	151	1	n∑	n∑	PROPN
ejpam-3494	151	2	k=0	k=0	PROPN
ejpam-3494	151	3	f	f	PROPN
ejpam-3494	151	4	(	(	PUNCT
ejpam-3494	151	5	k)(h(t))bn	k)(h(t))bn	PROPN
ejpam-3494	151	6	,	,	PUNCT
ejpam-3494	151	7	k(h	k(h	PROPN
ejpam-3494	151	8	′(t	′(t	NOUN
ejpam-3494	151	9	)	)	PUNCT
ejpam-3494	151	10	,	,	PUNCT
ejpam-3494	151	11	h′′(t	h′′(t	NOUN
ejpam-3494	151	12	)	)	PUNCT
ejpam-3494	151	13	,	,	PUNCT
ejpam-3494	151	14	.	.	PUNCT
ejpam-3494	151	15	.	.	PUNCT
ejpam-3494	151	16	.	.	PUNCT
ejpam-3494	151	17	,	,	PUNCT
ejpam-3494	151	18	h(n−k+1)(t	h(n−k+1)(t	PROPN
ejpam-3494	151	19	)	)	PUNCT
ejpam-3494	151	20	)	)	PUNCT
ejpam-3494	151	21	.	.	PUNCT
ejpam-3494	152	1	(	(	PUNCT
ejpam-3494	152	2	28	28	X
ejpam-3494	152	3	)	)	PUNCT
ejpam-3494	152	4	replacing	replace	VERB
ejpam-3494	152	5	t	t	NOUN
ejpam-3494	152	6	by	by	ADP
ejpam-3494	152	7	−t	−t	NOUN
ejpam-3494	152	8	in	in	ADP
ejpam-3494	152	9	the	the	DET
ejpam-3494	152	10	generating	generate	VERB
ejpam-3494	152	11	function	function	NOUN
ejpam-3494	152	12	for	for	ADP
ejpam-3494	152	13	the	the	DET
ejpam-3494	152	14	r	r	NOUN
ejpam-3494	152	15	-	-	PUNCT
ejpam-3494	152	16	dowling	dowle	VERB
ejpam-3494	152	17	numbers	number	NOUN
ejpam-3494	152	18	gn	gn	PROPN
ejpam-3494	152	19	,	,	PUNCT
ejpam-3494	152	20	β	β	X
ejpam-3494	152	21	,	,	PUNCT
ejpam-3494	152	22	r	r	NOUN
ejpam-3494	152	23	in	in	ADP
ejpam-3494	152	24	equation	equation	NOUN
ejpam-3494	152	25	(	(	PUNCT
ejpam-3494	152	26	10	10	NUM
ejpam-3494	152	27	)	)	PUNCT
ejpam-3494	152	28	,	,	PUNCT
ejpam-3494	152	29	yields	yield	VERB
ejpam-3494	152	30	∑	∑	PUNCT
ejpam-3494	152	31	n≥0	n≥0	PROPN
ejpam-3494	152	32	gn	gn	PROPN
ejpam-3494	152	33	,	,	PUNCT
ejpam-3494	152	34	β	β	X
ejpam-3494	152	35	,	,	PUNCT
ejpam-3494	152	36	r	r	NOUN
ejpam-3494	152	37	(	(	PUNCT
ejpam-3494	152	38	−t)n	−t)n	NOUN
ejpam-3494	152	39	n	n	CCONJ
ejpam-3494	152	40	!	!	PUNCT
ejpam-3494	153	1	=	=	PRON
ejpam-3494	153	2	e−rt	e−rt	X
ejpam-3494	153	3	·	·	PUNCT
ejpam-3494	153	4	e	e	X
ejpam-3494	153	5	1	1	NUM
ejpam-3494	153	6	βeβt	βeβt	ADJ
ejpam-3494	153	7	e	e	NOUN
ejpam-3494	153	8	1	1	NUM
ejpam-3494	153	9	β	β	X
ejpam-3494	153	10	;	;	PUNCT
ejpam-3494	153	11	equivalently	equivalently	ADV
ejpam-3494	153	12	,	,	PUNCT
ejpam-3494	153	13	e	e	PROPN
ejpam-3494	153	14	1	1	NUM
ejpam-3494	153	15	β	β	X
ejpam-3494	153	16	∑	∑	PUNCT
ejpam-3494	153	17	n≥0	n≥0	PROPN
ejpam-3494	153	18	(	(	PUNCT
ejpam-3494	153	19	−1)ngn	−1)ngn	PROPN
ejpam-3494	153	20	,	,	PUNCT
ejpam-3494	153	21	β	β	X
ejpam-3494	153	22	,	,	PUNCT
ejpam-3494	153	23	r	r	NOUN
ejpam-3494	153	24	tn	tn	NOUN
ejpam-3494	153	25	n	n	ADV
ejpam-3494	153	26	!	!	PUNCT
ejpam-3494	154	1	=	=	PUNCT
ejpam-3494	154	2	e	e	X
ejpam-3494	154	3	1	1	NUM
ejpam-3494	154	4	βeβt	βeβt	NOUN
ejpam-3494	154	5	·	·	PUNCT
ejpam-3494	154	6	e−rt	e−rt	X
ejpam-3494	154	7	.	.	PUNCT
ejpam-3494	155	1	(	(	PUNCT
ejpam-3494	155	2	29	29	NUM
ejpam-3494	155	3	)	)	PUNCT
ejpam-3494	155	4	then	then	ADV
ejpam-3494	155	5	taking	take	VERB
ejpam-3494	155	6	kth	kth	PROPN
ejpam-3494	155	7	derivative	derivative	ADJ
ejpam-3494	155	8	both	both	DET
ejpam-3494	155	9	sides	side	NOUN
ejpam-3494	155	10	of	of	ADP
ejpam-3494	155	11	(	(	PUNCT
ejpam-3494	155	12	29	29	NUM
ejpam-3494	155	13	)	)	PUNCT
ejpam-3494	155	14	with	with	ADP
ejpam-3494	155	15	respect	respect	NOUN
ejpam-3494	155	16	to	to	ADP
ejpam-3494	155	17	t	t	NOUN
ejpam-3494	155	18	yields	yield	NOUN
ejpam-3494	155	19	e	e	ADP
ejpam-3494	155	20	1	1	NUM
ejpam-3494	155	21	β	β	VERB
ejpam-3494	155	22	∞∑	∞∑	NUM
ejpam-3494	155	23	n	n	X
ejpam-3494	155	24	=	=	SYM
ejpam-3494	155	25	k	k	X
ejpam-3494	155	26	(	(	PUNCT
ejpam-3494	155	27	−1)kgn	−1)kgn	PROPN
ejpam-3494	155	28	,	,	PUNCT
ejpam-3494	155	29	β	β	X
ejpam-3494	155	30	,	,	PUNCT
ejpam-3494	155	31	r	r	NOUN
ejpam-3494	155	32	tn−k	tn−k	NOUN
ejpam-3494	155	33	(	(	PUNCT
ejpam-3494	155	34	n−	n−	NOUN
ejpam-3494	155	35	k	k	NOUN
ejpam-3494	155	36	)	)	PUNCT
ejpam-3494	155	37	!	!	PUNCT
ejpam-3494	156	1	=	=	PRON
ejpam-3494	157	1	dk	dk	PRON
ejpam-3494	157	2	dtk	dtk	PROPN
ejpam-3494	157	3	(	(	PUNCT
ejpam-3494	157	4	e	e	PROPN
ejpam-3494	157	5	1	1	NUM
ejpam-3494	157	6	βeβt	βeβt	NOUN
ejpam-3494	157	7	·	·	PUNCT
ejpam-3494	157	8	e−rt	e−rt	X
ejpam-3494	157	9	)	)	PUNCT
ejpam-3494	157	10	.	.	PUNCT
ejpam-3494	158	1	(	(	PUNCT
ejpam-3494	158	2	30	30	X
ejpam-3494	158	3	)	)	PUNCT
ejpam-3494	158	4	taking	take	VERB
ejpam-3494	158	5	f(u	f(u	PROPN
ejpam-3494	158	6	)	)	PUNCT
ejpam-3494	159	1	=	=	PUNCT
ejpam-3494	159	2	e	e	X
ejpam-3494	159	3	1	1	NUM
ejpam-3494	159	4	u	u	NOUN
ejpam-3494	159	5	and	and	CCONJ
ejpam-3494	159	6	h(t	h(t	NUM
ejpam-3494	159	7	)	)	PUNCT
ejpam-3494	159	8	=	=	NOUN
ejpam-3494	159	9	βeβt	βeβt	NOUN
ejpam-3494	159	10	in	in	ADP
ejpam-3494	159	11	(	(	PUNCT
ejpam-3494	159	12	28	28	NUM
ejpam-3494	159	13	)	)	PUNCT
ejpam-3494	159	14	and	and	CCONJ
ejpam-3494	159	15	making	make	VERB
ejpam-3494	159	16	use	use	NOUN
ejpam-3494	159	17	of	of	ADP
ejpam-3494	159	18	(	(	PUNCT
ejpam-3494	159	19	26	26	NUM
ejpam-3494	159	20	)	)	PUNCT
ejpam-3494	159	21	give	give	VERB
ejpam-3494	159	22	dk	dk	PROPN
ejpam-3494	159	23	(	(	PUNCT
ejpam-3494	159	24	e	e	PROPN
ejpam-3494	159	25	1	1	NUM
ejpam-3494	159	26	βeβt	βeβt	ADJ
ejpam-3494	159	27	)	)	PUNCT
ejpam-3494	159	28	dtk	dtk	PROPN
ejpam-3494	160	1	=	=	SYM
ejpam-3494	160	2	dk	dk	PROPN
ejpam-3494	160	3	(	(	PUNCT
ejpam-3494	160	4	f	f	X
ejpam-3494	160	5	◦	◦	VERB
ejpam-3494	160	6	h(t	h(t	NUM
ejpam-3494	160	7	)	)	PUNCT
ejpam-3494	160	8	)	)	PUNCT
ejpam-3494	160	9	dtk	dtk	PROPN
ejpam-3494	160	10	=	=	SYM
ejpam-3494	160	11	k∑	k∑	PROPN
ejpam-3494	161	1	j=1	j=1	PROPN
ejpam-3494	161	2	dj(e1	dj(e1	PROPN
ejpam-3494	161	3	/	/	SYM
ejpam-3494	161	4	u	u	NOUN
ejpam-3494	161	5	)	)	PUNCT
ejpam-3494	161	6	duj	duj	NOUN
ejpam-3494	161	7	bk	bk	ADP
ejpam-3494	161	8	,	,	PUNCT
ejpam-3494	161	9	j(β(βeβt	j(β(βeβt	NOUN
ejpam-3494	161	10	)	)	PUNCT
ejpam-3494	161	11	,	,	PUNCT
ejpam-3494	161	12	β2(βeβt	β2(βeβt	NOUN
ejpam-3494	161	13	)	)	PUNCT
ejpam-3494	161	14	,	,	PUNCT
ejpam-3494	161	15	.	.	PUNCT
ejpam-3494	161	16	.	.	PUNCT
ejpam-3494	162	1	.	.	PUNCT
ejpam-3494	163	1	,	,	PUNCT
ejpam-3494	163	2	βk−j+1(βeβt	βk−j+1(βeβt	NUM
ejpam-3494	163	3	)	)	PUNCT
ejpam-3494	163	4	)	)	PUNCT
ejpam-3494	164	1	=	=	PUNCT
ejpam-3494	164	2	k∑	k∑	PROPN
ejpam-3494	165	1	j=1	j=1	NOUN
ejpam-3494	165	2	(	(	PUNCT
ejpam-3494	165	3	−1)je1	−1)je1	PROPN
ejpam-3494	165	4	/	/	SYM
ejpam-3494	165	5	u	u	NOUN
ejpam-3494	165	6	j∑	j∑	PROPN
ejpam-3494	165	7	i=1	i=1	PROPN
ejpam-3494	165	8	l(j	l(j	PROPN
ejpam-3494	165	9	,	,	PUNCT
ejpam-3494	165	10	i	i	NOUN
ejpam-3494	165	11	)	)	PUNCT
ejpam-3494	165	12	·	·	PUNCT
ejpam-3494	165	13	1	1	NUM
ejpam-3494	165	14	uj+i	uj+i	NUM
ejpam-3494	165	15	bk	bk	VERB
ejpam-3494	165	16	,	,	PUNCT
ejpam-3494	165	17	j(β(βeβt	j(β(βeβt	NOUN
ejpam-3494	165	18	)	)	PUNCT
ejpam-3494	165	19	,	,	PUNCT
ejpam-3494	165	20	β2(βeβt	β2(βeβt	NOUN
ejpam-3494	165	21	)	)	PUNCT
ejpam-3494	165	22	,	,	PUNCT
ejpam-3494	165	23	.	.	PUNCT
ejpam-3494	165	24	.	.	PUNCT
ejpam-3494	165	25	.	.	PUNCT
ejpam-3494	166	1	,	,	PUNCT
ejpam-3494	166	2	βk−j+1(βeβt	βk−j+1(βeβt	NUM
ejpam-3494	166	3	)	)	PUNCT
ejpam-3494	166	4	)	)	PUNCT
ejpam-3494	167	1	=	=	PUNCT
ejpam-3494	167	2	e	e	X
ejpam-3494	167	3	1	1	NUM
ejpam-3494	167	4	βeβt	βeβt	NOUN
ejpam-3494	167	5	k∑	k∑	VERB
ejpam-3494	168	1	j=1	j=1	NOUN
ejpam-3494	168	2	(	(	PUNCT
ejpam-3494	168	3	−1)j	−1)j	NOUN
ejpam-3494	168	4	j∑	j∑	PROPN
ejpam-3494	168	5	i=1	i=1	PROPN
ejpam-3494	169	1	l(j	l(j	PROPN
ejpam-3494	169	2	,	,	PUNCT
ejpam-3494	169	3	i	i	NOUN
ejpam-3494	169	4	)	)	PUNCT
ejpam-3494	169	5	·	·	PUNCT
ejpam-3494	169	6	1	1	NUM
ejpam-3494	169	7	(	(	PUNCT
ejpam-3494	169	8	βeβt)j+i	βeβt)j+i	NOUN
ejpam-3494	169	9	bk	bk	PROPN
ejpam-3494	169	10	,	,	PUNCT
ejpam-3494	169	11	j(β(βeβt	j(β(βeβt	NOUN
ejpam-3494	169	12	)	)	PUNCT
ejpam-3494	169	13	,	,	PUNCT
ejpam-3494	169	14	β2(βeβt	β2(βeβt	NOUN
ejpam-3494	169	15	)	)	PUNCT
ejpam-3494	169	16	,	,	PUNCT
ejpam-3494	169	17	.	.	PUNCT
ejpam-3494	169	18	.	.	PUNCT
ejpam-3494	169	19	.	.	PUNCT
ejpam-3494	170	1	,	,	PUNCT
ejpam-3494	170	2	βk−j+1(βeβt	βk−j+1(βeβt	NUM
ejpam-3494	170	3	)	)	PUNCT
ejpam-3494	170	4	)	)	PUNCT
ejpam-3494	170	5	,	,	PUNCT
ejpam-3494	170	6	where	where	SCONJ
ejpam-3494	170	7	u(t	u(t	NOUN
ejpam-3494	170	8	)	)	PUNCT
ejpam-3494	171	1	=	=	PUNCT
ejpam-3494	171	2	βeβt	βeβt	NOUN
ejpam-3494	171	3	.	.	PUNCT
ejpam-3494	172	1	further	far	ADV
ejpam-3494	172	2	by	by	ADP
ejpam-3494	172	3	virtue	virtue	NOUN
ejpam-3494	172	4	of	of	ADP
ejpam-3494	172	5	bk	bk	PROPN
ejpam-3494	172	6	,	,	PUNCT
ejpam-3494	172	7	j(abx1	j(abx1	PROPN
ejpam-3494	172	8	,	,	PUNCT
ejpam-3494	172	9	ab	ab	PROPN
ejpam-3494	172	10	2x2	2x2	NUM
ejpam-3494	172	11	,	,	PUNCT
ejpam-3494	172	12	.	.	PUNCT
ejpam-3494	172	13	.	.	PUNCT
ejpam-3494	172	14	.	.	PUNCT
ejpam-3494	173	1	,	,	PUNCT
ejpam-3494	173	2	ab	ab	PROPN
ejpam-3494	173	3	k−j+1xk−j+1	k−j+1xk−j+1	PROPN
ejpam-3494	173	4	)	)	PUNCT
ejpam-3494	173	5	=	=	SYM
ejpam-3494	173	6	ajbkbk	ajbkbk	PROPN
ejpam-3494	173	7	,	,	PUNCT
ejpam-3494	173	8	j(x1	j(x1	PROPN
ejpam-3494	173	9	,	,	PUNCT
ejpam-3494	173	10	x2	x2	PROPN
ejpam-3494	173	11	,	,	PUNCT
ejpam-3494	173	12	.	.	PUNCT
ejpam-3494	173	13	.	.	PUNCT
ejpam-3494	173	14	.	.	PUNCT
ejpam-3494	174	1	,	,	PUNCT
ejpam-3494	174	2	xk−j+1	xk−j+1	PROPN
ejpam-3494	174	3	)	)	PUNCT
ejpam-3494	174	4	and	and	CCONJ
ejpam-3494	174	5	bk	bk	PROPN
ejpam-3494	174	6	,	,	PUNCT
ejpam-3494	174	7	j	j	PROPN
ejpam-3494	174	8	(	(	PUNCT
ejpam-3494	174	9	k−j+1︷	k−j+1︷	NOUN
ejpam-3494	174	10	︸︸	︸︸	PUNCT
ejpam-3494	174	11	︷	︷	PROPN
ejpam-3494	174	12	1	1	NUM
ejpam-3494	174	13	,	,	PUNCT
ejpam-3494	174	14	1	1	NUM
ejpam-3494	174	15	,	,	PUNCT
ejpam-3494	174	16	.	.	PUNCT
ejpam-3494	174	17	.	.	PUNCT
ejpam-3494	175	1	.	.	PUNCT
ejpam-3494	176	1	,	,	PUNCT
ejpam-3494	176	2	1	1	X
ejpam-3494	176	3	)	)	PUNCT
ejpam-3494	176	4	=	=	SYM
ejpam-3494	176	5	s(k	s(k	PROPN
ejpam-3494	176	6	,	,	PUNCT
ejpam-3494	176	7	j	j	PROPN
ejpam-3494	176	8	)	)	PUNCT
ejpam-3494	176	9	r.	r.	PROPN
ejpam-3494	176	10	b.	b.	PROPN
ejpam-3494	176	11	corcino	corcino	PROPN
ejpam-3494	176	12	et	et	PROPN
ejpam-3494	176	13	al	al	PROPN
ejpam-3494	176	14	.	.	PUNCT
ejpam-3494	176	15	/	/	SYM
ejpam-3494	176	16	eur	eur	PROPN
ejpam-3494	176	17	.	.	PUNCT
ejpam-3494	177	1	j.	j.	PROPN
ejpam-3494	177	2	pure	pure	PROPN
ejpam-3494	177	3	appl	appl	PROPN
ejpam-3494	177	4	.	.	PROPN
ejpam-3494	177	5	math	math	PROPN
ejpam-3494	177	6	,	,	PUNCT
ejpam-3494	177	7	12	12	NUM
ejpam-3494	177	8	(	(	PUNCT
ejpam-3494	177	9	3	3	NUM
ejpam-3494	177	10	)	)	PUNCT
ejpam-3494	177	11	(	(	PUNCT
ejpam-3494	177	12	2019	2019	NUM
ejpam-3494	177	13	)	)	PUNCT
ejpam-3494	177	14	,	,	PUNCT
ejpam-3494	177	15	1122	1122	NUM
ejpam-3494	177	16	-	-	SYM
ejpam-3494	177	17	1137	1137	NUM
ejpam-3494	177	18	1131	1131	NUM
ejpam-3494	177	19	listed	list	VERB
ejpam-3494	177	20	in	in	ADP
ejpam-3494	177	21	[	[	X
ejpam-3494	177	22	5	5	NUM
ejpam-3494	177	23	]	]	PUNCT
ejpam-3494	177	24	,	,	PUNCT
ejpam-3494	177	25	[	[	X
ejpam-3494	177	26	p.135	p.135	NOUN
ejpam-3494	177	27	]	]	PUNCT
ejpam-3494	177	28	,	,	PUNCT
ejpam-3494	177	29	where	where	SCONJ
ejpam-3494	177	30	a	a	PRON
ejpam-3494	177	31	and	and	CCONJ
ejpam-3494	177	32	b	b	NOUN
ejpam-3494	177	33	are	be	AUX
ejpam-3494	177	34	complex	complex	ADJ
ejpam-3494	177	35	numbers	number	NOUN
ejpam-3494	177	36	,	,	PUNCT
ejpam-3494	177	37	we	we	PRON
ejpam-3494	177	38	obtain	obtain	VERB
ejpam-3494	177	39	dk	dk	PROPN
ejpam-3494	177	40	(	(	PUNCT
ejpam-3494	177	41	e	e	PROPN
ejpam-3494	177	42	1	1	NUM
ejpam-3494	177	43	βeβt	βeβt	ADJ
ejpam-3494	177	44	)	)	PUNCT
ejpam-3494	177	45	dtk	dtk	PROPN
ejpam-3494	177	46	=	=	SYM
ejpam-3494	178	1	e	e	PROPN
ejpam-3494	178	2	1	1	NUM
ejpam-3494	178	3	βeβt	βeβt	NOUN
ejpam-3494	178	4	k∑	k∑	VERB
ejpam-3494	179	1	j=1	j=1	NOUN
ejpam-3494	179	2	(	(	PUNCT
ejpam-3494	179	3	−1)j	−1)j	NOUN
ejpam-3494	179	4	j∑	j∑	PROPN
ejpam-3494	179	5	i=1	i=1	PROPN
ejpam-3494	180	1	l(j	l(j	PROPN
ejpam-3494	180	2	,	,	PUNCT
ejpam-3494	180	3	i	i	NOUN
ejpam-3494	180	4	)	)	PUNCT
ejpam-3494	180	5	·	·	PUNCT
ejpam-3494	180	6	1	1	NUM
ejpam-3494	180	7	(	(	PUNCT
ejpam-3494	180	8	βeβt)j+i	βeβt)j+i	NOUN
ejpam-3494	180	9	·	·	PUNCT
ejpam-3494	180	10	(	(	PUNCT
ejpam-3494	180	11	βeβt)jβkbk	βeβt)jβkbk	INTJ
ejpam-3494	180	12	,	,	PUNCT
ejpam-3494	180	13	j	j	PROPN
ejpam-3494	180	14	(	(	PUNCT
ejpam-3494	180	15	k−j+1︷	k−j+1︷	NOUN
ejpam-3494	180	16	︸︸	︸︸	PUNCT
ejpam-3494	180	17	︷	︷	PROPN
ejpam-3494	180	18	1	1	NUM
ejpam-3494	180	19	,	,	PUNCT
ejpam-3494	180	20	1	1	NUM
ejpam-3494	180	21	,	,	PUNCT
ejpam-3494	180	22	.	.	PUNCT
ejpam-3494	180	23	.	.	PUNCT
ejpam-3494	180	24	.	.	PUNCT
ejpam-3494	181	1	,	,	PUNCT
ejpam-3494	181	2	1	1	X
ejpam-3494	181	3	)	)	PUNCT
ejpam-3494	181	4	=	=	PUNCT
ejpam-3494	181	5	e	e	NOUN
ejpam-3494	181	6	1	1	NUM
ejpam-3494	181	7	βeβt	βeβt	NOUN
ejpam-3494	181	8	k∑	k∑	VERB
ejpam-3494	182	1	j=1	j=1	NOUN
ejpam-3494	182	2	(	(	PUNCT
ejpam-3494	182	3	−1)j	−1)j	NOUN
ejpam-3494	182	4	j∑	j∑	PROPN
ejpam-3494	182	5	i=1	i=1	PROPN
ejpam-3494	183	1	l(j	l(j	PROPN
ejpam-3494	183	2	,	,	PUNCT
ejpam-3494	183	3	i	i	NOUN
ejpam-3494	183	4	)	)	PUNCT
ejpam-3494	183	5	·	·	PUNCT
ejpam-3494	184	1	β	β	X
ejpam-3494	184	2	k−i	k−i	NOUN
ejpam-3494	184	3	(	(	PUNCT
ejpam-3494	184	4	eβt)i	eβt)i	PROPN
ejpam-3494	184	5	s(k	s(k	ADP
ejpam-3494	184	6	,	,	PUNCT
ejpam-3494	184	7	j	j	NOUN
ejpam-3494	184	8	)	)	PUNCT
ejpam-3494	184	9	.	.	PUNCT
ejpam-3494	185	1	hence	hence	ADV
ejpam-3494	185	2	,	,	PUNCT
ejpam-3494	185	3	using	use	VERB
ejpam-3494	185	4	leibniz	leibniz	PROPN
ejpam-3494	185	5	formula	formula	NOUN
ejpam-3494	185	6	,	,	PUNCT
ejpam-3494	185	7	dn	dn	NOUN
ejpam-3494	185	8	dzn	dzn	NOUN
ejpam-3494	185	9	(	(	PUNCT
ejpam-3494	185	10	e	e	NOUN
ejpam-3494	185	11	1	1	NUM
ejpam-3494	185	12	βeβt	βeβt	NOUN
ejpam-3494	185	13	·	·	PUNCT
ejpam-3494	185	14	e−rt	e−rt	X
ejpam-3494	185	15	)	)	PUNCT
ejpam-3494	186	1	=	=	SYM
ejpam-3494	187	1	n∑	n∑	NOUN
ejpam-3494	187	2	k=0	k=0	PROPN
ejpam-3494	187	3	(	(	PUNCT
ejpam-3494	187	4	n	n	X
ejpam-3494	187	5	k	k	X
ejpam-3494	187	6	)	)	PUNCT
ejpam-3494	188	1	dk	dk	PROPN
ejpam-3494	188	2	dtk	dtk	PROPN
ejpam-3494	188	3	e	e	PROPN
ejpam-3494	188	4	1	1	NUM
ejpam-3494	188	5	βeβt	βeβt	ADJ
ejpam-3494	188	6	dn−k	dn−k	NOUN
ejpam-3494	188	7	dtn−k	dtn−k	NOUN
ejpam-3494	188	8	e−rt	e−rt	X
ejpam-3494	188	9	=	=	SYM
ejpam-3494	188	10	n∑	n∑	NOUN
ejpam-3494	188	11	k=0	k=0	PROPN
ejpam-3494	188	12	(	(	PUNCT
ejpam-3494	188	13	n	n	X
ejpam-3494	188	14	k	k	X
ejpam-3494	188	15	)	)	PUNCT
ejpam-3494	188	16	e	e	PROPN
ejpam-3494	188	17	1	1	NUM
ejpam-3494	188	18	βeβt	βeβt	NOUN
ejpam-3494	188	19	k∑	k∑	NOUN
ejpam-3494	189	1	j=1	j=1	NOUN
ejpam-3494	189	2	(	(	PUNCT
ejpam-3494	189	3	−1)j	−1)j	NOUN
ejpam-3494	189	4	j∑	j∑	PROPN
ejpam-3494	189	5	i=1	i=1	PROPN
ejpam-3494	190	1	l(j	l(j	PROPN
ejpam-3494	190	2	,	,	PUNCT
ejpam-3494	190	3	i	i	NOUN
ejpam-3494	190	4	)	)	PUNCT
ejpam-3494	190	5	·	·	PUNCT
ejpam-3494	191	1	β	β	X
ejpam-3494	191	2	k−i	k−i	NOUN
ejpam-3494	191	3	(	(	PUNCT
ejpam-3494	191	4	eβt)i	eβt)i	PROPN
ejpam-3494	191	5	s(k	s(k	ADV
ejpam-3494	191	6	,	,	PUNCT
ejpam-3494	191	7	j	j	NOUN
ejpam-3494	191	8	)	)	PUNCT
ejpam-3494	191	9			NOUN
ejpam-3494	191	10	·	·	PUNCT
ejpam-3494	191	11	(	(	PUNCT
ejpam-3494	191	12	−r)n−ke−rt	−r)n−ke−rt	X
ejpam-3494	191	13	.	.	PUNCT
ejpam-3494	191	14	thus	thus	ADV
ejpam-3494	191	15	,	,	PUNCT
ejpam-3494	191	16	replacing	replace	VERB
ejpam-3494	191	17	k	k	X
ejpam-3494	191	18	by	by	ADP
ejpam-3494	191	19	n	n	ADV
ejpam-3494	191	20	and	and	CCONJ
ejpam-3494	191	21	evaluating	evaluate	VERB
ejpam-3494	191	22	at	at	ADP
ejpam-3494	191	23	t	t	NOUN
ejpam-3494	191	24	=	=	SYM
ejpam-3494	191	25	0	0	NUM
ejpam-3494	191	26	in	in	ADP
ejpam-3494	191	27	equation	equation	NOUN
ejpam-3494	191	28	(	(	PUNCT
ejpam-3494	191	29	30	30	NUM
ejpam-3494	191	30	)	)	PUNCT
ejpam-3494	191	31	give	give	VERB
ejpam-3494	191	32	e	e	NOUN
ejpam-3494	191	33	1	1	NUM
ejpam-3494	191	34	β	β	X
ejpam-3494	191	35	(	(	PUNCT
ejpam-3494	191	36	−1)ngn	−1)ngn	PROPN
ejpam-3494	191	37	,	,	PUNCT
ejpam-3494	191	38	β	β	X
ejpam-3494	191	39	,	,	PUNCT
ejpam-3494	191	40	r	r	NOUN
ejpam-3494	191	41	=	=	SYM
ejpam-3494	191	42	n∑	n∑	NOUN
ejpam-3494	191	43	k=0	k=0	PROPN
ejpam-3494	191	44	(	(	PUNCT
ejpam-3494	191	45	n	n	X
ejpam-3494	191	46	k	k	PROPN
ejpam-3494	191	47	)	)	PUNCT
ejpam-3494	191	48	k∑	k∑	PROPN
ejpam-3494	192	1	j=1	j=1	NOUN
ejpam-3494	192	2	(	(	PUNCT
ejpam-3494	192	3	−1)je	−1)je	PROPN
ejpam-3494	192	4	1	1	NUM
ejpam-3494	192	5	β	β	NOUN
ejpam-3494	192	6	j∑	j∑	PROPN
ejpam-3494	192	7	i=1	i=1	PROPN
ejpam-3494	192	8	l(j	l(j	PROPN
ejpam-3494	192	9	,	,	PUNCT
ejpam-3494	192	10	i	i	NOUN
ejpam-3494	192	11	)	)	PUNCT
ejpam-3494	192	12	·	·	PUNCT
ejpam-3494	193	1	βk−is(k	βk−is(k	PROPN
ejpam-3494	193	2	,	,	PUNCT
ejpam-3494	193	3	j	j	PROPN
ejpam-3494	193	4	)	)	PUNCT
ejpam-3494	193	5	·	·	PUNCT
ejpam-3494	193	6	(	(	PUNCT
ejpam-3494	193	7	−r)n−k	−r)n−k	VERB
ejpam-3494	193	8	;	;	PUNCT
ejpam-3494	193	9	rearranging	rearrange	VERB
ejpam-3494	193	10	the	the	DET
ejpam-3494	193	11	above	above	ADJ
ejpam-3494	193	12	sum	sum	NOUN
ejpam-3494	193	13	and	and	CCONJ
ejpam-3494	193	14	using	use	VERB
ejpam-3494	193	15	the	the	DET
ejpam-3494	193	16	fact	fact	NOUN
ejpam-3494	193	17	that	that	SCONJ
ejpam-3494	193	18	l(0	l(0	PROPN
ejpam-3494	193	19	,	,	PUNCT
ejpam-3494	193	20	i	i	NOUN
ejpam-3494	193	21	)	)	PUNCT
ejpam-3494	193	22	=	=	SYM
ejpam-3494	193	23	0	0	NUM
ejpam-3494	193	24	for	for	ADP
ejpam-3494	193	25	all	all	DET
ejpam-3494	193	26	positive	positive	ADJ
ejpam-3494	193	27	integers	integer	NOUN
ejpam-3494	193	28	i	i	PRON
ejpam-3494	193	29	,	,	PUNCT
ejpam-3494	193	30	we	we	PRON
ejpam-3494	193	31	get	get	VERB
ejpam-3494	193	32	gn	gn	PROPN
ejpam-3494	193	33	,	,	PUNCT
ejpam-3494	193	34	β	β	X
ejpam-3494	193	35	,	,	PUNCT
ejpam-3494	193	36	r	r	NOUN
ejpam-3494	193	37	=	=	SYM
ejpam-3494	193	38	n∑	n∑	PROPN
ejpam-3494	193	39	i=0	i=0	PROPN
ejpam-3494	193	40	(	(	PUNCT
ejpam-3494	193	41	−1)n−j	−1)n−j	CCONJ
ejpam-3494	193	42	i∑	i∑	PROPN
ejpam-3494	194	1	j=0	j=0	PROPN
ejpam-3494	194	2	{	{	PUNCT
ejpam-3494	194	3	n∑	n∑	NOUN
ejpam-3494	194	4	k	k	PROPN
ejpam-3494	194	5	=	=	PROPN
ejpam-3494	194	6	j	j	PROPN
ejpam-3494	194	7	(	(	PUNCT
ejpam-3494	194	8	n	n	NOUN
ejpam-3494	194	9	k	k	NOUN
ejpam-3494	194	10	)	)	PUNCT
ejpam-3494	194	11	βk−j(−r)n−ks(k	βk−j(−r)n−ks(k	PROPN
ejpam-3494	194	12	,	,	PUNCT
ejpam-3494	194	13	j	j	NOUN
ejpam-3494	194	14	)	)	PUNCT
ejpam-3494	194	15	}	}	PUNCT
ejpam-3494	194	16	βj−il(j	βj−il(j	PROPN
ejpam-3494	194	17	,	,	PUNCT
ejpam-3494	194	18	i	i	NOUN
ejpam-3494	194	19	)	)	PUNCT
ejpam-3494	194	20	.	.	PUNCT
ejpam-3494	195	1	applying	apply	VERB
ejpam-3494	195	2	the	the	DET
ejpam-3494	195	3	property	property	NOUN
ejpam-3494	195	4	of	of	ADP
ejpam-3494	195	5	r	r	NOUN
ejpam-3494	195	6	-	-	PUNCT
ejpam-3494	195	7	whitney	whitney	NOUN
ejpam-3494	195	8	numbers	number	NOUN
ejpam-3494	195	9	of	of	ADP
ejpam-3494	195	10	the	the	DET
ejpam-3494	195	11	second	second	ADJ
ejpam-3494	195	12	kind	kind	NOUN
ejpam-3494	195	13	in	in	ADP
ejpam-3494	195	14	equation	equation	NOUN
ejpam-3494	195	15	(	(	PUNCT
ejpam-3494	195	16	8)	8)	NUM
ejpam-3494	195	17	yields	yield	NOUN
ejpam-3494	195	18	gn	gn	PROPN
ejpam-3494	195	19	,	,	PUNCT
ejpam-3494	195	20	β	β	X
ejpam-3494	195	21	,	,	PUNCT
ejpam-3494	195	22	r	r	NOUN
ejpam-3494	195	23	=	=	SYM
ejpam-3494	195	24	n∑	n∑	PROPN
ejpam-3494	195	25	i=0	i=0	PROPN
ejpam-3494	195	26	(	(	PUNCT
ejpam-3494	195	27	−1)n−j	−1)n−j	CCONJ
ejpam-3494	195	28	i∑	i∑	PROPN
ejpam-3494	195	29	j=0	j=0	PROPN
ejpam-3494	195	30	wβ,−r(n	wβ,−r(n	PROPN
ejpam-3494	195	31	,	,	PUNCT
ejpam-3494	195	32	j)β	j)β	NOUN
ejpam-3494	195	33	j−il(j	j−il(j	PROPN
ejpam-3494	195	34	,	,	PUNCT
ejpam-3494	195	35	i	i	PROPN
ejpam-3494	195	36	)	)	PUNCT
ejpam-3494	195	37	.	.	PUNCT
ejpam-3494	196	1	this	this	PRON
ejpam-3494	196	2	is	be	AUX
ejpam-3494	196	3	exactly	exactly	ADV
ejpam-3494	196	4	the	the	DET
ejpam-3494	196	5	formula	formula	NOUN
ejpam-3494	196	6	in	in	ADP
ejpam-3494	196	7	(	(	PUNCT
ejpam-3494	196	8	25	25	NUM
ejpam-3494	196	9	)	)	PUNCT
ejpam-3494	196	10	.	.	PUNCT
ejpam-3494	197	1	the	the	DET
ejpam-3494	197	2	following	follow	VERB
ejpam-3494	197	3	corollary	corollary	NOUN
ejpam-3494	197	4	is	be	AUX
ejpam-3494	197	5	a	a	DET
ejpam-3494	197	6	direct	direct	ADJ
ejpam-3494	197	7	consequence	consequence	NOUN
ejpam-3494	197	8	of	of	ADP
ejpam-3494	197	9	theorem	theorem	NOUN
ejpam-3494	197	10	4.1	4.1	NUM
ejpam-3494	197	11	.	.	PUNCT
ejpam-3494	198	1	corollary	corollary	ADJ
ejpam-3494	198	2	4.2	4.2	NUM
ejpam-3494	198	3	.	.	PUNCT
ejpam-3494	199	1	for	for	ADP
ejpam-3494	199	2	n	n	PRON
ejpam-3494	199	3	∈	∈	PROPN
ejpam-3494	199	4	n	n	CCONJ
ejpam-3494	199	5	,	,	PUNCT
ejpam-3494	199	6	the	the	DET
ejpam-3494	199	7	r	r	NOUN
ejpam-3494	199	8	-	-	PUNCT
ejpam-3494	199	9	dowling	dowle	VERB
ejpam-3494	199	10	numbers	number	NOUN
ejpam-3494	199	11	gi	gi	ADP
ejpam-3494	199	12	,	,	PUNCT
ejpam-3494	199	13	β	β	X
ejpam-3494	199	14	,	,	PUNCT
ejpam-3494	199	15	r	r	NOUN
ejpam-3494	199	16	equal	equal	ADJ
ejpam-3494	199	17	to	to	ADP
ejpam-3494	199	18	the	the	DET
ejpam-3494	199	19	sum	sum	NOUN
ejpam-3494	199	20	of	of	ADP
ejpam-3494	199	21	the	the	DET
ejpam-3494	199	22	entries	entry	NOUN
ejpam-3494	199	23	of	of	ADP
ejpam-3494	199	24	the	the	DET
ejpam-3494	199	25	ith	ith	PROPN
ejpam-3494	199	26	row	row	NOUN
ejpam-3494	199	27	of	of	ADP
ejpam-3494	199	28	the	the	DET
ejpam-3494	199	29	product	product	NOUN
ejpam-3494	199	30	of	of	ADP
ejpam-3494	199	31	two	two	NUM
ejpam-3494	199	32	matrices	matrix	NOUN
ejpam-3494	199	33	[	[	PUNCT
ejpam-3494	199	34	(	(	PUNCT
ejpam-3494	199	35	−1)i−jwβ,−r(i	−1)i−jwβ,−r(i	ADP
ejpam-3494	199	36	,	,	PUNCT
ejpam-3494	199	37	j	j	NOUN
ejpam-3494	199	38	)	)	PUNCT
ejpam-3494	199	39	]	]	PUNCT
ejpam-3494	200	1	n×n	n×n	PROPN
ejpam-3494	200	2	[	[	PUNCT
ejpam-3494	200	3	βj−il(i	βj−il(i	PROPN
ejpam-3494	200	4	,	,	PUNCT
ejpam-3494	200	5	j	j	NOUN
ejpam-3494	200	6	)	)	PUNCT
ejpam-3494	200	7	]	]	PUNCT
ejpam-3494	201	1	n×n	n×n	PROPN
ejpam-3494	201	2	,	,	PUNCT
ejpam-3494	201	3	(	(	PUNCT
ejpam-3494	201	4	31	31	NUM
ejpam-3494	201	5	)	)	PUNCT
ejpam-3494	201	6	whose	whose	DET
ejpam-3494	201	7	entries	entry	NOUN
ejpam-3494	201	8	are	be	AUX
ejpam-3494	201	9	respectively	respectively	ADV
ejpam-3494	201	10	r	r	NOUN
ejpam-3494	201	11	-	-	PUNCT
ejpam-3494	201	12	whitney	whitney	NOUN
ejpam-3494	201	13	numbers	number	NOUN
ejpam-3494	201	14	of	of	ADP
ejpam-3494	201	15	the	the	DET
ejpam-3494	201	16	second	second	ADJ
ejpam-3494	201	17	kind	kind	NOUN
ejpam-3494	201	18	and	and	CCONJ
ejpam-3494	201	19	the	the	DET
ejpam-3494	201	20	lah	lah	NOUN
ejpam-3494	201	21	numbers	number	NOUN
ejpam-3494	201	22	.	.	PUNCT
ejpam-3494	202	1	proof	proof	NOUN
ejpam-3494	202	2	.	.	PUNCT
ejpam-3494	203	1	we	we	PRON
ejpam-3494	203	2	can	can	AUX
ejpam-3494	203	3	rewrite	rewrite	VERB
ejpam-3494	203	4	the	the	DET
ejpam-3494	203	5	formula	formula	NOUN
ejpam-3494	203	6	in	in	ADP
ejpam-3494	203	7	theorem	theorem	ADJ
ejpam-3494	203	8	4.1	4.1	NUM
ejpam-3494	203	9	as	as	ADP
ejpam-3494	203	10	gi	gi	NOUN
ejpam-3494	203	11	,	,	PUNCT
ejpam-3494	203	12	β	β	X
ejpam-3494	203	13	,	,	PUNCT
ejpam-3494	203	14	r	r	NOUN
ejpam-3494	203	15	=	=	PUNCT
ejpam-3494	203	16	i∑	i∑	PROPN
ejpam-3494	203	17	l=0	l=0	PROPN
ejpam-3494	203	18	til	til	PROPN
ejpam-3494	203	19	,	,	PUNCT
ejpam-3494	203	20	i	i	PROPN
ejpam-3494	203	21	=	=	NOUN
ejpam-3494	203	22	0	0	NUM
ejpam-3494	203	23	,	,	PUNCT
ejpam-3494	203	24	1	1	NUM
ejpam-3494	203	25	,	,	PUNCT
ejpam-3494	203	26	2	2	NUM
ejpam-3494	203	27	,	,	PUNCT
ejpam-3494	203	28	.	.	PUNCT
ejpam-3494	203	29	.	.	PUNCT
ejpam-3494	204	1	.	.	PUNCT
ejpam-3494	205	1	,	,	PUNCT
ejpam-3494	205	2	n	n	CCONJ
ejpam-3494	205	3	,	,	PUNCT
ejpam-3494	205	4	r.	r.	PROPN
ejpam-3494	205	5	b.	b.	PROPN
ejpam-3494	205	6	corcino	corcino	PROPN
ejpam-3494	205	7	et	et	PROPN
ejpam-3494	205	8	al	al	PROPN
ejpam-3494	205	9	.	.	PUNCT
ejpam-3494	205	10	/	/	SYM
ejpam-3494	205	11	eur	eur	PROPN
ejpam-3494	205	12	.	.	PUNCT
ejpam-3494	206	1	j.	j.	PROPN
ejpam-3494	206	2	pure	pure	PROPN
ejpam-3494	206	3	appl	appl	PROPN
ejpam-3494	206	4	.	.	PROPN
ejpam-3494	206	5	math	math	PROPN
ejpam-3494	206	6	,	,	PUNCT
ejpam-3494	206	7	12	12	NUM
ejpam-3494	206	8	(	(	PUNCT
ejpam-3494	206	9	3	3	NUM
ejpam-3494	206	10	)	)	PUNCT
ejpam-3494	206	11	(	(	PUNCT
ejpam-3494	206	12	2019	2019	NUM
ejpam-3494	206	13	)	)	PUNCT
ejpam-3494	206	14	,	,	PUNCT
ejpam-3494	206	15	1122	1122	NUM
ejpam-3494	206	16	-	-	SYM
ejpam-3494	206	17	1137	1137	NUM
ejpam-3494	206	18	1132	1132	NUM
ejpam-3494	207	1	where	where	SCONJ
ejpam-3494	207	2	til	til	PROPN
ejpam-3494	207	3	=	=	SYM
ejpam-3494	207	4	i∑	i∑	PROPN
ejpam-3494	207	5	j=0	j=0	PROPN
ejpam-3494	207	6	(	(	PUNCT
ejpam-3494	207	7	−1)i−jwβ,−r(i	−1)i−jwβ,−r(i	ADV
ejpam-3494	207	8	,	,	PUNCT
ejpam-3494	207	9	j)β	j)β	NOUN
ejpam-3494	207	10	j−ll(j	j−ll(j	PROPN
ejpam-3494	207	11	,	,	PUNCT
ejpam-3494	207	12	l	l	NOUN
ejpam-3494	207	13	)	)	PUNCT
ejpam-3494	207	14	,	,	PUNCT
ejpam-3494	207	15	l	l	NOUN
ejpam-3494	207	16	=	=	SYM
ejpam-3494	207	17	0	0	NUM
ejpam-3494	207	18	,	,	PUNCT
ejpam-3494	207	19	1	1	NUM
ejpam-3494	207	20	,	,	PUNCT
ejpam-3494	207	21	2	2	NUM
ejpam-3494	207	22	,	,	PUNCT
ejpam-3494	207	23	.	.	PUNCT
ejpam-3494	207	24	.	.	PUNCT
ejpam-3494	207	25	.	.	PUNCT
ejpam-3494	208	1	i.	i.	PROPN
ejpam-3494	208	2	clearly	clearly	ADV
ejpam-3494	208	3	,	,	PUNCT
ejpam-3494	208	4	til	til	ADV
ejpam-3494	208	5	is	be	AUX
ejpam-3494	208	6	the	the	DET
ejpam-3494	208	7	(	(	PUNCT
ejpam-3494	208	8	i	i	PROPN
ejpam-3494	208	9	,	,	PUNCT
ejpam-3494	208	10	l)-entry	l)-entry	NOUN
ejpam-3494	208	11	of	of	ADP
ejpam-3494	208	12	the	the	DET
ejpam-3494	208	13	following	follow	VERB
ejpam-3494	208	14	product	product	NOUN
ejpam-3494	208	15	of	of	ADP
ejpam-3494	208	16	two	two	NUM
ejpam-3494	208	17	matrices	matrix	NOUN
ejpam-3494	208	18	[	[	PUNCT
ejpam-3494	208	19	(	(	PUNCT
ejpam-3494	208	20	−1)i−jwβ,−r(i	−1)i−jwβ,−r(i	ADP
ejpam-3494	208	21	,	,	PUNCT
ejpam-3494	208	22	j	j	NOUN
ejpam-3494	208	23	)	)	PUNCT
ejpam-3494	208	24	]	]	PUNCT
ejpam-3494	209	1	n×n	n×n	PROPN
ejpam-3494	209	2	[	[	PUNCT
ejpam-3494	209	3	βj−il(i	βj−il(i	PROPN
ejpam-3494	209	4	,	,	PUNCT
ejpam-3494	209	5	j	j	NOUN
ejpam-3494	209	6	)	)	PUNCT
ejpam-3494	209	7	]	]	PUNCT
ejpam-3494	210	1	n×n	n×n	PROPN
ejpam-3494	210	2	,	,	PUNCT
ejpam-3494	210	3	(	(	PUNCT
ejpam-3494	210	4	32	32	NUM
ejpam-3494	210	5	)	)	PUNCT
ejpam-3494	210	6	containing	contain	VERB
ejpam-3494	210	7	the	the	DET
ejpam-3494	210	8	r	r	NOUN
ejpam-3494	210	9	-	-	PUNCT
ejpam-3494	210	10	whitney	whitney	NOUN
ejpam-3494	210	11	numbers	number	NOUN
ejpam-3494	210	12	of	of	ADP
ejpam-3494	210	13	the	the	DET
ejpam-3494	210	14	second	second	ADJ
ejpam-3494	210	15	kind	kind	NOUN
ejpam-3494	210	16	and	and	CCONJ
ejpam-3494	210	17	lah	lah	NOUN
ejpam-3494	210	18	numbers	number	NOUN
ejpam-3494	210	19	,	,	PUNCT
ejpam-3494	210	20	respectively	respectively	ADV
ejpam-3494	210	21	.	.	PUNCT
ejpam-3494	211	1	to	to	PART
ejpam-3494	211	2	illustrate	illustrate	VERB
ejpam-3494	211	3	this	this	DET
ejpam-3494	211	4	corollary	corollary	NOUN
ejpam-3494	211	5	,	,	PUNCT
ejpam-3494	211	6	let	let	VERB
ejpam-3494	211	7	us	we	PRON
ejpam-3494	211	8	consider	consider	VERB
ejpam-3494	211	9	the	the	DET
ejpam-3494	211	10	case	case	NOUN
ejpam-3494	211	11	where	where	SCONJ
ejpam-3494	211	12	β	β	X
ejpam-3494	211	13	=	=	SYM
ejpam-3494	211	14	1	1	NUM
ejpam-3494	211	15	,	,	PUNCT
ejpam-3494	211	16	r	r	NOUN
ejpam-3494	211	17	=	=	SYM
ejpam-3494	211	18	2	2	NUM
ejpam-3494	211	19	,	,	PUNCT
ejpam-3494	211	20	n	n	NOUN
ejpam-3494	211	21	=	=	SYM
ejpam-3494	211	22	6	6	NUM
ejpam-3494	211	23	.	.	PUNCT
ejpam-3494	212	1	that	that	PRON
ejpam-3494	212	2	is	be	AUX
ejpam-3494	212	3	,	,	PUNCT
ejpam-3494	212	4	[	[	PUNCT
ejpam-3494	212	5	(	(	PUNCT
ejpam-3494	212	6	−1)i−jw1,−2(i	−1)i−jw1,−2(i	X
ejpam-3494	212	7	,	,	PUNCT
ejpam-3494	212	8	j	j	PROPN
ejpam-3494	212	9	)	)	PUNCT
ejpam-3494	212	10	]	]	PUNCT
ejpam-3494	213	1	6×6	6×6	NUM
ejpam-3494	213	2	[	[	PUNCT
ejpam-3494	213	3	βi−jl(i	βi−jl(i	NUM
ejpam-3494	213	4	,	,	PUNCT
ejpam-3494	213	5	j	j	PROPN
ejpam-3494	213	6	)	)	PUNCT
ejpam-3494	213	7	]	]	PUNCT
ejpam-3494	214	1	6×6	6×6	NUM
ejpam-3494	214	2	=	=	PUNCT
ejpam-3494	214	3			VERB
ejpam-3494	214	4	1	1	NUM
ejpam-3494	214	5	0	0	NUM
ejpam-3494	214	6	0	0	NUM
ejpam-3494	214	7	0	0	NUM
ejpam-3494	214	8	0	0	NUM
ejpam-3494	214	9	0	0	NUM
ejpam-3494	214	10	2	2	NUM
ejpam-3494	214	11	1	1	NUM
ejpam-3494	214	12	0	0	NUM
ejpam-3494	214	13	0	0	NUM
ejpam-3494	214	14	0	0	NUM
ejpam-3494	214	15	0	0	NUM
ejpam-3494	214	16	4	4	NUM
ejpam-3494	214	17	3	3	NUM
ejpam-3494	214	18	1	1	NUM
ejpam-3494	214	19	0	0	NUM
ejpam-3494	214	20	0	0	NUM
ejpam-3494	214	21	0	0	NUM
ejpam-3494	214	22	8	8	NUM
ejpam-3494	214	23	7	7	NUM
ejpam-3494	214	24	3	3	NUM
ejpam-3494	214	25	1	1	NUM
ejpam-3494	214	26	0	0	NUM
ejpam-3494	214	27	0	0	NUM
ejpam-3494	214	28	16	16	NUM
ejpam-3494	214	29	15	15	NUM
ejpam-3494	214	30	7	7	NUM
ejpam-3494	214	31	2	2	NUM
ejpam-3494	214	32	1	1	NUM
ejpam-3494	214	33	0	0	NUM
ejpam-3494	214	34	32	32	NUM
ejpam-3494	214	35	31	31	NUM
ejpam-3494	214	36	15	15	NUM
ejpam-3494	214	37	5	5	NUM
ejpam-3494	214	38	0	0	NUM
ejpam-3494	214	39	1	1	NUM
ejpam-3494	214	40			NOUN
ejpam-3494	214	41			VERB
ejpam-3494	214	42	1	1	NUM
ejpam-3494	214	43	0	0	NUM
ejpam-3494	214	44	0	0	NUM
ejpam-3494	214	45	0	0	NUM
ejpam-3494	214	46	0	0	NUM
ejpam-3494	214	47	0	0	NUM
ejpam-3494	214	48	0	0	NUM
ejpam-3494	214	49	1	1	NUM
ejpam-3494	214	50	0	0	NUM
ejpam-3494	214	51	0	0	NUM
ejpam-3494	214	52	0	0	NUM
ejpam-3494	214	53	0	0	NUM
ejpam-3494	214	54	0	0	NUM
ejpam-3494	214	55	2	2	NUM
ejpam-3494	214	56	1	1	NUM
ejpam-3494	214	57	0	0	NUM
ejpam-3494	214	58	0	0	NUM
ejpam-3494	214	59	0	0	NUM
ejpam-3494	214	60	0	0	NUM
ejpam-3494	214	61	6	6	NUM
ejpam-3494	214	62	6	6	NUM
ejpam-3494	214	63	1	1	NUM
ejpam-3494	214	64	0	0	NUM
ejpam-3494	214	65	0	0	NUM
ejpam-3494	214	66	0	0	NUM
ejpam-3494	214	67	24	24	NUM
ejpam-3494	214	68	36	36	NUM
ejpam-3494	214	69	12	12	NUM
ejpam-3494	214	70	1	1	NUM
ejpam-3494	214	71	0	0	NUM
ejpam-3494	214	72	0	0	NUM
ejpam-3494	214	73	120	120	NUM
ejpam-3494	214	74	240	240	NUM
ejpam-3494	214	75	120	120	NUM
ejpam-3494	214	76	20	20	NUM
ejpam-3494	214	77	1	1	NUM
ejpam-3494	214	78			NOUN
ejpam-3494	214	79	=	=	SYM
ejpam-3494	214	80			NOUN
ejpam-3494	215	1	1	1	NUM
ejpam-3494	215	2	0	0	NUM
ejpam-3494	215	3	0	0	NUM
ejpam-3494	215	4	0	0	NUM
ejpam-3494	215	5	0	0	NUM
ejpam-3494	215	6	0	0	NUM
ejpam-3494	215	7	2	2	NUM
ejpam-3494	215	8	1	1	NUM
ejpam-3494	215	9	0	0	NUM
ejpam-3494	215	10	0	0	NUM
ejpam-3494	215	11	0	0	NUM
ejpam-3494	215	12	0	0	NUM
ejpam-3494	215	13	4	4	NUM
ejpam-3494	215	14	5	5	NUM
ejpam-3494	215	15	1	1	NUM
ejpam-3494	215	16	0	0	NUM
ejpam-3494	215	17	0	0	NUM
ejpam-3494	215	18	0	0	NUM
ejpam-3494	215	19	8	8	NUM
ejpam-3494	215	20	19	19	NUM
ejpam-3494	215	21	9	9	NUM
ejpam-3494	215	22	1	1	NUM
ejpam-3494	215	23	0	0	NUM
ejpam-3494	215	24	0	0	NUM
ejpam-3494	215	25	16	16	NUM
ejpam-3494	215	26	65	65	NUM
ejpam-3494	215	27	55	55	NUM
ejpam-3494	215	28	14	14	NUM
ejpam-3494	215	29	1	1	NUM
ejpam-3494	215	30	0	0	NUM
ejpam-3494	215	31	32	32	NUM
ejpam-3494	215	32	211	211	NUM
ejpam-3494	215	33	285	285	NUM
ejpam-3494	215	34	125	125	NUM
ejpam-3494	215	35	20	20	NUM
ejpam-3494	215	36	1	1	NUM
ejpam-3494	215	37			NUM
ejpam-3494	215	38	.	.	PUNCT
ejpam-3494	216	1	(	(	PUNCT
ejpam-3494	216	2	33	33	NUM
ejpam-3494	216	3	)	)	PUNCT
ejpam-3494	216	4	hence	hence	ADV
ejpam-3494	216	5	,	,	PUNCT
ejpam-3494	216	6	summing	sum	VERB
ejpam-3494	216	7	up	up	ADP
ejpam-3494	216	8	the	the	DET
ejpam-3494	216	9	entries	entry	NOUN
ejpam-3494	216	10	of	of	ADP
ejpam-3494	216	11	each	each	DET
ejpam-3494	216	12	row	row	NOUN
ejpam-3494	216	13	of	of	ADP
ejpam-3494	216	14	the	the	DET
ejpam-3494	216	15	matrix	matrix	NOUN
ejpam-3494	216	16	in	in	ADP
ejpam-3494	216	17	(	(	PUNCT
ejpam-3494	216	18	33	33	NUM
ejpam-3494	216	19	)	)	PUNCT
ejpam-3494	216	20	gives	give	VERB
ejpam-3494	216	21	the	the	DET
ejpam-3494	216	22	following	follow	VERB
ejpam-3494	216	23	column	column	NOUN
ejpam-3494	216	24	vector	vector	NOUN
ejpam-3494	216	25	whose	whose	DET
ejpam-3494	216	26	entries	entry	NOUN
ejpam-3494	216	27	are	be	AUX
ejpam-3494	216	28	the	the	DET
ejpam-3494	216	29	r	r	NOUN
ejpam-3494	216	30	-	-	PUNCT
ejpam-3494	216	31	dowling	dowle	VERB
ejpam-3494	216	32	numbers	number	NOUN
ejpam-3494	216	33	with	with	ADP
ejpam-3494	216	34	β	β	X
ejpam-3494	216	35	=	=	SYM
ejpam-3494	216	36	1	1	NUM
ejpam-3494	216	37	and	and	CCONJ
ejpam-3494	216	38	r	r	NOUN
ejpam-3494	216	39	=	=	SYM
ejpam-3494	216	40	2	2	NUM
ejpam-3494	216	41	1	1	NUM
ejpam-3494	216	42	2	2	NUM
ejpam-3494	216	43	+	+	CCONJ
ejpam-3494	216	44	1	1	NUM
ejpam-3494	216	45	4	4	NUM
ejpam-3494	216	46	+	+	SYM
ejpam-3494	216	47	5	5	NUM
ejpam-3494	216	48	+	+	CCONJ
ejpam-3494	216	49	1	1	NUM
ejpam-3494	216	50	8	8	NUM
ejpam-3494	216	51	+	+	NUM
ejpam-3494	216	52	19	19	NUM
ejpam-3494	216	53	+	+	CCONJ
ejpam-3494	216	54	9	9	NUM
ejpam-3494	216	55	+	+	CCONJ
ejpam-3494	216	56	1	1	NUM
ejpam-3494	216	57	16	16	NUM
ejpam-3494	216	58	+	+	CCONJ
ejpam-3494	216	59	65	65	NUM
ejpam-3494	216	60	+	+	NUM
ejpam-3494	216	61	55	55	NUM
ejpam-3494	216	62	+	+	NUM
ejpam-3494	216	63	14	14	NUM
ejpam-3494	216	64	+	+	CCONJ
ejpam-3494	216	65	1	1	NUM
ejpam-3494	216	66	32	32	NUM
ejpam-3494	216	67	+	+	CCONJ
ejpam-3494	216	68	211	211	NUM
ejpam-3494	216	69	+	+	CCONJ
ejpam-3494	216	70	285	285	NUM
ejpam-3494	216	71	+	+	SYM
ejpam-3494	216	72	125	125	NUM
ejpam-3494	216	73	+	+	NUM
ejpam-3494	216	74	20	20	NUM
ejpam-3494	216	75	+	+	SYM
ejpam-3494	216	76	1	1	NUM
ejpam-3494	216	77			NOUN
ejpam-3494	216	78	=	=	NOUN
ejpam-3494	216	79			NOUN
ejpam-3494	216	80	1	1	NUM
ejpam-3494	216	81	3	3	NUM
ejpam-3494	216	82	10	10	NUM
ejpam-3494	216	83	37	37	NUM
ejpam-3494	216	84	151	151	NUM
ejpam-3494	216	85	674	674	NUM
ejpam-3494	216	86			NOUN
ejpam-3494	216	87	=	=	SYM
ejpam-3494	216	88			NOUN
ejpam-3494	216	89	g0,1,2	g0,1,2	NOUN
ejpam-3494	216	90	g1,1,2	g1,1,2	PROPN
ejpam-3494	216	91	g2,1,2	g2,1,2	PROPN
ejpam-3494	216	92	g3,1,2	g3,1,2	ADJ
ejpam-3494	216	93	g4,1,2	g4,1,2	PROPN
ejpam-3494	216	94	g5,1,2	g5,1,2	PROPN
ejpam-3494	216	95			NUM
ejpam-3494	216	96	.	.	PUNCT
ejpam-3494	217	1	clearly	clearly	ADV
ejpam-3494	217	2	,	,	PUNCT
ejpam-3494	217	3	the	the	DET
ejpam-3494	217	4	r	r	PROPN
ejpam-3494	217	5	-	-	PUNCT
ejpam-3494	217	6	whitney	whitney	NOUN
ejpam-3494	217	7	numbers	number	NOUN
ejpam-3494	217	8	of	of	ADP
ejpam-3494	217	9	the	the	DET
ejpam-3494	217	10	second	second	ADJ
ejpam-3494	217	11	kind	kind	NOUN
ejpam-3494	217	12	wβ	wβ	ADP
ejpam-3494	217	13	,	,	PUNCT
ejpam-3494	217	14	r(i	r(i	X
ejpam-3494	217	15	,	,	PUNCT
ejpam-3494	217	16	l	l	NOUN
ejpam-3494	217	17	)	)	PUNCT
ejpam-3494	217	18	can	can	AUX
ejpam-3494	217	19	be	be	AUX
ejpam-3494	217	20	expressed	express	VERB
ejpam-3494	217	21	as	as	ADP
ejpam-3494	217	22	wβ	wβ	ADP
ejpam-3494	217	23	,	,	PUNCT
ejpam-3494	217	24	r(i	r(i	X
ejpam-3494	217	25	,	,	PUNCT
ejpam-3494	217	26	l	l	NOUN
ejpam-3494	217	27	)	)	PUNCT
ejpam-3494	217	28	=	=	SYM
ejpam-3494	218	1	i∑	i∑	PROPN
ejpam-3494	218	2	j=0	j=0	PROPN
ejpam-3494	218	3	(	(	PUNCT
ejpam-3494	218	4	−1)i−jwβ,−r(i	−1)i−jwβ,−r(i	ADV
ejpam-3494	218	5	,	,	PUNCT
ejpam-3494	218	6	j)β	j)β	NOUN
ejpam-3494	218	7	j−ll(j	j−ll(j	PROPN
ejpam-3494	218	8	,	,	PUNCT
ejpam-3494	218	9	l	l	NOUN
ejpam-3494	218	10	)	)	PUNCT
ejpam-3494	218	11	.	.	PUNCT
ejpam-3494	219	1	that	that	PRON
ejpam-3494	219	2	is	be	AUX
ejpam-3494	219	3	,	,	PUNCT
ejpam-3494	219	4	[	[	X
ejpam-3494	219	5	wβ	wβ	ADP
ejpam-3494	219	6	,	,	PUNCT
ejpam-3494	219	7	r(i	r(i	X
ejpam-3494	219	8	,	,	PUNCT
ejpam-3494	219	9	j)]n+1×n+1	j)]n+1×n+1	PROPN
ejpam-3494	219	10	=	=	PRON
ejpam-3494	219	11	[	[	PUNCT
ejpam-3494	219	12	(	(	PUNCT
ejpam-3494	219	13	−1)i−jwβ,−r(i	−1)i−jwβ,−r(i	ADP
ejpam-3494	219	14	,	,	PUNCT
ejpam-3494	219	15	j	j	NOUN
ejpam-3494	219	16	)	)	PUNCT
ejpam-3494	219	17	]	]	PUNCT
ejpam-3494	220	1	n+1×n+1	n+1×n+1	NOUN
ejpam-3494	220	2	[	[	PUNCT
ejpam-3494	220	3	βi−jl(i	βi−jl(i	X
ejpam-3494	220	4	,	,	PUNCT
ejpam-3494	220	5	j	j	NOUN
ejpam-3494	220	6	)	)	PUNCT
ejpam-3494	220	7	]	]	PUNCT
ejpam-3494	220	8	n+1×n+1	n+1×n+1	NOUN
ejpam-3494	220	9	.	.	PUNCT
ejpam-3494	221	1	using	use	VERB
ejpam-3494	221	2	(	(	PUNCT
ejpam-3494	221	3	24	24	NUM
ejpam-3494	221	4	)	)	PUNCT
ejpam-3494	221	5	,	,	PUNCT
ejpam-3494	221	6	we	we	PRON
ejpam-3494	221	7	obtain	obtain	VERB
ejpam-3494	221	8	the	the	DET
ejpam-3494	221	9	following	follow	VERB
ejpam-3494	221	10	matrix	matrix	NOUN
ejpam-3494	221	11	identity	identity	NOUN
ejpam-3494	221	12	.	.	PUNCT
ejpam-3494	222	1	[	[	PUNCT
ejpam-3494	222	2	(	(	PUNCT
ejpam-3494	222	3	−1)i−jwβ	−1)i−jwβ	ADP
ejpam-3494	222	4	,	,	PUNCT
ejpam-3494	222	5	r(i	r(i	PROPN
ejpam-3494	222	6	,	,	PUNCT
ejpam-3494	222	7	j	j	NOUN
ejpam-3494	222	8	)	)	PUNCT
ejpam-3494	222	9	]	]	PUNCT
ejpam-3494	223	1	n+1×n+1	n+1×n+1	NOUN
ejpam-3494	223	2	[	[	PUNCT
ejpam-3494	223	3	(	(	PUNCT
ejpam-3494	223	4	−1)i−jwβ,−r(i	−1)i−jwβ,−r(i	ADP
ejpam-3494	223	5	,	,	PUNCT
ejpam-3494	223	6	j	j	NOUN
ejpam-3494	223	7	)	)	PUNCT
ejpam-3494	223	8	]	]	PUNCT
ejpam-3494	224	1	n+1×n+1	n+1×n+1	NOUN
ejpam-3494	224	2	[	[	PUNCT
ejpam-3494	224	3	βi−jl(i	βi−jl(i	X
ejpam-3494	224	4	,	,	PUNCT
ejpam-3494	224	5	j	j	NOUN
ejpam-3494	224	6	)	)	PUNCT
ejpam-3494	224	7	]	]	PUNCT
ejpam-3494	224	8	n+1×n+1	n+1×n+1	NOUN
ejpam-3494	224	9	=	=	SYM
ejpam-3494	224	10	in+1	in+1	PROPN
ejpam-3494	224	11	.	.	PUNCT
ejpam-3494	224	12	r.	r.	PROPN
ejpam-3494	224	13	b.	b.	PROPN
ejpam-3494	224	14	corcino	corcino	PROPN
ejpam-3494	224	15	et	et	PROPN
ejpam-3494	224	16	al	al	PROPN
ejpam-3494	224	17	.	.	PUNCT
ejpam-3494	224	18	/	/	SYM
ejpam-3494	224	19	eur	eur	PROPN
ejpam-3494	224	20	.	.	PUNCT
ejpam-3494	225	1	j.	j.	PROPN
ejpam-3494	225	2	pure	pure	PROPN
ejpam-3494	225	3	appl	appl	PROPN
ejpam-3494	225	4	.	.	PROPN
ejpam-3494	225	5	math	math	PROPN
ejpam-3494	225	6	,	,	PUNCT
ejpam-3494	225	7	12	12	NUM
ejpam-3494	225	8	(	(	PUNCT
ejpam-3494	225	9	3	3	NUM
ejpam-3494	225	10	)	)	PUNCT
ejpam-3494	225	11	(	(	PUNCT
ejpam-3494	225	12	2019	2019	NUM
ejpam-3494	225	13	)	)	PUNCT
ejpam-3494	225	14	,	,	PUNCT
ejpam-3494	225	15	1122	1122	NUM
ejpam-3494	225	16	-	-	SYM
ejpam-3494	225	17	1137	1137	NUM
ejpam-3494	225	18	1133	1133	NUM
ejpam-3494	225	19	5	5	NUM
ejpam-3494	225	20	.	.	PUNCT
ejpam-3494	226	1	a	a	DET
ejpam-3494	226	2	q	q	NOUN
ejpam-3494	226	3	-	-	PUNCT
ejpam-3494	226	4	analogue	analogue	NOUN
ejpam-3494	226	5	a	a	DET
ejpam-3494	226	6	q	q	NOUN
ejpam-3494	226	7	-	-	PUNCT
ejpam-3494	226	8	analogue	analogue	NOUN
ejpam-3494	226	9	is	be	AUX
ejpam-3494	226	10	a	a	DET
ejpam-3494	226	11	generalization	generalization	NOUN
ejpam-3494	226	12	of	of	ADP
ejpam-3494	226	13	a	a	DET
ejpam-3494	226	14	known	know	VERB
ejpam-3494	226	15	expression	expression	NOUN
ejpam-3494	226	16	parameterized	parameterize	VERB
ejpam-3494	226	17	by	by	ADP
ejpam-3494	226	18	a	a	DET
ejpam-3494	226	19	quantity	quantity	NOUN
ejpam-3494	226	20	q	q	NOUN
ejpam-3494	226	21	that	that	PRON
ejpam-3494	226	22	reduces	reduce	VERB
ejpam-3494	226	23	to	to	ADP
ejpam-3494	226	24	the	the	DET
ejpam-3494	226	25	known	know	VERB
ejpam-3494	226	26	expression	expression	NOUN
ejpam-3494	226	27	in	in	ADP
ejpam-3494	226	28	the	the	DET
ejpam-3494	226	29	limit	limit	NOUN
ejpam-3494	226	30	,	,	PUNCT
ejpam-3494	226	31	as	as	ADP
ejpam-3494	226	32	q	q	NOUN
ejpam-3494	226	33	→	→	SYM
ejpam-3494	226	34	1	1	NUM
ejpam-3494	226	35	.	.	X
ejpam-3494	227	1	for	for	ADP
ejpam-3494	227	2	example	example	NOUN
ejpam-3494	227	3	,	,	PUNCT
ejpam-3494	227	4	the	the	DET
ejpam-3494	227	5	q	q	NOUN
ejpam-3494	227	6	-	-	PUNCT
ejpam-3494	227	7	analogue	analogue	NOUN
ejpam-3494	227	8	of	of	ADP
ejpam-3494	227	9	n	n	CCONJ
ejpam-3494	227	10	,	,	PUNCT
ejpam-3494	227	11	n	n	CCONJ
ejpam-3494	227	12	!	!	PUNCT
ejpam-3494	227	13	,	,	PUNCT
ejpam-3494	227	14	(	(	PUNCT
ejpam-3494	227	15	n)k	n)k	ADV
ejpam-3494	227	16	and	and	CCONJ
ejpam-3494	227	17	(	(	PUNCT
ejpam-3494	227	18	n	n	X
ejpam-3494	227	19	k	k	NOUN
ejpam-3494	227	20	)	)	PUNCT
ejpam-3494	227	21	are	be	AUX
ejpam-3494	227	22	respectively	respectively	ADV
ejpam-3494	227	23	given	give	VERB
ejpam-3494	227	24	by	by	ADP
ejpam-3494	227	25	[	[	PUNCT
ejpam-3494	227	26	n]q	n]q	NOUN
ejpam-3494	227	27	=	=	SYM
ejpam-3494	227	28	1	1	NUM
ejpam-3494	227	29	+	+	CCONJ
ejpam-3494	227	30	q	q	NOUN
ejpam-3494	227	31	+	+	NUM
ejpam-3494	227	32	q2	q2	NOUN
ejpam-3494	227	33	+	+	X
ejpam-3494	227	34	·	·	PUNCT
ejpam-3494	227	35	·	·	PUNCT
ejpam-3494	227	36	·	·	PUNCT
ejpam-3494	227	37	+	+	NUM
ejpam-3494	227	38	qn−1	qn−1	PROPN
ejpam-3494	227	39	=	=	SYM
ejpam-3494	227	40	1−	1−	NUM
ejpam-3494	227	41	qn	qn	NOUN
ejpam-3494	227	42	1−	1−	NUM
ejpam-3494	227	43	q	q	NOUN
ejpam-3494	227	44	;	;	PUNCT
ejpam-3494	227	45	[	[	X
ejpam-3494	227	46	n]q	n]q	X
ejpam-3494	227	47	!	!	PUNCT
ejpam-3494	227	48	=	=	PUNCT
ejpam-3494	228	1	[	[	X
ejpam-3494	228	2	n]q[n−	n]q[n−	PRON
ejpam-3494	228	3	1]q	1]q	NUM
ejpam-3494	228	4	·	·	PUNCT
ejpam-3494	228	5	·	·	PUNCT
ejpam-3494	228	6	·	·	PUNCT
ejpam-3494	229	1	[	[	X
ejpam-3494	229	2	2]q[1]q	2]q[1]q	NUM
ejpam-3494	229	3	;	;	PUNCT
ejpam-3494	229	4	[	[	X
ejpam-3494	229	5	n]k	n]k	ADP
ejpam-3494	229	6	,	,	PUNCT
ejpam-3494	229	7	q	q	NOUN
ejpam-3494	229	8	=	=	PUNCT
ejpam-3494	230	1	[	[	X
ejpam-3494	230	2	n]q[n−	n]q[n−	PRON
ejpam-3494	230	3	1]q	1]q	NUM
ejpam-3494	230	4	·	·	PUNCT
ejpam-3494	230	5	·	·	PUNCT
ejpam-3494	230	6	·	·	PUNCT
ejpam-3494	231	1	[	[	X
ejpam-3494	231	2	n−	n−	NOUN
ejpam-3494	231	3	k	k	NOUN
ejpam-3494	232	1	+	+	PROPN
ejpam-3494	232	2	1]q	1]q	NUM
ejpam-3494	232	3	;	;	PUNCT
ejpam-3494	232	4	[	[	PUNCT
ejpam-3494	232	5	n	n	X
ejpam-3494	232	6	k	k	X
ejpam-3494	232	7	]	]	X
ejpam-3494	232	8	q	q	X
ejpam-3494	233	1	=	=	PUNCT
ejpam-3494	233	2	[	[	X
ejpam-3494	233	3	n]q	n]q	X
ejpam-3494	233	4	!	!	PUNCT
ejpam-3494	234	1	[	[	X
ejpam-3494	234	2	k]q![n−	k]q![n−	PRON
ejpam-3494	234	3	k]q	k]q	NOUN
ejpam-3494	234	4	!	!	PUNCT
ejpam-3494	234	5	=	=	PUNCT
ejpam-3494	235	1	[	[	X
ejpam-3494	235	2	n]k	n]k	ADP
ejpam-3494	235	3	,	,	PUNCT
ejpam-3494	235	4	q	q	PROPN
ejpam-3494	235	5	k	k	NOUN
ejpam-3494	235	6	!	!	PUNCT
ejpam-3494	235	7	.	.	PUNCT
ejpam-3494	236	1	recently	recently	ADV
ejpam-3494	236	2	,	,	PUNCT
ejpam-3494	236	3	r.	r.	PROPN
ejpam-3494	236	4	corcino	corcino	PROPN
ejpam-3494	236	5	et	et	PROPN
ejpam-3494	236	6	.	.	PUNCT
ejpam-3494	237	1	al	al	PROPN
ejpam-3494	238	1	[	[	X
ejpam-3494	238	2	9	9	NUM
ejpam-3494	238	3	]	]	PUNCT
ejpam-3494	238	4	defined	define	VERB
ejpam-3494	238	5	a	a	DET
ejpam-3494	238	6	q	q	NOUN
ejpam-3494	238	7	-	-	PUNCT
ejpam-3494	238	8	analogue	analogue	NOUN
ejpam-3494	238	9	of	of	ADP
ejpam-3494	238	10	r	r	NOUN
ejpam-3494	238	11	-	-	PUNCT
ejpam-3494	238	12	whitney	whitney	NOUN
ejpam-3494	238	13	numbers	number	NOUN
ejpam-3494	238	14	of	of	ADP
ejpam-3494	238	15	the	the	DET
ejpam-3494	238	16	second	second	ADJ
ejpam-3494	238	17	kind	kind	NOUN
ejpam-3494	238	18	by	by	ADP
ejpam-3494	238	19	means	mean	NOUN
ejpam-3494	238	20	of	of	ADP
ejpam-3494	238	21	the	the	DET
ejpam-3494	238	22	following	follow	VERB
ejpam-3494	238	23	recurrence	recurrence	NOUN
ejpam-3494	238	24	relation	relation	PROPN
ejpam-3494	238	25	:	:	PUNCT
ejpam-3494	238	26	wm	wm	PROPN
ejpam-3494	238	27	,	,	PUNCT
ejpam-3494	238	28	r[n	r[n	NOUN
ejpam-3494	238	29	,	,	PUNCT
ejpam-3494	238	30	k]q	k]q	NOUN
ejpam-3494	238	31	=	=	SYM
ejpam-3494	238	32	qm(k−1)+rwm	qm(k−1)+rwm	PROPN
ejpam-3494	238	33	,	,	PUNCT
ejpam-3494	238	34	r[n−	r[n−	PROPN
ejpam-3494	238	35	1	1	NUM
ejpam-3494	238	36	,	,	PUNCT
ejpam-3494	238	37	k	k	PROPN
ejpam-3494	239	1	−	−	PROPN
ejpam-3494	240	1	1]q	1]q	PROPN
ejpam-3494	241	1	+	+	NUM
ejpam-3494	241	2	[	[	X
ejpam-3494	241	3	mk	mk	X
ejpam-3494	241	4	+	+	CCONJ
ejpam-3494	241	5	r]qwm	r]qwm	NOUN
ejpam-3494	241	6	,	,	PUNCT
ejpam-3494	241	7	r[n−	r[n−	PROPN
ejpam-3494	241	8	1	1	NUM
ejpam-3494	241	9	,	,	PUNCT
ejpam-3494	241	10	k]q	k]q	PROPN
ejpam-3494	241	11	.	.	PUNCT
ejpam-3494	242	1	(	(	PUNCT
ejpam-3494	242	2	34	34	NUM
ejpam-3494	242	3	)	)	PUNCT
ejpam-3494	242	4	when	when	SCONJ
ejpam-3494	242	5	q	q	NOUN
ejpam-3494	242	6	→	→	SYM
ejpam-3494	242	7	1	1	NUM
ejpam-3494	242	8	,	,	PUNCT
ejpam-3494	242	9	this	this	PRON
ejpam-3494	242	10	will	will	AUX
ejpam-3494	242	11	reduce	reduce	VERB
ejpam-3494	242	12	to	to	ADP
ejpam-3494	242	13	wm	wm	PROPN
ejpam-3494	242	14	,	,	PUNCT
ejpam-3494	242	15	r(n	r(n	PROPN
ejpam-3494	242	16	,	,	PUNCT
ejpam-3494	242	17	k	k	NOUN
ejpam-3494	242	18	)	)	PUNCT
ejpam-3494	242	19	=	=	SYM
ejpam-3494	242	20	wm	wm	PROPN
ejpam-3494	242	21	,	,	PUNCT
ejpam-3494	242	22	r(n−	r(n−	NOUN
ejpam-3494	242	23	1	1	NUM
ejpam-3494	242	24	,	,	PUNCT
ejpam-3494	242	25	k	k	PROPN
ejpam-3494	242	26	−	−	PROPN
ejpam-3494	242	27	1	1	NUM
ejpam-3494	242	28	)	)	PUNCT
ejpam-3494	242	29	+	+	CCONJ
ejpam-3494	242	30	(	(	PUNCT
ejpam-3494	242	31	mk	mk	X
ejpam-3494	242	32	+	+	CCONJ
ejpam-3494	242	33	r)wm	r)wm	PROPN
ejpam-3494	242	34	,	,	PUNCT
ejpam-3494	242	35	r(n−	r(n−	NOUN
ejpam-3494	242	36	1	1	NUM
ejpam-3494	242	37	,	,	PUNCT
ejpam-3494	242	38	k	k	NOUN
ejpam-3494	242	39	)	)	PUNCT
ejpam-3494	242	40	.	.	PUNCT
ejpam-3494	243	1	one	one	PRON
ejpam-3494	243	2	can	can	AUX
ejpam-3494	243	3	easily	easily	ADV
ejpam-3494	243	4	verify	verify	VERB
ejpam-3494	243	5	that	that	SCONJ
ejpam-3494	243	6	wm	wm	PROPN
ejpam-3494	243	7	,	,	PUNCT
ejpam-3494	243	8	r[n	r[n	NOUN
ejpam-3494	243	9	,	,	PUNCT
ejpam-3494	243	10	0	0	NUM
ejpam-3494	243	11	]	]	PUNCT
ejpam-3494	243	12	=	=	PUNCT
ejpam-3494	244	1	[	[	X
ejpam-3494	244	2	r]nq	r]nq	X
ejpam-3494	244	3	.	.	PUNCT
ejpam-3494	245	1	the	the	DET
ejpam-3494	245	2	q	q	ADJ
ejpam-3494	245	3	-	-	PUNCT
ejpam-3494	245	4	analogue	analogue	NOUN
ejpam-3494	245	5	wm	wm	PROPN
ejpam-3494	245	6	,	,	PUNCT
ejpam-3494	245	7	r[n	r[n	PROPN
ejpam-3494	245	8	,	,	PUNCT
ejpam-3494	245	9	k]q	k]q	VERB
ejpam-3494	245	10	possessed	possess	VERB
ejpam-3494	245	11	several	several	ADJ
ejpam-3494	245	12	properties	property	NOUN
ejpam-3494	245	13	including	include	VERB
ejpam-3494	245	14	the	the	DET
ejpam-3494	245	15	following	follow	VERB
ejpam-3494	245	16	relation	relation	NOUN
ejpam-3494	245	17	n∑	n∑	PROPN
ejpam-3494	245	18	k=0	k=0	PROPN
ejpam-3494	245	19	wm	wm	PROPN
ejpam-3494	245	20	,	,	PUNCT
ejpam-3494	245	21	r[n	r[n	NOUN
ejpam-3494	245	22	,	,	PUNCT
ejpam-3494	245	23	k]q[t−	k]q[t−	NOUN
ejpam-3494	245	24	r|m]k	r|m]k	NUM
ejpam-3494	245	25	,	,	PUNCT
ejpam-3494	245	26	q	q	NOUN
ejpam-3494	246	1	=	=	PUNCT
ejpam-3494	247	1	[	[	X
ejpam-3494	247	2	t]nq	t]nq	NOUN
ejpam-3494	247	3	.	.	PUNCT
ejpam-3494	248	1	(	(	PUNCT
ejpam-3494	248	2	35	35	NUM
ejpam-3494	248	3	)	)	PUNCT
ejpam-3494	248	4	for	for	ADP
ejpam-3494	248	5	the	the	DET
ejpam-3494	248	6	r	r	PROPN
ejpam-3494	248	7	-	-	PUNCT
ejpam-3494	248	8	whitney	whitney	NOUN
ejpam-3494	248	9	numbers	number	NOUN
ejpam-3494	248	10	of	of	ADP
ejpam-3494	248	11	the	the	DET
ejpam-3494	248	12	first	first	ADJ
ejpam-3494	248	13	kind	kind	NOUN
ejpam-3494	248	14	,	,	PUNCT
ejpam-3494	248	15	their	their	PRON
ejpam-3494	248	16	q	q	NOUN
ejpam-3494	248	17	-	-	PUNCT
ejpam-3494	248	18	analogue	analogue	NOUN
ejpam-3494	248	19	may	may	AUX
ejpam-3494	248	20	be	be	AUX
ejpam-3494	248	21	defined	define	VERB
ejpam-3494	248	22	by	by	ADP
ejpam-3494	248	23	n∑	n∑	PROPN
ejpam-3494	248	24	k=0	k=0	PROPN
ejpam-3494	248	25	(	(	PUNCT
ejpam-3494	248	26	−1)n−kwm	−1)n−kwm	ADJ
ejpam-3494	248	27	,	,	PUNCT
ejpam-3494	248	28	r[n	r[n	NOUN
ejpam-3494	248	29	,	,	PUNCT
ejpam-3494	248	30	k]q[t	k]q[t	X
ejpam-3494	248	31	]	]	X
ejpam-3494	249	1	k	k	X
ejpam-3494	249	2	q	q	PUNCT
ejpam-3494	250	1	=	=	PUNCT
ejpam-3494	250	2	[	[	X
ejpam-3494	250	3	t−	t−	PROPN
ejpam-3494	250	4	r|m]n	r|m]n	PROPN
ejpam-3494	250	5	,	,	PUNCT
ejpam-3494	250	6	q.	q.	PROPN
ejpam-3494	250	7	(	(	PUNCT
ejpam-3494	250	8	36	36	NUM
ejpam-3494	250	9	)	)	PUNCT
ejpam-3494	250	10	to	to	PART
ejpam-3494	250	11	compute	compute	VERB
ejpam-3494	250	12	the	the	DET
ejpam-3494	250	13	first	first	ADJ
ejpam-3494	250	14	values	value	NOUN
ejpam-3494	250	15	of	of	ADP
ejpam-3494	250	16	wm	wm	PROPN
ejpam-3494	250	17	,	,	PUNCT
ejpam-3494	250	18	r[n	r[n	NOUN
ejpam-3494	250	19	,	,	PUNCT
ejpam-3494	250	20	k]q	k]q	PROPN
ejpam-3494	250	21	,	,	PUNCT
ejpam-3494	250	22	we	we	PRON
ejpam-3494	250	23	need	need	VERB
ejpam-3494	250	24	to	to	PART
ejpam-3494	250	25	derive	derive	VERB
ejpam-3494	250	26	the	the	DET
ejpam-3494	250	27	triangular	triangular	NOUN
ejpam-3494	250	28	recurrence	recurrence	NOUN
ejpam-3494	250	29	relation	relation	NOUN
ejpam-3494	250	30	for	for	ADP
ejpam-3494	250	31	wm	wm	PROPN
ejpam-3494	250	32	,	,	PUNCT
ejpam-3494	250	33	r[n	r[n	NOUN
ejpam-3494	250	34	,	,	PUNCT
ejpam-3494	250	35	k]q	k]q	PROPN
ejpam-3494	250	36	.	.	PUNCT
ejpam-3494	251	1	using	use	VERB
ejpam-3494	251	2	(	(	PUNCT
ejpam-3494	251	3	36	36	NUM
ejpam-3494	251	4	)	)	PUNCT
ejpam-3494	251	5	and	and	CCONJ
ejpam-3494	251	6	the	the	DET
ejpam-3494	251	7	identity	identity	NOUN
ejpam-3494	251	8	[	[	X
ejpam-3494	251	9	t−	t−	X
ejpam-3494	251	10	n]q	n]q	NOUN
ejpam-3494	251	11	=	=	SYM
ejpam-3494	251	12	1	1	NUM
ejpam-3494	251	13	qn	qn	NOUN
ejpam-3494	251	14	(	(	PUNCT
ejpam-3494	251	15	[	[	X
ejpam-3494	251	16	t]q	t]q	NOUN
ejpam-3494	251	17	−	−	VERB
ejpam-3494	252	1	[	[	X
ejpam-3494	252	2	n]q	n]q	NOUN
ejpam-3494	252	3	)	)	PUNCT
ejpam-3494	252	4	,	,	PUNCT
ejpam-3494	252	5	we	we	PRON
ejpam-3494	252	6	have	have	VERB
ejpam-3494	252	7	n+1∑	n+1∑	PROPN
ejpam-3494	252	8	k=0	k=0	PROPN
ejpam-3494	252	9	(	(	PUNCT
ejpam-3494	252	10	−1)n+1−kwm	−1)n+1−kwm	PROPN
ejpam-3494	252	11	,	,	PUNCT
ejpam-3494	252	12	r[n+	r[n+	NOUN
ejpam-3494	252	13	1	1	NUM
ejpam-3494	252	14	,	,	PUNCT
ejpam-3494	252	15	k]q[t	k]q[t	AUX
ejpam-3494	252	16	]	]	X
ejpam-3494	253	1	k	k	X
ejpam-3494	253	2	q	q	PUNCT
ejpam-3494	254	1	=	=	PUNCT
ejpam-3494	254	2	[	[	PUNCT
ejpam-3494	254	3	t−	t−	PROPN
ejpam-3494	254	4	r|m]n+1,q	r|m]n+1,q	NOUN
ejpam-3494	254	5	=	=	PUNCT
ejpam-3494	255	1	[	[	X
ejpam-3494	255	2	t−	t−	PROPN
ejpam-3494	255	3	(	(	PUNCT
ejpam-3494	255	4	r	r	NOUN
ejpam-3494	255	5	+	+	NUM
ejpam-3494	255	6	nm)]q[t−	nm)]q[t−	PROPN
ejpam-3494	255	7	r|m]n+1,q	r|m]n+1,q	NOUN
ejpam-3494	255	8	r.	r.	PROPN
ejpam-3494	255	9	b.	b.	PROPN
ejpam-3494	255	10	corcino	corcino	PROPN
ejpam-3494	255	11	et	et	PROPN
ejpam-3494	255	12	al	al	PROPN
ejpam-3494	255	13	.	.	PUNCT
ejpam-3494	255	14	/	/	SYM
ejpam-3494	255	15	eur	eur	PROPN
ejpam-3494	255	16	.	.	PUNCT
ejpam-3494	256	1	j.	j.	PROPN
ejpam-3494	256	2	pure	pure	PROPN
ejpam-3494	256	3	appl	appl	PROPN
ejpam-3494	256	4	.	.	PROPN
ejpam-3494	256	5	math	math	PROPN
ejpam-3494	256	6	,	,	PUNCT
ejpam-3494	256	7	12	12	NUM
ejpam-3494	256	8	(	(	PUNCT
ejpam-3494	256	9	3	3	NUM
ejpam-3494	256	10	)	)	PUNCT
ejpam-3494	256	11	(	(	PUNCT
ejpam-3494	256	12	2019	2019	NUM
ejpam-3494	256	13	)	)	PUNCT
ejpam-3494	256	14	,	,	PUNCT
ejpam-3494	256	15	1122	1122	NUM
ejpam-3494	256	16	-	-	SYM
ejpam-3494	256	17	1137	1137	NUM
ejpam-3494	256	18	1134	1134	NUM
ejpam-3494	256	19	=	=	SYM
ejpam-3494	256	20	(	(	PUNCT
ejpam-3494	256	21	1	1	NUM
ejpam-3494	256	22	qr+nm	qr+nm	NUM
ejpam-3494	256	23	(	(	PUNCT
ejpam-3494	256	24	[	[	X
ejpam-3494	256	25	t]q	t]q	NOUN
ejpam-3494	256	26	−	−	NOUN
ejpam-3494	257	1	[	[	X
ejpam-3494	257	2	r	r	X
ejpam-3494	257	3	+	+	NUM
ejpam-3494	257	4	nm]q	nm]q	PROPN
ejpam-3494	257	5	)	)	PUNCT
ejpam-3494	257	6	)	)	PUNCT
ejpam-3494	258	1	n∑	n∑	PROPN
ejpam-3494	258	2	k=0	k=0	PROPN
ejpam-3494	258	3	(	(	PUNCT
ejpam-3494	258	4	−1)n−kwm	−1)n−kwm	ADJ
ejpam-3494	258	5	,	,	PUNCT
ejpam-3494	258	6	r[n	r[n	NOUN
ejpam-3494	258	7	,	,	PUNCT
ejpam-3494	258	8	k]q[t	k]q[t	X
ejpam-3494	258	9	]	]	X
ejpam-3494	258	10	k	k	X
ejpam-3494	258	11	q	q	PUNCT
ejpam-3494	258	12	=	=	PUNCT
ejpam-3494	258	13	n+1∑	n+1∑	ADJ
ejpam-3494	258	14	k=0	k=0	PROPN
ejpam-3494	258	15	1	1	NUM
ejpam-3494	258	16	qr+nm	qr+nm	PROPN
ejpam-3494	258	17	(	(	PUNCT
ejpam-3494	258	18	−1)n−k+1wm	−1)n−k+1wm	NOUN
ejpam-3494	258	19	,	,	PUNCT
ejpam-3494	258	20	r[n	r[n	NOUN
ejpam-3494	258	21	,	,	PUNCT
ejpam-3494	258	22	k	k	PROPN
ejpam-3494	258	23	−	−	PROPN
ejpam-3494	258	24	1]q[t	1]q[t	NUM
ejpam-3494	258	25	]	]	X
ejpam-3494	259	1	k	k	X
ejpam-3494	259	2	q	q	PUNCT
ejpam-3494	260	1	+	+	CCONJ
ejpam-3494	260	2	n+1∑	n+1∑	PROPN
ejpam-3494	260	3	k=0	k=0	PROPN
ejpam-3494	260	4	−[r	−[r	PROPN
ejpam-3494	260	5	+	+	CCONJ
ejpam-3494	260	6	nm]q	nm]q	PROPN
ejpam-3494	260	7	qr+nm	qr+nm	PROPN
ejpam-3494	260	8	(	(	PUNCT
ejpam-3494	260	9	−1)n−kwm	−1)n−kwm	PROPN
ejpam-3494	260	10	,	,	PUNCT
ejpam-3494	260	11	r[n	r[n	NOUN
ejpam-3494	260	12	,	,	PUNCT
ejpam-3494	260	13	k]q[t	k]q[t	X
ejpam-3494	260	14	]	]	X
ejpam-3494	261	1	k	k	X
ejpam-3494	261	2	q	q	PUNCT
ejpam-3494	261	3	=	=	PUNCT
ejpam-3494	261	4	n+1∑	n+1∑	ADJ
ejpam-3494	261	5	k=0	k=0	PROPN
ejpam-3494	261	6	(	(	PUNCT
ejpam-3494	261	7	−1)n−k+1	−1)n−k+1	X
ejpam-3494	261	8	qr+nm	qr+nm	PROPN
ejpam-3494	261	9	{	{	PUNCT
ejpam-3494	261	10	wm	wm	PROPN
ejpam-3494	261	11	,	,	PUNCT
ejpam-3494	261	12	r[n	r[n	PROPN
ejpam-3494	261	13	,	,	PUNCT
ejpam-3494	261	14	k	k	PROPN
ejpam-3494	262	1	−	−	PROPN
ejpam-3494	262	2	1]q	1]q	PROPN
ejpam-3494	263	1	+	+	PUNCT
ejpam-3494	264	1	[	[	X
ejpam-3494	264	2	r	r	X
ejpam-3494	264	3	+	+	NUM
ejpam-3494	264	4	nm]qwm	nm]qwm	PRON
ejpam-3494	264	5	,	,	PUNCT
ejpam-3494	264	6	r[n	r[n	NOUN
ejpam-3494	264	7	,	,	PUNCT
ejpam-3494	264	8	k]q	k]q	NOUN
ejpam-3494	264	9	}	}	PUNCT
ejpam-3494	265	1	[	[	X
ejpam-3494	265	2	t]kq	t]kq	PROPN
ejpam-3494	265	3	.	.	PUNCT
ejpam-3494	266	1	thus	thus	ADV
ejpam-3494	266	2	,	,	PUNCT
ejpam-3494	266	3	comparing	compare	VERB
ejpam-3494	266	4	the	the	DET
ejpam-3494	266	5	coefficients	coefficient	NOUN
ejpam-3494	266	6	of	of	ADP
ejpam-3494	266	7	[	[	X
ejpam-3494	266	8	t]kq	t]kq	PROPN
ejpam-3494	266	9	,	,	PUNCT
ejpam-3494	266	10	we	we	PRON
ejpam-3494	266	11	easily	easily	ADV
ejpam-3494	266	12	obtain	obtain	VERB
ejpam-3494	266	13	the	the	DET
ejpam-3494	266	14	following	follow	VERB
ejpam-3494	266	15	triangular	triangular	NOUN
ejpam-3494	266	16	recurrence	recurrence	NOUN
ejpam-3494	266	17	relation	relation	PROPN
ejpam-3494	266	18	qr+nmwm	qr+nmwm	PROPN
ejpam-3494	266	19	,	,	PUNCT
ejpam-3494	266	20	r[n+	r[n+	NOUN
ejpam-3494	266	21	1	1	NUM
ejpam-3494	266	22	,	,	PUNCT
ejpam-3494	266	23	k]q	k]q	NOUN
ejpam-3494	266	24	=	=	SYM
ejpam-3494	266	25	wm	wm	PROPN
ejpam-3494	266	26	,	,	PUNCT
ejpam-3494	266	27	r[n	r[n	PROPN
ejpam-3494	266	28	,	,	PUNCT
ejpam-3494	266	29	k	k	PROPN
ejpam-3494	266	30	−	−	PROPN
ejpam-3494	267	1	1]q	1]q	PROPN
ejpam-3494	268	1	+	+	PUNCT
ejpam-3494	269	1	[	[	X
ejpam-3494	269	2	r	r	X
ejpam-3494	269	3	+	+	NUM
ejpam-3494	269	4	nm]qwm	nm]qwm	PRON
ejpam-3494	269	5	,	,	PUNCT
ejpam-3494	269	6	r[n	r[n	NOUN
ejpam-3494	269	7	,	,	PUNCT
ejpam-3494	269	8	k]q	k]q	PROPN
ejpam-3494	269	9	.	.	PUNCT
ejpam-3494	270	1	(	(	PUNCT
ejpam-3494	270	2	37	37	NUM
ejpam-3494	270	3	)	)	PUNCT
ejpam-3494	270	4	now	now	ADV
ejpam-3494	270	5	,	,	PUNCT
ejpam-3494	270	6	to	to	PART
ejpam-3494	270	7	derive	derive	VERB
ejpam-3494	270	8	the	the	DET
ejpam-3494	270	9	orthogonality	orthogonality	NOUN
ejpam-3494	270	10	relations	relation	NOUN
ejpam-3494	270	11	for	for	ADP
ejpam-3494	270	12	wm	wm	PROPN
ejpam-3494	270	13	,	,	PUNCT
ejpam-3494	270	14	r[n	r[n	NOUN
ejpam-3494	270	15	,	,	PUNCT
ejpam-3494	270	16	k]q	k]q	NOUN
ejpam-3494	270	17	and	and	CCONJ
ejpam-3494	270	18	wm	wm	PROPN
ejpam-3494	270	19	,	,	PUNCT
ejpam-3494	270	20	r[n	r[n	NOUN
ejpam-3494	270	21	,	,	PUNCT
ejpam-3494	270	22	k]q	k]q	PROPN
ejpam-3494	270	23	,	,	PUNCT
ejpam-3494	270	24	we	we	PRON
ejpam-3494	270	25	first	first	ADV
ejpam-3494	270	26	rewrite	rewrite	PROPN
ejpam-3494	270	27	(	(	PUNCT
ejpam-3494	270	28	36	36	NUM
ejpam-3494	270	29	)	)	PUNCT
ejpam-3494	270	30	as	as	ADP
ejpam-3494	270	31	k∑	k∑	PROPN
ejpam-3494	270	32	j=0	j=0	PROPN
ejpam-3494	270	33	wm	wm	PROPN
ejpam-3494	270	34	,	,	PUNCT
ejpam-3494	270	35	r[k	r[k	PROPN
ejpam-3494	270	36	,	,	PUNCT
ejpam-3494	270	37	j]q[t	j]q[t	ADV
ejpam-3494	270	38	]	]	X
ejpam-3494	270	39	j	j	PROPN
ejpam-3494	270	40	q	q	X
ejpam-3494	271	1	=	=	PUNCT
ejpam-3494	272	1	[	[	X
ejpam-3494	272	2	t−	t−	PROPN
ejpam-3494	272	3	r|m]k	r|m]k	PROPN
ejpam-3494	272	4	,	,	PUNCT
ejpam-3494	272	5	q	q	NOUN
ejpam-3494	272	6	and	and	CCONJ
ejpam-3494	272	7	substituting	substitute	VERB
ejpam-3494	272	8	to	to	ADP
ejpam-3494	272	9	(	(	PUNCT
ejpam-3494	272	10	35	35	NUM
ejpam-3494	272	11	)	)	PUNCT
ejpam-3494	272	12	yields	yield	NOUN
ejpam-3494	272	13	[	[	X
ejpam-3494	272	14	t]nq	t]nq	NOUN
ejpam-3494	272	15	=	=	SYM
ejpam-3494	272	16	n∑	n∑	PROPN
ejpam-3494	272	17	k=0	k=0	PROPN
ejpam-3494	272	18	wm	wm	PROPN
ejpam-3494	272	19	,	,	PUNCT
ejpam-3494	272	20	r[n	r[n	NOUN
ejpam-3494	272	21	,	,	PUNCT
ejpam-3494	272	22	k]q[t−	k]q[t−	NOUN
ejpam-3494	272	23	r|m]k	r|m]k	NUM
ejpam-3494	272	24	,	,	PUNCT
ejpam-3494	272	25	q	q	NOUN
ejpam-3494	272	26	=	=	SYM
ejpam-3494	272	27	n∑	n∑	PROPN
ejpam-3494	272	28	k=0	k=0	PROPN
ejpam-3494	272	29	wm	wm	PROPN
ejpam-3494	272	30	,	,	PUNCT
ejpam-3494	272	31	r[n	r[n	PROPN
ejpam-3494	272	32	,	,	PUNCT
ejpam-3494	272	33	k]q	k]q	PROPN
ejpam-3494	272	34	k∑	k∑	VERB
ejpam-3494	272	35	j=0	j=0	PROPN
ejpam-3494	272	36	(	(	PUNCT
ejpam-3494	272	37	−1)k−jwm	−1)k−jwm	NOUN
ejpam-3494	272	38	,	,	PUNCT
ejpam-3494	272	39	r[k	r[k	PROPN
ejpam-3494	272	40	,	,	PUNCT
ejpam-3494	272	41	j]q[t	j]q[t	ADV
ejpam-3494	272	42	]	]	X
ejpam-3494	272	43	j	j	PROPN
ejpam-3494	272	44	q	q	PROPN
ejpam-3494	273	1	=	=	SYM
ejpam-3494	273	2	n∑	n∑	PROPN
ejpam-3494	273	3	j=0	j=0	PROPN
ejpam-3494	273	4			PUNCT
ejpam-3494	273	5	n∑	n∑	NOUN
ejpam-3494	273	6	k	k	PROPN
ejpam-3494	273	7	=	=	PROPN
ejpam-3494	273	8	j	j	PROPN
ejpam-3494	273	9	(	(	PUNCT
ejpam-3494	273	10	−1)k−jwm	−1)k−jwm	NOUN
ejpam-3494	273	11	,	,	PUNCT
ejpam-3494	273	12	r[n	r[n	NOUN
ejpam-3494	273	13	,	,	PUNCT
ejpam-3494	273	14	k]qwm	k]qwm	PROPN
ejpam-3494	273	15	,	,	PUNCT
ejpam-3494	273	16	r[k	r[k	PROPN
ejpam-3494	273	17	,	,	PUNCT
ejpam-3494	273	18	j]q	j]q	ADJ
ejpam-3494	273	19			NOUN
ejpam-3494	273	20	[	[	X
ejpam-3494	273	21	t]jq	t]jq	NOUN
ejpam-3494	273	22	.	.	PUNCT
ejpam-3494	274	1	hence	hence	ADV
ejpam-3494	274	2	,	,	PUNCT
ejpam-3494	274	3	we	we	PRON
ejpam-3494	274	4	obtain	obtain	VERB
ejpam-3494	274	5	the	the	DET
ejpam-3494	274	6	first	first	ADJ
ejpam-3494	274	7	form	form	NOUN
ejpam-3494	274	8	of	of	ADP
ejpam-3494	274	9	the	the	DET
ejpam-3494	274	10	desired	desire	VERB
ejpam-3494	274	11	orthogonality	orthogonality	NOUN
ejpam-3494	274	12	relation	relation	NOUN
ejpam-3494	274	13	n∑	n∑	PROPN
ejpam-3494	275	1	k	k	PROPN
ejpam-3494	275	2	=	=	PROPN
ejpam-3494	275	3	j	j	PROPN
ejpam-3494	275	4	(	(	PUNCT
ejpam-3494	275	5	−1)k−jwm	−1)k−jwm	NOUN
ejpam-3494	275	6	,	,	PUNCT
ejpam-3494	275	7	r[n	r[n	NOUN
ejpam-3494	275	8	,	,	PUNCT
ejpam-3494	275	9	k]qwm	k]qwm	PROPN
ejpam-3494	275	10	,	,	PUNCT
ejpam-3494	275	11	r[k	r[k	PROPN
ejpam-3494	275	12	,	,	PUNCT
ejpam-3494	275	13	j]q	j]q	NOUN
ejpam-3494	275	14	=	=	SYM
ejpam-3494	275	15	δn	δn	PROPN
ejpam-3494	275	16	,	,	PUNCT
ejpam-3494	275	17	j	j	PROPN
ejpam-3494	275	18	,	,	PUNCT
ejpam-3494	275	19	(	(	PUNCT
ejpam-3494	275	20	38	38	NUM
ejpam-3494	275	21	)	)	PUNCT
ejpam-3494	275	22	where	where	SCONJ
ejpam-3494	275	23	δn	δn	NOUN
ejpam-3494	275	24	,	,	PUNCT
ejpam-3494	275	25	j	j	PROPN
ejpam-3494	275	26	is	be	AUX
ejpam-3494	275	27	the	the	DET
ejpam-3494	275	28	well	well	ADV
ejpam-3494	275	29	-	-	PUNCT
ejpam-3494	275	30	known	know	VERB
ejpam-3494	275	31	kronecker	kronecker	NOUN
ejpam-3494	275	32	delta	delta	NOUN
ejpam-3494	275	33	.	.	PUNCT
ejpam-3494	276	1	by	by	ADP
ejpam-3494	276	2	applying	apply	VERB
ejpam-3494	276	3	similar	similar	ADJ
ejpam-3494	276	4	argument	argument	NOUN
ejpam-3494	276	5	,	,	PUNCT
ejpam-3494	276	6	that	that	ADV
ejpam-3494	276	7	is	is	ADV
ejpam-3494	276	8	,	,	PUNCT
ejpam-3494	276	9	by	by	ADP
ejpam-3494	276	10	substituting	substitute	VERB
ejpam-3494	276	11	(	(	PUNCT
ejpam-3494	276	12	35	35	NUM
ejpam-3494	276	13	)	)	PUNCT
ejpam-3494	276	14	to	to	ADP
ejpam-3494	276	15	(	(	PUNCT
ejpam-3494	276	16	36	36	NUM
ejpam-3494	276	17	)	)	PUNCT
ejpam-3494	276	18	,	,	PUNCT
ejpam-3494	276	19	we	we	PRON
ejpam-3494	276	20	obtain	obtain	VERB
ejpam-3494	276	21	the	the	DET
ejpam-3494	276	22	second	second	ADJ
ejpam-3494	276	23	form	form	NOUN
ejpam-3494	276	24	of	of	ADP
ejpam-3494	276	25	the	the	DET
ejpam-3494	276	26	orthogonality	orthogonality	NOUN
ejpam-3494	276	27	relation	relation	NOUN
ejpam-3494	276	28	n∑	n∑	PROPN
ejpam-3494	277	1	k	k	PROPN
ejpam-3494	277	2	=	=	PROPN
ejpam-3494	277	3	j	j	X
ejpam-3494	277	4	(	(	PUNCT
ejpam-3494	277	5	−1)n−kwm	−1)n−kwm	ADJ
ejpam-3494	277	6	,	,	PUNCT
ejpam-3494	277	7	r[n	r[n	NOUN
ejpam-3494	277	8	,	,	PUNCT
ejpam-3494	277	9	k]qwm	k]qwm	PROPN
ejpam-3494	277	10	,	,	PUNCT
ejpam-3494	277	11	r[k	r[k	PROPN
ejpam-3494	277	12	,	,	PUNCT
ejpam-3494	277	13	j]q	j]q	NOUN
ejpam-3494	277	14	=	=	SYM
ejpam-3494	277	15	δn	δn	PROPN
ejpam-3494	277	16	,	,	PUNCT
ejpam-3494	277	17	j	j	PROPN
ejpam-3494	277	18	,	,	PUNCT
ejpam-3494	277	19	(	(	PUNCT
ejpam-3494	277	20	39	39	NUM
ejpam-3494	277	21	)	)	PUNCT
ejpam-3494	277	22	furthermore	furthermore	ADV
ejpam-3494	277	23	,	,	PUNCT
ejpam-3494	277	24	the	the	DET
ejpam-3494	277	25	orthogonality	orthogonality	NOUN
ejpam-3494	277	26	relations	relation	NOUN
ejpam-3494	277	27	in	in	ADP
ejpam-3494	277	28	(	(	PUNCT
ejpam-3494	277	29	38	38	NUM
ejpam-3494	277	30	)	)	PUNCT
ejpam-3494	277	31	and	and	CCONJ
ejpam-3494	277	32	(	(	PUNCT
ejpam-3494	277	33	39	39	NUM
ejpam-3494	277	34	)	)	PUNCT
ejpam-3494	277	35	immediately	immediately	ADV
ejpam-3494	277	36	imply	imply	VERB
ejpam-3494	277	37	the	the	DET
ejpam-3494	277	38	following	follow	VERB
ejpam-3494	277	39	inverse	inverse	NOUN
ejpam-3494	277	40	relations	relation	NOUN
ejpam-3494	277	41	:	:	PUNCT
ejpam-3494	277	42	fn	fn	PROPN
ejpam-3494	277	43	=	=	SYM
ejpam-3494	277	44	n∑	n∑	PROPN
ejpam-3494	277	45	k=0	k=0	PROPN
ejpam-3494	277	46	(	(	PUNCT
ejpam-3494	277	47	−1)n−kwm	−1)n−kwm	ADJ
ejpam-3494	277	48	,	,	PUNCT
ejpam-3494	277	49	r[n	r[n	NOUN
ejpam-3494	277	50	,	,	PUNCT
ejpam-3494	277	51	k]qgk	k]qgk	X
ejpam-3494	278	1	⇐	⇐	PROPN
ejpam-3494	278	2	⇒	⇒	PROPN
ejpam-3494	278	3	gn	gn	PROPN
ejpam-3494	279	1	=	=	PUNCT
ejpam-3494	279	2	n∑	n∑	PROPN
ejpam-3494	279	3	k=0	k=0	PROPN
ejpam-3494	279	4	wm	wm	PROPN
ejpam-3494	279	5	,	,	PUNCT
ejpam-3494	279	6	r[n	r[n	NOUN
ejpam-3494	279	7	,	,	PUNCT
ejpam-3494	279	8	k]qfk	k]qfk	NOUN
ejpam-3494	279	9	(	(	PUNCT
ejpam-3494	279	10	40	40	NUM
ejpam-3494	279	11	)	)	PUNCT
ejpam-3494	279	12	references	reference	NOUN
ejpam-3494	279	13	1135	1135	NUM
ejpam-3494	279	14	fk	fk	NOUN
ejpam-3494	279	15	=	=	PUNCT
ejpam-3494	280	1	∞∑	∞∑	NUM
ejpam-3494	280	2	n	n	CCONJ
ejpam-3494	280	3	=	=	SYM
ejpam-3494	280	4	k	k	X
ejpam-3494	280	5	(	(	PUNCT
ejpam-3494	280	6	−1)n−kwm	−1)n−kwm	ADJ
ejpam-3494	280	7	,	,	PUNCT
ejpam-3494	280	8	r[n	r[n	NOUN
ejpam-3494	280	9	,	,	PUNCT
ejpam-3494	280	10	k]qgn	k]qgn	VERB
ejpam-3494	280	11	⇐	⇐	ADJ
ejpam-3494	280	12	⇒	⇒	NOUN
ejpam-3494	280	13	gk	gk	PROPN
ejpam-3494	280	14	=	=	PUNCT
ejpam-3494	281	1	∞∑	∞∑	NUM
ejpam-3494	281	2	n	n	CCONJ
ejpam-3494	281	3	=	=	SYM
ejpam-3494	281	4	k	k	PROPN
ejpam-3494	281	5	wm	wm	PROPN
ejpam-3494	281	6	,	,	PUNCT
ejpam-3494	281	7	r[n	r[n	NOUN
ejpam-3494	281	8	,	,	PUNCT
ejpam-3494	281	9	k]qfn	k]qfn	NOUN
ejpam-3494	281	10	.	.	PUNCT
ejpam-3494	282	1	(	(	PUNCT
ejpam-3494	282	2	41	41	NUM
ejpam-3494	282	3	)	)	PUNCT
ejpam-3494	282	4	parallel	parallel	NOUN
ejpam-3494	282	5	to	to	ADP
ejpam-3494	282	6	cheon	cheon	NOUN
ejpam-3494	282	7	and	and	CCONJ
ejpam-3494	282	8	jung	jung	PROPN
ejpam-3494	283	1	[	[	X
ejpam-3494	283	2	4	4	NUM
ejpam-3494	283	3	]	]	PUNCT
ejpam-3494	283	4	,	,	PUNCT
ejpam-3494	283	5	a	a	DET
ejpam-3494	283	6	q	q	NOUN
ejpam-3494	283	7	-	-	PUNCT
ejpam-3494	283	8	analogue	analogue	NOUN
ejpam-3494	283	9	of	of	ADP
ejpam-3494	283	10	r	r	NOUN
ejpam-3494	283	11	-	-	PUNCT
ejpam-3494	283	12	whitney	whitney	NOUN
ejpam-3494	283	13	-	-	PUNCT
ejpam-3494	283	14	lah	lah	PROPN
ejpam-3494	283	15	numbers	number	NOUN
ejpam-3494	283	16	lβ	lβ	ADP
ejpam-3494	283	17	,	,	PUNCT
ejpam-3494	283	18	r[n	r[n	VERB
ejpam-3494	283	19	,	,	PUNCT
ejpam-3494	283	20	k]q	k]q	NOUN
ejpam-3494	283	21	may	may	AUX
ejpam-3494	283	22	be	be	AUX
ejpam-3494	283	23	defined	define	VERB
ejpam-3494	283	24	by	by	ADP
ejpam-3494	283	25	lβ	lβ	PROPN
ejpam-3494	283	26	,	,	PUNCT
ejpam-3494	283	27	r[n	r[n	NOUN
ejpam-3494	283	28	,	,	PUNCT
ejpam-3494	283	29	k]q	k]q	NOUN
ejpam-3494	283	30	=	=	SYM
ejpam-3494	283	31	n∑	n∑	NOUN
ejpam-3494	283	32	j=0	j=0	PROPN
ejpam-3494	283	33	wβ	wβ	ADP
ejpam-3494	283	34	,	,	PUNCT
ejpam-3494	283	35	r[n	r[n	NOUN
ejpam-3494	283	36	,	,	PUNCT
ejpam-3494	283	37	j]qwβ	j]qwβ	NUM
ejpam-3494	283	38	,	,	PUNCT
ejpam-3494	283	39	r[j	r[j	NOUN
ejpam-3494	283	40	,	,	PUNCT
ejpam-3494	283	41	k]q	k]q	PROPN
ejpam-3494	283	42	.	.	PUNCT
ejpam-3494	284	1	(	(	PUNCT
ejpam-3494	284	2	42	42	NUM
ejpam-3494	284	3	)	)	PUNCT
ejpam-3494	284	4	this	this	PRON
ejpam-3494	284	5	can	can	AUX
ejpam-3494	284	6	be	be	AUX
ejpam-3494	284	7	written	write	VERB
ejpam-3494	284	8	as	as	ADP
ejpam-3494	284	9	(	(	PUNCT
ejpam-3494	284	10	−1)nlβ	−1)nlβ	PROPN
ejpam-3494	284	11	,	,	PUNCT
ejpam-3494	284	12	r[n	r[n	NOUN
ejpam-3494	284	13	,	,	PUNCT
ejpam-3494	284	14	k]q	k]q	NOUN
ejpam-3494	284	15	=	=	SYM
ejpam-3494	284	16	n∑	n∑	X
ejpam-3494	284	17	j=0	j=0	PROPN
ejpam-3494	284	18	(	(	PUNCT
ejpam-3494	284	19	−1)n−jwβ	−1)n−jwβ	PROPN
ejpam-3494	284	20	,	,	PUNCT
ejpam-3494	284	21	r[n	r[n	NOUN
ejpam-3494	284	22	,	,	PUNCT
ejpam-3494	284	23	j]q(−1)jwβ	j]q(−1)jwβ	PROPN
ejpam-3494	284	24	,	,	PUNCT
ejpam-3494	284	25	r[j	r[j	NOUN
ejpam-3494	284	26	,	,	PUNCT
ejpam-3494	284	27	k]q	k]q	PROPN
ejpam-3494	284	28	.	.	PUNCT
ejpam-3494	285	1	(	(	PUNCT
ejpam-3494	285	2	43	43	NUM
ejpam-3494	285	3	)	)	PUNCT
ejpam-3494	285	4	using	use	VERB
ejpam-3494	285	5	the	the	DET
ejpam-3494	285	6	inverse	inverse	NOUN
ejpam-3494	285	7	relation	relation	NOUN
ejpam-3494	285	8	in	in	ADP
ejpam-3494	285	9	(	(	PUNCT
ejpam-3494	285	10	40	40	NUM
ejpam-3494	285	11	)	)	PUNCT
ejpam-3494	285	12	with	with	ADP
ejpam-3494	285	13	fn	fn	NOUN
ejpam-3494	285	14	=	=	SYM
ejpam-3494	285	15	(	(	PUNCT
ejpam-3494	285	16	−1)nlβ	−1)nlβ	PROPN
ejpam-3494	285	17	,	,	PUNCT
ejpam-3494	285	18	r[n	r[n	NOUN
ejpam-3494	285	19	,	,	PUNCT
ejpam-3494	285	20	k]q	k]q	NOUN
ejpam-3494	285	21	and	and	CCONJ
ejpam-3494	285	22	gj	gj	NOUN
ejpam-3494	285	23	=	=	SYM
ejpam-3494	285	24	(	(	PUNCT
ejpam-3494	285	25	−1)jwβ	−1)jwβ	PROPN
ejpam-3494	285	26	,	,	PUNCT
ejpam-3494	285	27	r[j	r[j	NOUN
ejpam-3494	285	28	,	,	PUNCT
ejpam-3494	285	29	k]q	k]q	PROPN
ejpam-3494	285	30	,	,	PUNCT
ejpam-3494	285	31	relation	relation	NOUN
ejpam-3494	285	32	(	(	PUNCT
ejpam-3494	285	33	43	43	NUM
ejpam-3494	285	34	)	)	PUNCT
ejpam-3494	285	35	implies	imply	VERB
ejpam-3494	285	36	the	the	DET
ejpam-3494	285	37	following	follow	VERB
ejpam-3494	285	38	relation	relation	NOUN
ejpam-3494	285	39	(	(	PUNCT
ejpam-3494	285	40	−1)nwβ	−1)nwβ	PROPN
ejpam-3494	285	41	,	,	PUNCT
ejpam-3494	285	42	r[n	r[n	NOUN
ejpam-3494	285	43	,	,	PUNCT
ejpam-3494	285	44	k]q	k]q	NOUN
ejpam-3494	285	45	=	=	SYM
ejpam-3494	285	46	n∑	n∑	NOUN
ejpam-3494	285	47	j=0	j=0	PROPN
ejpam-3494	285	48	wβ	wβ	ADP
ejpam-3494	285	49	,	,	PUNCT
ejpam-3494	285	50	r[n	r[n	NOUN
ejpam-3494	285	51	,	,	PUNCT
ejpam-3494	285	52	j]q(−1)jlβ	j]q(−1)jlβ	NOUN
ejpam-3494	285	53	,	,	PUNCT
ejpam-3494	285	54	r[j	r[j	NOUN
ejpam-3494	285	55	,	,	PUNCT
ejpam-3494	285	56	k]q	k]q	AUX
ejpam-3494	285	57	wβ	wβ	ADP
ejpam-3494	285	58	,	,	PUNCT
ejpam-3494	285	59	r[n	r[n	NOUN
ejpam-3494	285	60	,	,	PUNCT
ejpam-3494	285	61	k]q	k]q	NOUN
ejpam-3494	285	62	=	=	SYM
ejpam-3494	285	63	n∑	n∑	X
ejpam-3494	285	64	j=0	j=0	PROPN
ejpam-3494	285	65	(	(	PUNCT
ejpam-3494	285	66	−1)n−jwβ	−1)n−jwβ	PROPN
ejpam-3494	285	67	,	,	PUNCT
ejpam-3494	285	68	r[n	r[n	NOUN
ejpam-3494	285	69	,	,	PUNCT
ejpam-3494	285	70	j]qlβ	j]qlβ	NOUN
ejpam-3494	285	71	,	,	PUNCT
ejpam-3494	285	72	r[j	r[j	NOUN
ejpam-3494	285	73	,	,	PUNCT
ejpam-3494	285	74	k]q	k]q	X
ejpam-3494	285	75	(	(	PUNCT
ejpam-3494	285	76	44	44	NUM
ejpam-3494	285	77	)	)	PUNCT
ejpam-3494	285	78	summing	sum	VERB
ejpam-3494	285	79	up	up	ADP
ejpam-3494	285	80	both	both	DET
ejpam-3494	285	81	sides	side	NOUN
ejpam-3494	285	82	of	of	ADP
ejpam-3494	285	83	(	(	PUNCT
ejpam-3494	285	84	44	44	NUM
ejpam-3494	285	85	)	)	PUNCT
ejpam-3494	285	86	over	over	ADP
ejpam-3494	285	87	k	k	PROPN
ejpam-3494	285	88	yields	yield	NOUN
ejpam-3494	285	89	n∑	n∑	PROPN
ejpam-3494	285	90	k=0	k=0	PROPN
ejpam-3494	285	91	wβ	wβ	ADP
ejpam-3494	285	92	,	,	PUNCT
ejpam-3494	285	93	r[n	r[n	NOUN
ejpam-3494	285	94	,	,	PUNCT
ejpam-3494	285	95	k]q	k]q	NOUN
ejpam-3494	285	96	=	=	SYM
ejpam-3494	285	97	n∑	n∑	PROPN
ejpam-3494	285	98	k=0	k=0	PROPN
ejpam-3494	285	99	wβ	wβ	ADP
ejpam-3494	285	100	,	,	PUNCT
ejpam-3494	285	101	r[n	r[n	NOUN
ejpam-3494	285	102	,	,	PUNCT
ejpam-3494	285	103	k]q	k]q	PROPN
ejpam-3494	285	104	n∑	n∑	PROPN
ejpam-3494	285	105	j=0	j=0	PROPN
ejpam-3494	285	106	(	(	PUNCT
ejpam-3494	285	107	−1)n−jwβ	−1)n−jwβ	PROPN
ejpam-3494	285	108	,	,	PUNCT
ejpam-3494	285	109	r[n	r[n	NOUN
ejpam-3494	285	110	,	,	PUNCT
ejpam-3494	285	111	j]qlβ	j]qlβ	NOUN
ejpam-3494	285	112	,	,	PUNCT
ejpam-3494	285	113	r[j	r[j	NOUN
ejpam-3494	285	114	,	,	PUNCT
ejpam-3494	285	115	k]q	k]q	VERB
ejpam-3494	285	116	dβ	dβ	NOUN
ejpam-3494	285	117	,	,	PUNCT
ejpam-3494	285	118	r[n]q	r[n]q	NOUN
ejpam-3494	285	119	=	=	SYM
ejpam-3494	285	120	n∑	n∑	X
ejpam-3494	285	121	j=0	j=0	PROPN
ejpam-3494	285	122	(	(	PUNCT
ejpam-3494	285	123	−1)n−j	−1)n−j	X
ejpam-3494	285	124	{	{	PUNCT
ejpam-3494	285	125	j∑	j∑	PROPN
ejpam-3494	285	126	k=0	k=0	PROPN
ejpam-3494	285	127	lβ	lβ	PROPN
ejpam-3494	285	128	,	,	PUNCT
ejpam-3494	285	129	r[j	r[j	NOUN
ejpam-3494	285	130	,	,	PUNCT
ejpam-3494	285	131	k]q	k]q	NOUN
ejpam-3494	285	132	}	}	PUNCT
ejpam-3494	285	133	wβ	wβ	ADP
ejpam-3494	285	134	,	,	PUNCT
ejpam-3494	285	135	r[n	r[n	NOUN
ejpam-3494	285	136	,	,	PUNCT
ejpam-3494	285	137	j]q	j]q	ADJ
ejpam-3494	285	138	.	.	PUNCT
ejpam-3494	286	1	(	(	PUNCT
ejpam-3494	286	2	45	45	NUM
ejpam-3494	286	3	)	)	PUNCT
ejpam-3494	286	4	remark	remark	NOUN
ejpam-3494	286	5	5.1	5.1	NUM
ejpam-3494	286	6	.	.	PUNCT
ejpam-3494	287	1	the	the	DET
ejpam-3494	287	2	explicit	explicit	ADJ
ejpam-3494	287	3	formula	formula	NOUN
ejpam-3494	287	4	in	in	ADP
ejpam-3494	287	5	(	(	PUNCT
ejpam-3494	287	6	45	45	NUM
ejpam-3494	287	7	)	)	PUNCT
ejpam-3494	287	8	implies	imply	VERB
ejpam-3494	287	9	that	that	SCONJ
ejpam-3494	287	10	the	the	DET
ejpam-3494	287	11	(	(	PUNCT
ejpam-3494	287	12	q	q	ADJ
ejpam-3494	287	13	,	,	PUNCT
ejpam-3494	287	14	r)-dowling	r)-dowle	VERB
ejpam-3494	287	15	numbers	number	NOUN
ejpam-3494	287	16	dβ	dβ	ADJ
ejpam-3494	287	17	,	,	PUNCT
ejpam-3494	287	18	r[n]q	r[n]q	NOUN
ejpam-3494	287	19	are	be	AUX
ejpam-3494	287	20	equal	equal	ADJ
ejpam-3494	287	21	to	to	PART
ejpam-3494	287	22	eidle	eidle	VERB
ejpam-3494	287	23	,	,	PUNCT
ejpam-3494	287	24	where	where	SCONJ
ejpam-3494	287	25	d	d	NOUN
ejpam-3494	287	26	and	and	CCONJ
ejpam-3494	287	27	l	l	NOUN
ejpam-3494	287	28	are	be	AUX
ejpam-3494	287	29	matrices	matrix	NOUN
ejpam-3494	287	30	whose	whose	DET
ejpam-3494	287	31	entries	entry	NOUN
ejpam-3494	287	32	arewβ	arewβ	VERB
ejpam-3494	287	33	,	,	PUNCT
ejpam-3494	287	34	r[n	r[n	NOUN
ejpam-3494	287	35	,	,	PUNCT
ejpam-3494	287	36	j]q	j]q	NOUN
ejpam-3494	287	37	and	and	CCONJ
ejpam-3494	287	38	lβ	lβ	PROPN
ejpam-3494	287	39	,	,	PUNCT
ejpam-3494	287	40	r[n	r[n	NOUN
ejpam-3494	287	41	,	,	PUNCT
ejpam-3494	287	42	k]q	k]q	PROPN
ejpam-3494	287	43	,	,	PUNCT
ejpam-3494	287	44	respectively	respectively	ADV
ejpam-3494	287	45	,	,	PUNCT
ejpam-3494	287	46	ei	ei	X
ejpam-3494	287	47	is	be	AUX
ejpam-3494	287	48	the	the	DET
ejpam-3494	287	49	i−	i−	PROPN
ejpam-3494	287	50	th	th	PROPN
ejpam-3494	287	51	unit	unit	NOUN
ejpam-3494	287	52	vector	vector	NOUN
ejpam-3494	287	53	,	,	PUNCT
ejpam-3494	287	54	and	and	CCONJ
ejpam-3494	287	55	e	e	NOUN
ejpam-3494	287	56	is	be	AUX
ejpam-3494	287	57	the	the	DET
ejpam-3494	287	58	vector	vector	NOUN
ejpam-3494	287	59	with	with	ADP
ejpam-3494	287	60	all	all	DET
ejpam-3494	287	61	entries	entry	NOUN
ejpam-3494	287	62	equal	equal	ADJ
ejpam-3494	287	63	to	to	ADP
ejpam-3494	287	64	1	1	NUM
ejpam-3494	287	65	.	.	PUNCT
ejpam-3494	288	1	acknowledgements	acknowledgement	NOUN
ejpam-3494	288	2	this	this	DET
ejpam-3494	288	3	research	research	NOUN
ejpam-3494	288	4	has	have	AUX
ejpam-3494	288	5	been	be	AUX
ejpam-3494	288	6	funded	fund	VERB
ejpam-3494	288	7	by	by	ADP
ejpam-3494	288	8	cebu	cebu	PROPN
ejpam-3494	288	9	normal	normal	ADJ
ejpam-3494	288	10	university	university	PROPN
ejpam-3494	288	11	(	(	PUNCT
ejpam-3494	288	12	cnu	cnu	PROPN
ejpam-3494	288	13	)	)	PUNCT
ejpam-3494	288	14	and	and	CCONJ
ejpam-3494	288	15	the	the	DET
ejpam-3494	288	16	commission	commission	NOUN
ejpam-3494	288	17	on	on	ADP
ejpam-3494	288	18	higher	high	ADJ
ejpam-3494	288	19	education	education	NOUN
ejpam-3494	288	20	grants	grant	NOUN
ejpam-3494	288	21	-	-	PUNCT
ejpam-3494	288	22	in	in	ADP
ejpam-3494	288	23	-	-	PUNCT
ejpam-3494	288	24	aid	aid	NOUN
ejpam-3494	288	25	for	for	ADP
ejpam-3494	288	26	research	research	NOUN
ejpam-3494	288	27	(	(	PUNCT
ejpam-3494	288	28	ched	che	VERB
ejpam-3494	288	29	-	-	PUNCT
ejpam-3494	288	30	gia	gia	NOUN
ejpam-3494	288	31	)	)	PUNCT
ejpam-3494	288	32	.	.	PUNCT
ejpam-3494	289	1	references	reference	NOUN
ejpam-3494	289	2	[	[	X
ejpam-3494	289	3	1	1	NUM
ejpam-3494	289	4	]	]	PUNCT
ejpam-3494	289	5	k.	k.	PROPN
ejpam-3494	289	6	n.	n.	PROPN
ejpam-3494	289	7	boyadzhiev	boyadzhiev	PROPN
ejpam-3494	289	8	,	,	PUNCT
ejpam-3494	289	9	lah	lah	PROPN
ejpam-3494	289	10	numbers	number	NOUN
ejpam-3494	289	11	,	,	PUNCT
ejpam-3494	289	12	laguerre	laguerre	NOUN
ejpam-3494	289	13	polynomials	polynomial	NOUN
ejpam-3494	289	14	of	of	ADP
ejpam-3494	289	15	order	order	NOUN
ejpam-3494	289	16	negative	negative	ADJ
ejpam-3494	289	17	one	one	NUM
ejpam-3494	289	18	,	,	PUNCT
ejpam-3494	289	19	and	and	CCONJ
ejpam-3494	289	20	the	the	DET
ejpam-3494	289	21	nth	nth	NOUN
ejpam-3494	289	22	derivative	derivative	NOUN
ejpam-3494	289	23	of	of	ADP
ejpam-3494	289	24	exp(1	exp(1	NOUN
ejpam-3494	289	25	/	/	SYM
ejpam-3494	289	26	x	x	NOUN
ejpam-3494	289	27	)	)	PUNCT
ejpam-3494	289	28	,	,	PUNCT
ejpam-3494	289	29	acta	acta	PROPN
ejpam-3494	289	30	univ	univ	PROPN
ejpam-3494	289	31	.	.	PUNCT
ejpam-3494	290	1	sapientiae	sapientiae	PROPN
ejpam-3494	290	2	math	math	PROPN
ejpam-3494	290	3	.	.	PUNCT
ejpam-3494	291	1	8	8	NUM
ejpam-3494	291	2	(	(	PUNCT
ejpam-3494	291	3	2016)(1	2016)(1	NOUN
ejpam-3494	291	4	)	)	PUNCT
ejpam-3494	291	5	,	,	PUNCT
ejpam-3494	291	6	22–31	22–31	NUM
ejpam-3494	291	7	.	.	PUNCT
ejpam-3494	291	8	references	reference	NOUN
ejpam-3494	291	9	1136	1136	NUM
ejpam-3494	291	10	[	[	X
ejpam-3494	291	11	2	2	NUM
ejpam-3494	291	12	]	]	PUNCT
ejpam-3494	291	13	k.	k.	PROPN
ejpam-3494	291	14	n.	n.	PROPN
ejpam-3494	291	15	boyadzhiev	boyadzhiev	PROPN
ejpam-3494	291	16	,	,	PUNCT
ejpam-3494	291	17	exponential	exponential	ADJ
ejpam-3494	291	18	polynomials	polynomial	NOUN
ejpam-3494	291	19	,	,	PUNCT
ejpam-3494	291	20	stirling	stirling	NOUN
ejpam-3494	291	21	numbers	number	NOUN
ejpam-3494	291	22	,	,	PUNCT
ejpam-3494	291	23	and	and	CCONJ
ejpam-3494	291	24	evaluation	evaluation	NOUN
ejpam-3494	291	25	of	of	ADP
ejpam-3494	291	26	some	some	DET
ejpam-3494	291	27	gamma	gamma	NOUN
ejpam-3494	291	28	integrals	integral	NOUN
ejpam-3494	291	29	,	,	PUNCT
ejpam-3494	291	30	abstract	abstract	ADJ
ejpam-3494	291	31	and	and	CCONJ
ejpam-3494	291	32	applied	apply	VERB
ejpam-3494	291	33	analysis	analysis	NOUN
ejpam-3494	291	34	volume	volume	NOUN
ejpam-3494	291	35	2009	2009	NUM
ejpam-3494	291	36	,	,	PUNCT
ejpam-3494	291	37	article	article	NOUN
ejpam-3494	291	38	i	i	PROPN
ejpam-3494	291	39	d	d	PROPN
ejpam-3494	291	40	168672	168672	NUM
ejpam-3494	291	41	.	.	PUNCT
ejpam-3494	292	1	[	[	X
ejpam-3494	292	2	3	3	X
ejpam-3494	292	3	]	]	X
ejpam-3494	292	4	a.z	a.z	PROPN
ejpam-3494	292	5	.	.	PROPN
ejpam-3494	292	6	broder	broder	PROPN
ejpam-3494	292	7	,	,	PUNCT
ejpam-3494	292	8	the	the	DET
ejpam-3494	292	9	r	r	NOUN
ejpam-3494	292	10	-	-	PUNCT
ejpam-3494	292	11	stirling	stirling	NOUN
ejpam-3494	292	12	numbers	number	NOUN
ejpam-3494	292	13	,	,	PUNCT
ejpam-3494	292	14	discrete	discrete	ADJ
ejpam-3494	292	15	math	math	NOUN
ejpam-3494	292	16	.	.	PUNCT
ejpam-3494	293	1	49(1984	49(1984	X
ejpam-3494	293	2	)	)	PUNCT
ejpam-3494	293	3	,	,	PUNCT
ejpam-3494	294	1	241–259	241–259	NUM
ejpam-3494	294	2	.	.	PUNCT
ejpam-3494	295	1	[	[	X
ejpam-3494	295	2	4	4	NUM
ejpam-3494	295	3	]	]	X
ejpam-3494	295	4	g.s	g.s	PROPN
ejpam-3494	295	5	.	.	PROPN
ejpam-3494	295	6	cheon	cheon	PROPN
ejpam-3494	295	7	and	and	CCONJ
ejpam-3494	295	8	j.h	j.h	PROPN
ejpam-3494	295	9	jung	jung	PROPN
ejpam-3494	295	10	.	.	PUNCT
ejpam-3494	296	1	(	(	PUNCT
ejpam-3494	296	2	2012	2012	NUM
ejpam-3494	296	3	)	)	PUNCT
ejpam-3494	296	4	.	.	PUNCT
ejpam-3494	297	1	r	r	X
ejpam-3494	297	2	-	-	PUNCT
ejpam-3494	297	3	whitney	whitney	NOUN
ejpam-3494	297	4	numbers	number	NOUN
ejpam-3494	297	5	of	of	ADP
ejpam-3494	297	6	dowling	dowle	VERB
ejpam-3494	297	7	lattices	lattice	NOUN
ejpam-3494	297	8	.	.	PUNCT
ejpam-3494	298	1	discrete	discrete	ADJ
ejpam-3494	298	2	mathematics	mathematic	NOUN
ejpam-3494	298	3	,	,	PUNCT
ejpam-3494	298	4	15	15	NUM
ejpam-3494	298	5	,	,	PUNCT
ejpam-3494	298	6	2337	2337	NUM
ejpam-3494	298	7	-	-	SYM
ejpam-3494	298	8	2348	2348	NUM
ejpam-3494	298	9	.	.	PUNCT
ejpam-3494	299	1	[	[	X
ejpam-3494	299	2	5	5	X
ejpam-3494	299	3	]	]	PUNCT
ejpam-3494	299	4	l.	l.	PROPN
ejpam-3494	299	5	comtet	comtet	PROPN
ejpam-3494	299	6	,	,	PUNCT
ejpam-3494	299	7	advanced	advanced	ADJ
ejpam-3494	299	8	combinatorics	combinatoric	NOUN
ejpam-3494	299	9	.	.	PUNCT
ejpam-3494	300	1	d.	d.	PROPN
ejpam-3494	300	2	reidel	reidel	PROPN
ejpam-3494	300	3	publishing	publishing	PROPN
ejpam-3494	300	4	company	company	PROPN
ejpam-3494	300	5	inc	inc	PROPN
ejpam-3494	300	6	.	.	PROPN
ejpam-3494	300	7	,	,	PUNCT
ejpam-3494	300	8	1974	1974	NUM
ejpam-3494	300	9	.	.	PUNCT
ejpam-3494	301	1	[	[	X
ejpam-3494	301	2	6	6	NUM
ejpam-3494	301	3	]	]	PUNCT
ejpam-3494	301	4	c.	c.	PROPN
ejpam-3494	301	5	b.	b.	PROPN
ejpam-3494	301	6	corcino	corcino	PROPN
ejpam-3494	301	7	,	,	PUNCT
ejpam-3494	301	8	an	an	DET
ejpam-3494	301	9	asymptotic	asymptotic	ADJ
ejpam-3494	301	10	formula	formula	NOUN
ejpam-3494	301	11	for	for	ADP
ejpam-3494	301	12	the	the	DET
ejpam-3494	301	13	r	r	NOUN
ejpam-3494	301	14	-	-	PUNCT
ejpam-3494	301	15	bell	bell	NOUN
ejpam-3494	301	16	numbers	number	NOUN
ejpam-3494	301	17	,	,	PUNCT
ejpam-3494	301	18	matimyas	matimyas	PROPN
ejpam-3494	301	19	mat	mat	NOUN
ejpam-3494	301	20	.	.	PROPN
ejpam-3494	301	21	24	24	NUM
ejpam-3494	301	22	(	(	PUNCT
ejpam-3494	301	23	2001	2001	NUM
ejpam-3494	301	24	)	)	PUNCT
ejpam-3494	301	25	,	,	PUNCT
ejpam-3494	301	26	9–18	9–18	NOUN
ejpam-3494	301	27	.	.	PUNCT
ejpam-3494	302	1	[	[	X
ejpam-3494	302	2	7	7	X
ejpam-3494	302	3	]	]	X
ejpam-3494	302	4	r.b	r.b	PROPN
ejpam-3494	302	5	.	.	PROPN
ejpam-3494	302	6	corcino	corcino	PROPN
ejpam-3494	302	7	,	,	PUNCT
ejpam-3494	302	8	the	the	DET
ejpam-3494	302	9	(	(	PUNCT
ejpam-3494	302	10	r	r	NOUN
ejpam-3494	302	11	,	,	PUNCT
ejpam-3494	302	12	β)-stirling	β)-stirle	VERB
ejpam-3494	302	13	numbers	number	NOUN
ejpam-3494	302	14	,	,	PUNCT
ejpam-3494	302	15	mindanao	mindanao	PROPN
ejpam-3494	302	16	forum	forum	PROPN
ejpam-3494	302	17	,	,	PUNCT
ejpam-3494	302	18	14(2	14(2	NUM
ejpam-3494	302	19	)	)	PUNCT
ejpam-3494	302	20	(	(	PUNCT
ejpam-3494	302	21	1999	1999	NUM
ejpam-3494	302	22	)	)	PUNCT
ejpam-3494	302	23	,	,	PUNCT
ejpam-3494	302	24	91	91	NUM
ejpam-3494	302	25	-	-	SYM
ejpam-3494	302	26	99	99	NUM
ejpam-3494	302	27	.	.	PUNCT
ejpam-3494	303	1	[	[	X
ejpam-3494	303	2	8	8	NUM
ejpam-3494	303	3	]	]	SYM
ejpam-3494	303	4	asymptotic	asymptotic	ADJ
ejpam-3494	303	5	normality	normality	NOUN
ejpam-3494	303	6	of	of	ADP
ejpam-3494	303	7	the	the	DET
ejpam-3494	303	8	(	(	PUNCT
ejpam-3494	303	9	r	r	NOUN
ejpam-3494	303	10	,	,	PUNCT
ejpam-3494	303	11	β)-stirling	β)-stirling	NOUN
ejpam-3494	303	12	numbers	number	NOUN
ejpam-3494	303	13	,	,	PUNCT
ejpam-3494	303	14	ars	ar	VERB
ejpam-3494	303	15	combin	combin	NOUN
ejpam-3494	303	16	.	.	PUNCT
ejpam-3494	304	1	,	,	PUNCT
ejpam-3494	304	2	81	81	NUM
ejpam-3494	304	3	(	(	PUNCT
ejpam-3494	304	4	2006	2006	NUM
ejpam-3494	304	5	)	)	PUNCT
ejpam-3494	304	6	,	,	PUNCT
ejpam-3494	304	7	81–96	81–96	NUM
ejpam-3494	304	8	.	.	PUNCT
ejpam-3494	305	1	[	[	X
ejpam-3494	305	2	9	9	NUM
ejpam-3494	305	3	]	]	X
ejpam-3494	305	4	r.b	r.b	PROPN
ejpam-3494	305	5	.	.	PROPN
ejpam-3494	305	6	corcino	corcino	PROPN
ejpam-3494	305	7	,	,	PUNCT
ejpam-3494	305	8	m.j.r	m.j.r	PROPN
ejpam-3494	305	9	.	.	PUNCT
ejpam-3494	306	1	latayada	latayada	PROPN
ejpam-3494	306	2	,	,	PUNCT
ejpam-3494	306	3	and	and	CCONJ
ejpam-3494	306	4	m.a.p	m.a.p	ADJ
ejpam-3494	306	5	.	.	PUNCT
ejpam-3494	306	6	vega	vega	PROPN
ejpam-3494	306	7	,	,	PUNCT
ejpam-3494	306	8	hankel	hankel	NOUN
ejpam-3494	306	9	transform	transform	NOUN
ejpam-3494	306	10	of	of	ADP
ejpam-3494	306	11	(	(	PUNCT
ejpam-3494	306	12	q	q	ADJ
ejpam-3494	306	13	,	,	PUNCT
ejpam-3494	306	14	r)dowling	r)dowle	VERB
ejpam-3494	306	15	numbers	number	NOUN
ejpam-3494	306	16	,	,	PUNCT
ejpam-3494	306	17	eur	eur	PROPN
ejpam-3494	306	18	.	.	PUNCT
ejpam-3494	307	1	pure	pure	ADJ
ejpam-3494	307	2	appl	appl	PROPN
ejpam-3494	307	3	.	.	PUNCT
ejpam-3494	307	4	math	math	NOUN
ejpam-3494	307	5	.	.	PUNCT
ejpam-3494	308	1	,12(2)(2019	,12(2)(2019	PUNCT
ejpam-3494	308	2	)	)	PUNCT
ejpam-3494	308	3	,	,	PUNCT
ejpam-3494	309	1	279–293	279–293	NUM
ejpam-3494	309	2	.	.	PUNCT
ejpam-3494	310	1	[	[	X
ejpam-3494	310	2	10	10	NUM
ejpam-3494	310	3	]	]	X
ejpam-3494	310	4	r.b	r.b	PROPN
ejpam-3494	310	5	.	.	PROPN
ejpam-3494	310	6	corcino	corcino	PROPN
ejpam-3494	310	7	and	and	CCONJ
ejpam-3494	310	8	m.	m.	PROPN
ejpam-3494	310	9	herrera	herrera	PROPN
ejpam-3494	310	10	,	,	PUNCT
ejpam-3494	310	11	the	the	DET
ejpam-3494	310	12	limit	limit	NOUN
ejpam-3494	310	13	of	of	ADP
ejpam-3494	310	14	the	the	DET
ejpam-3494	310	15	differences	difference	NOUN
ejpam-3494	310	16	of	of	ADP
ejpam-3494	310	17	the	the	DET
ejpam-3494	310	18	generalized	generalized	ADJ
ejpam-3494	310	19	factorial	factorial	NOUN
ejpam-3494	310	20	,	,	PUNCT
ejpam-3494	310	21	its	its	PRON
ejpam-3494	310	22	qand	qand	NOUN
ejpam-3494	310	23	p	p	X
ejpam-3494	310	24	,	,	PUNCT
ejpam-3494	310	25	q	q	NOUN
ejpam-3494	310	26	-	-	PUNCT
ejpam-3494	310	27	analogue	analogue	NOUN
ejpam-3494	310	28	,	,	PUNCT
ejpam-3494	310	29	utilitas	utilitas	PROPN
ejpam-3494	310	30	mat	mat	NOUN
ejpam-3494	310	31	.	.	PROPN
ejpam-3494	310	32	,	,	PUNCT
ejpam-3494	310	33	vol	vol	NOUN
ejpam-3494	310	34	.	.	PROPN
ejpam-3494	310	35	72	72	NUM
ejpam-3494	310	36	(	(	PUNCT
ejpam-3494	310	37	2007	2007	NUM
ejpam-3494	310	38	)	)	PUNCT
ejpam-3494	311	1	pp	pp	ADP
ejpam-3494	311	2	.	.	PUNCT
ejpam-3494	312	1	33	33	NUM
ejpam-3494	312	2	-	-	SYM
ejpam-3494	312	3	49	49	NUM
ejpam-3494	312	4	.	.	PUNCT
ejpam-3494	313	1	[	[	X
ejpam-3494	313	2	11	11	NUM
ejpam-3494	313	3	]	]	X
ejpam-3494	313	4	r.b	r.b	PROPN
ejpam-3494	313	5	.	.	PROPN
ejpam-3494	313	6	corcino	corcino	PROPN
ejpam-3494	313	7	,	,	PUNCT
ejpam-3494	313	8	j.t	j.t	PROPN
ejpam-3494	313	9	.	.	PROPN
ejpam-3494	313	10	malusay	malusay	PROPN
ejpam-3494	313	11	,	,	PUNCT
ejpam-3494	313	12	j.	j.	PROPN
ejpam-3494	313	13	cillar	cillar	PROPN
ejpam-3494	313	14	,	,	PUNCT
ejpam-3494	313	15	g.	g.	PROPN
ejpam-3494	313	16	rama	rama	PROPN
ejpam-3494	313	17	,	,	PUNCT
ejpam-3494	313	18	o.	o.	PROPN
ejpam-3494	313	19	silang	silang	PROPN
ejpam-3494	313	20	,	,	PUNCT
ejpam-3494	313	21	i.	i.	PROPN
ejpam-3494	313	22	tacoloy	tacoloy	PROPN
ejpam-3494	313	23	,	,	PUNCT
ejpam-3494	313	24	analogies	analogy	NOUN
ejpam-3494	313	25	of	of	ADP
ejpam-3494	313	26	the	the	DET
ejpam-3494	313	27	qi	qi	NOUN
ejpam-3494	313	28	formula	formula	NOUN
ejpam-3494	313	29	for	for	ADP
ejpam-3494	313	30	some	some	DET
ejpam-3494	313	31	dowling	dowling	NOUN
ejpam-3494	313	32	type	type	NOUN
ejpam-3494	313	33	numbers	number	NOUN
ejpam-3494	313	34	,	,	PUNCT
ejpam-3494	313	35	accepted	accept	VERB
ejpam-3494	313	36	for	for	ADP
ejpam-3494	313	37	publication	publication	NOUN
ejpam-3494	313	38	in	in	ADP
ejpam-3494	313	39	utilitas	utilitas	PROPN
ejpam-3494	313	40	mathematica	mathematica	PROPN
ejpam-3494	313	41	(	(	PUNCT
ejpam-3494	313	42	2017	2017	NUM
ejpam-3494	313	43	)	)	PUNCT
ejpam-3494	313	44	.	.	PUNCT
ejpam-3494	314	1	[	[	X
ejpam-3494	314	2	12	12	NUM
ejpam-3494	314	3	]	]	X
ejpam-3494	314	4	r.b	r.b	PROPN
ejpam-3494	314	5	.	.	PROPN
ejpam-3494	314	6	corcino	corcino	PROPN
ejpam-3494	314	7	and	and	CCONJ
ejpam-3494	314	8	c.b	c.b	PROPN
ejpam-3494	314	9	.	.	PROPN
ejpam-3494	314	10	corcino	corcino	PROPN
ejpam-3494	314	11	,	,	PUNCT
ejpam-3494	314	12	on	on	ADP
ejpam-3494	314	13	generalized	generalized	ADJ
ejpam-3494	314	14	bell	bell	NOUN
ejpam-3494	314	15	polynomials	polynomial	NOUN
ejpam-3494	314	16	,	,	PUNCT
ejpam-3494	314	17	discrete	discrete	ADJ
ejpam-3494	314	18	dynamics	dynamic	NOUN
ejpam-3494	314	19	in	in	ADP
ejpam-3494	314	20	nature	nature	NOUN
ejpam-3494	314	21	and	and	CCONJ
ejpam-3494	314	22	society	society	NOUN
ejpam-3494	314	23	,	,	PUNCT
ejpam-3494	314	24	2011	2011	NUM
ejpam-3494	314	25	,	,	PUNCT
ejpam-3494	314	26	article	article	NOUN
ejpam-3494	314	27	i	i	PROPN
ejpam-3494	314	28	d	d	PROPN
ejpam-3494	314	29	623456	623456	NUM
ejpam-3494	314	30	,	,	PUNCT
ejpam-3494	314	31	doi	doi	NOUN
ejpam-3494	314	32	:	:	PUNCT
ejpam-3494	314	33	10.1155/2011/623456	10.1155/2011/623456	NUM
ejpam-3494	314	34	.	.	PUNCT
ejpam-3494	315	1	[	[	X
ejpam-3494	315	2	13	13	NUM
ejpam-3494	315	3	]	]	PUNCT
ejpam-3494	315	4	s.	s.	PROPN
ejpam-3494	315	5	daboul	daboul	PROPN
ejpam-3494	315	6	,	,	PUNCT
ejpam-3494	315	7	j.	j.	PROPN
ejpam-3494	315	8	mangaldan	mangaldan	PROPN
ejpam-3494	315	9	,	,	PUNCT
ejpam-3494	315	10	m.z	m.z	PROPN
ejpam-3494	315	11	.	.	PROPN
ejpam-3494	315	12	spivey	spivey	PROPN
ejpam-3494	315	13	,	,	PUNCT
ejpam-3494	315	14	and	and	CCONJ
ejpam-3494	315	15	p.j	p.j	PROPN
ejpam-3494	315	16	.	.	PROPN
ejpam-3494	315	17	taylor	taylor	PROPN
ejpam-3494	315	18	,	,	PUNCT
ejpam-3494	315	19	the	the	DET
ejpam-3494	315	20	lah	lah	NOUN
ejpam-3494	315	21	numbers	number	NOUN
ejpam-3494	315	22	and	and	CCONJ
ejpam-3494	315	23	the	the	DET
ejpam-3494	315	24	nth	nth	NOUN
ejpam-3494	315	25	derivative	derivative	NOUN
ejpam-3494	315	26	of	of	ADP
ejpam-3494	315	27	e1	e1	PROPN
ejpam-3494	315	28	/	/	SYM
ejpam-3494	315	29	x	x	PROPN
ejpam-3494	315	30	,	,	PUNCT
ejpam-3494	315	31	math	math	NOUN
ejpam-3494	315	32	.	.	PUNCT
ejpam-3494	316	1	mag	mag	PROPN
ejpam-3494	316	2	.	.	PUNCT
ejpam-3494	317	1	86(2013	86(2013	NUM
ejpam-3494	317	2	)	)	PUNCT
ejpam-3494	317	3	,	,	PUNCT
ejpam-3494	318	1	39–47	39–47	NUM
ejpam-3494	318	2	.	.	PUNCT
ejpam-3494	319	1	[	[	X
ejpam-3494	319	2	14	14	NUM
ejpam-3494	319	3	]	]	X
ejpam-3494	319	4	l.c	l.c	PROPN
ejpam-3494	319	5	.	.	PROPN
ejpam-3494	319	6	hsu	hsu	PROPN
ejpam-3494	319	7	and	and	CCONJ
ejpam-3494	319	8	p.j	p.j	PROPN
ejpam-3494	319	9	-	-	PUNCT
ejpam-3494	319	10	s.	s.	PROPN
ejpam-3494	319	11	shiue	shiue	PROPN
ejpam-3494	319	12	.	.	PUNCT
ejpam-3494	320	1	“	"	PUNCT
ejpam-3494	320	2	a	a	DET
ejpam-3494	320	3	unified	unified	ADJ
ejpam-3494	320	4	approach	approach	NOUN
ejpam-3494	320	5	to	to	ADP
ejpam-3494	320	6	generalized	generalize	VERB
ejpam-3494	320	7	stirling	stirling	NOUN
ejpam-3494	320	8	numbers	number	NOUN
ejpam-3494	320	9	.	.	PUNCT
ejpam-3494	320	10	”	"	PUNCT
ejpam-3494	320	11	advances	advance	NOUN
ejpam-3494	320	12	in	in	ADP
ejpam-3494	320	13	applied	applied	ADJ
ejpam-3494	320	14	math	math	NOUN
ejpam-3494	320	15	.	.	PUNCT
ejpam-3494	321	1	20	20	NUM
ejpam-3494	321	2	(	(	PUNCT
ejpam-3494	321	3	1998	1998	NUM
ejpam-3494	321	4	):	):	PUNCT
ejpam-3494	321	5	366	366	NUM
ejpam-3494	321	6	-	-	SYM
ejpam-3494	321	7	384	384	NUM
ejpam-3494	321	8	.	.	PUNCT
ejpam-3494	322	1	[	[	X
ejpam-3494	322	2	15	15	NUM
ejpam-3494	322	3	]	]	X
ejpam-3494	322	4	m.	m.	NOUN
ejpam-3494	322	5	koutras	koutra	NOUN
ejpam-3494	322	6	,	,	PUNCT
ejpam-3494	322	7	non	non	ADJ
ejpam-3494	322	8	-	-	ADJ
ejpam-3494	322	9	central	central	ADJ
ejpam-3494	322	10	stirling	stirling	NOUN
ejpam-3494	322	11	numbers	number	NOUN
ejpam-3494	322	12	and	and	CCONJ
ejpam-3494	322	13	applications	application	NOUN
ejpam-3494	322	14	,	,	PUNCT
ejpam-3494	322	15	discrete	discrete	ADJ
ejpam-3494	322	16	math	math	NOUN
ejpam-3494	322	17	.	.	PUNCT
ejpam-3494	323	1	42	42	NUM
ejpam-3494	323	2	(	(	PUNCT
ejpam-3494	323	3	1982	1982	NUM
ejpam-3494	323	4	)	)	PUNCT
ejpam-3494	323	5	,	,	PUNCT
ejpam-3494	323	6	73–89	73–89	NUM
ejpam-3494	323	7	.	.	PUNCT
ejpam-3494	324	1	[	[	X
ejpam-3494	324	2	16	16	NUM
ejpam-3494	324	3	]	]	PUNCT
ejpam-3494	324	4	i.	i.	PROPN
ejpam-3494	324	5	mező	mező	PROPN
ejpam-3494	324	6	,	,	PUNCT
ejpam-3494	324	7	a	a	DET
ejpam-3494	324	8	new	new	ADJ
ejpam-3494	324	9	formula	formula	NOUN
ejpam-3494	324	10	for	for	ADP
ejpam-3494	324	11	the	the	DET
ejpam-3494	324	12	bernoulli	bernoulli	NOUN
ejpam-3494	324	13	polynomials	polynomial	NOUN
ejpam-3494	324	14	,	,	PUNCT
ejpam-3494	324	15	results	result	VERB
ejpam-3494	324	16	math	math	NOUN
ejpam-3494	324	17	.	.	PUNCT
ejpam-3494	325	1	58(2010	58(2010	NUM
ejpam-3494	325	2	)	)	PUNCT
ejpam-3494	325	3	,	,	PUNCT
ejpam-3494	325	4	329	329	NUM
ejpam-3494	325	5	–	–	PUNCT
ejpam-3494	325	6	335	335	NUM
ejpam-3494	325	7	.	.	PUNCT
ejpam-3494	326	1	[	[	X
ejpam-3494	326	2	17	17	NUM
ejpam-3494	326	3	]	]	PUNCT
ejpam-3494	326	4	i.	i.	PROPN
ejpam-3494	326	5	mező	mező	PROPN
ejpam-3494	326	6	,	,	PUNCT
ejpam-3494	326	7	the	the	DET
ejpam-3494	326	8	r	r	NOUN
ejpam-3494	326	9	-	-	PUNCT
ejpam-3494	326	10	bell	bell	NOUN
ejpam-3494	326	11	numbers	number	NOUN
ejpam-3494	326	12	,	,	PUNCT
ejpam-3494	326	13	j.	j.	PROPN
ejpam-3494	326	14	integer	integer	PROPN
ejpam-3494	326	15	seq	seq	PROPN
ejpam-3494	326	16	.	.	PUNCT
ejpam-3494	327	1	14(2011	14(2011	NUM
ejpam-3494	327	2	)	)	PUNCT
ejpam-3494	327	3	,	,	PUNCT
ejpam-3494	327	4	article	article	NOUN
ejpam-3494	327	5	11.1.1	11.1.1	NUM
ejpam-3494	327	6	.	.	PUNCT
ejpam-3494	328	1	[	[	X
ejpam-3494	328	2	18	18	NUM
ejpam-3494	328	3	]	]	X
ejpam-3494	328	4	gábor	gábor	NOUN
ejpam-3494	328	5	nyul	nyul	PROPN
ejpam-3494	328	6	and	and	CCONJ
ejpam-3494	328	7	gabriella	gabriella	PROPN
ejpam-3494	328	8	rácz	rácz	PROPN
ejpam-3494	328	9	,	,	PUNCT
ejpam-3494	328	10	the	the	DET
ejpam-3494	328	11	r	r	PROPN
ejpam-3494	328	12	-	-	PUNCT
ejpam-3494	328	13	lah	lah	NOUN
ejpam-3494	328	14	numbers	number	NOUN
ejpam-3494	328	15	,	,	PUNCT
ejpam-3494	328	16	discrete	discrete	ADJ
ejpam-3494	328	17	math	math	NOUN
ejpam-3494	328	18	.	.	PUNCT
ejpam-3494	329	1	338(2015	338(2015	NUM
ejpam-3494	329	2	)	)	PUNCT
ejpam-3494	329	3	1660	1660	NUM
ejpam-3494	329	4	–	–	PUNCT
ejpam-3494	329	5	1666	1666	NUM
ejpam-3494	329	6	.	.	PUNCT
ejpam-3494	330	1	[	[	X
ejpam-3494	330	2	19	19	NUM
ejpam-3494	330	3	]	]	X
ejpam-3494	330	4	n.	n.	NOUN
ejpam-3494	330	5	privault	privault	NOUN
ejpam-3494	330	6	,	,	PUNCT
ejpam-3494	330	7	generalized	generalized	ADJ
ejpam-3494	330	8	bell	bell	NOUN
ejpam-3494	330	9	polynomials	polynomial	NOUN
ejpam-3494	330	10	and	and	CCONJ
ejpam-3494	330	11	the	the	DET
ejpam-3494	330	12	combinatorics	combinatoric	NOUN
ejpam-3494	330	13	of	of	ADP
ejpam-3494	330	14	poisson	poisson	PROPN
ejpam-3494	330	15	central	central	ADJ
ejpam-3494	330	16	moments	moment	NOUN
ejpam-3494	330	17	,	,	PUNCT
ejpam-3494	330	18	the	the	DET
ejpam-3494	330	19	electronic	electronic	ADJ
ejpam-3494	330	20	journal	journal	NOUN
ejpam-3494	330	21	of	of	ADP
ejpam-3494	330	22	combinatorics	combinatoric	NOUN
ejpam-3494	330	23	,	,	PUNCT
ejpam-3494	330	24	18	18	NUM
ejpam-3494	330	25	(	(	PUNCT
ejpam-3494	330	26	2011	2011	NUM
ejpam-3494	330	27	)	)	PUNCT
ejpam-3494	330	28	#	#	SYM
ejpam-3494	330	29	p54	p54	NOUN
ejpam-3494	330	30	.	.	PUNCT
ejpam-3494	331	1	references	reference	NOUN
ejpam-3494	331	2	1137	1137	NUM
ejpam-3494	331	3	[	[	X
ejpam-3494	331	4	20	20	NUM
ejpam-3494	331	5	]	]	SYM
ejpam-3494	331	6	s.m	s.m	PROPN
ejpam-3494	331	7	.	.	PROPN
ejpam-3494	331	8	tanny	tanny	PROPN
ejpam-3494	331	9	,	,	PUNCT
ejpam-3494	331	10	on	on	ADP
ejpam-3494	331	11	some	some	DET
ejpam-3494	331	12	numbers	number	NOUN
ejpam-3494	331	13	related	relate	VERB
ejpam-3494	331	14	to	to	ADP
ejpam-3494	331	15	bell	bell	NOUN
ejpam-3494	331	16	numbers	number	NOUN
ejpam-3494	331	17	,	,	PUNCT
ejpam-3494	331	18	canad	canad	PROPN
ejpam-3494	331	19	.	.	PUNCT
ejpam-3494	332	1	math	math	NOUN
ejpam-3494	332	2	.	.	PUNCT
ejpam-3494	333	1	bull	bull	NOUN
ejpam-3494	333	2	.	.	PUNCT
ejpam-3494	334	1	17(15	17(15	NUM
ejpam-3494	334	2	)	)	PUNCT
ejpam-3494	334	3	,	,	PUNCT
ejpam-3494	334	4	1975	1975	NUM
ejpam-3494	334	5	,	,	PUNCT
ejpam-3494	334	6	733	733	NUM
ejpam-3494	334	7	-	-	SYM
ejpam-3494	334	8	738	738	NUM
ejpam-3494	334	9	.	.	PUNCT
ejpam-3494	335	1	[	[	X
ejpam-3494	335	2	21	21	NUM
ejpam-3494	335	3	]	]	X
ejpam-3494	335	4	f.	f.	PROPN
ejpam-3494	335	5	qi	qi	PROPN
ejpam-3494	335	6	,	,	PUNCT
ejpam-3494	335	7	an	an	DET
ejpam-3494	335	8	explicit	explicit	ADJ
ejpam-3494	335	9	formula	formula	NOUN
ejpam-3494	335	10	for	for	ADP
ejpam-3494	335	11	the	the	DET
ejpam-3494	335	12	bell	bell	NOUN
ejpam-3494	335	13	numbers	number	NOUN
ejpam-3494	335	14	in	in	ADP
ejpam-3494	335	15	terms	term	NOUN
ejpam-3494	335	16	of	of	ADP
ejpam-3494	335	17	lah	lah	NOUN
ejpam-3494	335	18	and	and	CCONJ
ejpam-3494	335	19	stirling	stirling	NOUN
ejpam-3494	335	20	numbers	number	NOUN
ejpam-3494	335	21	,	,	PUNCT
ejpam-3494	335	22	mediterr	mediterr	PROPN
ejpam-3494	335	23	.	.	PUNCT
ejpam-3494	336	1	j.	j.	PROPN
ejpam-3494	336	2	math	math	PROPN
ejpam-3494	336	3	.	.	PUNCT
ejpam-3494	337	1	13	13	NUM
ejpam-3494	337	2	(	(	PUNCT
ejpam-3494	337	3	2016)(5	2016)(5	PROPN
ejpam-3494	337	4	)	)	PUNCT
ejpam-3494	337	5	,	,	PUNCT
ejpam-3494	337	6	2795–2800	2795–2800	NUM
ejpam-3494	337	7	.	.	PUNCT
ejpam-3494	338	1	[	[	X
ejpam-3494	338	2	22	22	NUM
ejpam-3494	338	3	]	]	PUNCT
ejpam-3494	338	4	j.	j.	PROPN
ejpam-3494	338	5	riordan	riordan	PROPN
ejpam-3494	338	6	,	,	PUNCT
ejpam-3494	338	7	introduction	introduction	NOUN
ejpam-3494	338	8	to	to	ADP
ejpam-3494	338	9	combinatorial	combinatorial	ADJ
ejpam-3494	338	10	analysis	analysis	NOUN
ejpam-3494	338	11	,	,	PUNCT
ejpam-3494	338	12	john	john	PROPN
ejpam-3494	338	13	wiley	wiley	PROPN
ejpam-3494	338	14	and	and	CCONJ
ejpam-3494	338	15	sons	sons	PROPN
ejpam-3494	338	16	inc	inc	PROPN
ejpam-3494	338	17	.	.	PROPN
ejpam-3494	338	18	,	,	PUNCT
ejpam-3494	338	19	1958	1958	NUM
ejpam-3494	338	20	.	.	PUNCT
ejpam-3494	339	1	[	[	X
ejpam-3494	339	2	23	23	NUM
ejpam-3494	339	3	]	]	PUNCT
ejpam-3494	339	4	x.-j	x.-j	PROPN
ejpam-3494	339	5	.	.	PUNCT
ejpam-3494	340	1	zhang	zhang	PROPN
ejpam-3494	340	2	,	,	PUNCT
ejpam-3494	340	3	f.	f.	PROPN
ejpam-3494	340	4	qi	qi	PROPN
ejpam-3494	340	5	,	,	PUNCT
ejpam-3494	340	6	and	and	CCONJ
ejpam-3494	340	7	w.-h	w.-h	NOUN
ejpam-3494	340	8	.	.	PUNCT
ejpam-3494	341	1	li	li	PROPN
ejpam-3494	341	2	,	,	PUNCT
ejpam-3494	341	3	properties	property	NOUN
ejpam-3494	341	4	of	of	ADP
ejpam-3494	341	5	three	three	NUM
ejpam-3494	341	6	functions	function	NOUN
ejpam-3494	341	7	relating	relate	VERB
ejpam-3494	341	8	to	to	ADP
ejpam-3494	341	9	the	the	DET
ejpam-3494	341	10	exponential	exponential	ADJ
ejpam-3494	341	11	function	function	NOUN
ejpam-3494	341	12	and	and	CCONJ
ejpam-3494	341	13	the	the	DET
ejpam-3494	341	14	existence	existence	NOUN
ejpam-3494	341	15	of	of	ADP
ejpam-3494	341	16	partitions	partition	NOUN
ejpam-3494	341	17	of	of	ADP
ejpam-3494	341	18	unity	unity	NOUN
ejpam-3494	341	19	,	,	PUNCT
ejpam-3494	341	20	int	int	NOUN
ejpam-3494	341	21	.	.	PUNCT
ejpam-3494	342	1	j.	j.	PROPN
ejpam-3494	342	2	open	open	PROPN
ejpam-3494	342	3	probl	probl	PROPN
ejpam-3494	342	4	.	.	PUNCT
ejpam-3494	343	1	comput	comput	NOUN
ejpam-3494	343	2	.	.	PUNCT
ejpam-3494	344	1	sci	sci	PROPN
ejpam-3494	344	2	.	.	PUNCT
ejpam-3494	344	3	math	math	PROPN
ejpam-3494	344	4	.	.	PUNCT
ejpam-3494	345	1	5	5	NUM
ejpam-3494	345	2	(	(	PUNCT
ejpam-3494	345	3	2012	2012	NUM
ejpam-3494	345	4	)	)	PUNCT
ejpam-3494	345	5	,	,	PUNCT
ejpam-3494	345	6	no	no	INTJ
ejpam-3494	345	7	.	.	NOUN
ejpam-3494	345	8	3	3	NUM
ejpam-3494	345	9	,	,	PUNCT
ejpam-3494	345	10	122–127	122–127	NUM
ejpam-3494	345	11	;	;	PUNCT
ejpam-3494	345	12	available	available	ADJ
ejpam-3494	345	13	online	online	ADV
ejpam-3494	345	14	at	at	ADP
ejpam-3494	345	15	https://doi.org/10.12816/0006128	https://doi.org/10.12816/0006128	NOUN
ejpam-3494	345	16	.	.	PUNCT