id	sid	tid	token	lemma	pos
ejpam-3900	1	1	european	european	PROPN
ejpam-3900	1	2	journal	journal	PROPN
ejpam-3900	1	3	of	of	ADP
ejpam-3900	1	4	pure	pure	ADJ
ejpam-3900	1	5	and	and	CCONJ
ejpam-3900	1	6	applied	apply	VERB
ejpam-3900	1	7	mathematics	mathematic	NOUN
ejpam-3900	1	8	vol	vol	NOUN
ejpam-3900	1	9	.	.	PUNCT
ejpam-3900	2	1	14	14	NUM
ejpam-3900	2	2	,	,	PUNCT
ejpam-3900	2	3	no	no	INTJ
ejpam-3900	2	4	.	.	NOUN
ejpam-3900	2	5	1	1	NUM
ejpam-3900	2	6	,	,	PUNCT
ejpam-3900	2	7	2021	2021	NUM
ejpam-3900	2	8	,	,	PUNCT
ejpam-3900	2	9	65	65	NUM
ejpam-3900	2	10	-	-	SYM
ejpam-3900	2	11	81	81	NUM
ejpam-3900	2	12	issn	issn	PROPN
ejpam-3900	2	13	1307	1307	NUM
ejpam-3900	2	14	-	-	SYM
ejpam-3900	2	15	5543	5543	NUM
ejpam-3900	2	16	–	–	PUNCT
ejpam-3900	2	17	ejpam.com	ejpam.com	X
ejpam-3900	2	18	published	publish	VERB
ejpam-3900	2	19	by	by	ADP
ejpam-3900	2	20	new	new	PROPN
ejpam-3900	2	21	york	york	PROPN
ejpam-3900	2	22	business	business	PROPN
ejpam-3900	2	23	global	global	ADJ
ejpam-3900	2	24	explicit	explicit	ADJ
ejpam-3900	2	25	formulas	formula	NOUN
ejpam-3900	2	26	for	for	ADP
ejpam-3900	2	27	the	the	DET
ejpam-3900	2	28	first	first	ADJ
ejpam-3900	2	29	form	form	NOUN
ejpam-3900	2	30	(	(	PUNCT
ejpam-3900	2	31	q	q	ADJ
ejpam-3900	2	32	,	,	PUNCT
ejpam-3900	2	33	r)-dowling	r)-dowle	VERB
ejpam-3900	2	34	numbers	number	NOUN
ejpam-3900	2	35	and	and	CCONJ
ejpam-3900	2	36	(	(	PUNCT
ejpam-3900	2	37	q	q	ADJ
ejpam-3900	2	38	,	,	PUNCT
ejpam-3900	2	39	r)-whitney	r)-whitney	ADJ
ejpam-3900	2	40	-	-	PUNCT
ejpam-3900	2	41	lah	lah	PROPN
ejpam-3900	2	42	numbers	number	NOUN
ejpam-3900	2	43	roberto	roberto	PROPN
ejpam-3900	2	44	b.	b.	PROPN
ejpam-3900	2	45	corcino1,2,∗	corcino1,2,∗	PROPN
ejpam-3900	2	46	,	,	PUNCT
ejpam-3900	2	47	jay	jay	PROPN
ejpam-3900	2	48	m.	m.	PROPN
ejpam-3900	2	49	ontolan1,2	ontolan1,2	PROPN
ejpam-3900	2	50	,	,	PUNCT
ejpam-3900	2	51	maria	maria	PROPN
ejpam-3900	2	52	rowena	rowena	PROPN
ejpam-3900	2	53	s.	s.	PROPN
ejpam-3900	2	54	lobrigas2	lobrigas2	PROPN
ejpam-3900	3	1	1	1	NUM
ejpam-3900	3	2	research	research	NOUN
ejpam-3900	3	3	institute	institute	NOUN
ejpam-3900	3	4	for	for	ADP
ejpam-3900	3	5	computational	computational	ADJ
ejpam-3900	3	6	mathematics	mathematic	NOUN
ejpam-3900	3	7	and	and	CCONJ
ejpam-3900	3	8	physics	physics	NOUN
ejpam-3900	3	9	,	,	PUNCT
ejpam-3900	3	10	cebu	cebu	NOUN
ejpam-3900	3	11	normal	normal	ADJ
ejpam-3900	3	12	university	university	NOUN
ejpam-3900	3	13	,	,	PUNCT
ejpam-3900	3	14	6000	6000	NUM
ejpam-3900	3	15	cebu	cebu	NOUN
ejpam-3900	3	16	city	city	NOUN
ejpam-3900	3	17	,	,	PUNCT
ejpam-3900	3	18	philippines	philippine	NOUN
ejpam-3900	3	19	2	2	NUM
ejpam-3900	3	20	mathematics	mathematics	NOUN
ejpam-3900	3	21	department	department	NOUN
ejpam-3900	3	22	,	,	PUNCT
ejpam-3900	3	23	cebu	cebu	NOUN
ejpam-3900	3	24	normal	normal	ADJ
ejpam-3900	3	25	university	university	NOUN
ejpam-3900	3	26	,	,	PUNCT
ejpam-3900	3	27	6000	6000	NUM
ejpam-3900	3	28	cebu	cebu	NOUN
ejpam-3900	3	29	city	city	NOUN
ejpam-3900	3	30	,	,	PUNCT
ejpam-3900	3	31	philippines	philippine	NOUN
ejpam-3900	3	32	abstract	abstract	ADJ
ejpam-3900	3	33	.	.	PUNCT
ejpam-3900	4	1	in	in	ADP
ejpam-3900	4	2	this	this	DET
ejpam-3900	4	3	paper	paper	NOUN
ejpam-3900	4	4	,	,	PUNCT
ejpam-3900	4	5	a	a	DET
ejpam-3900	4	6	q	q	NOUN
ejpam-3900	4	7	-	-	PUNCT
ejpam-3900	4	8	analogue	analogue	NOUN
ejpam-3900	4	9	of	of	ADP
ejpam-3900	4	10	r	r	NOUN
ejpam-3900	4	11	-	-	PUNCT
ejpam-3900	4	12	whitney	whitney	NOUN
ejpam-3900	4	13	-	-	PUNCT
ejpam-3900	4	14	lah	lah	NOUN
ejpam-3900	4	15	numbers	number	NOUN
ejpam-3900	4	16	,	,	PUNCT
ejpam-3900	4	17	also	also	ADV
ejpam-3900	4	18	known	know	VERB
ejpam-3900	4	19	as	as	ADP
ejpam-3900	4	20	(	(	PUNCT
ejpam-3900	4	21	q	q	NOUN
ejpam-3900	4	22	,	,	PUNCT
ejpam-3900	4	23	r)-whitneylah	r)-whitneylah	ADJ
ejpam-3900	4	24	number	number	NOUN
ejpam-3900	4	25	,	,	PUNCT
ejpam-3900	4	26	denoted	denote	VERB
ejpam-3900	4	27	by	by	ADP
ejpam-3900	4	28	lm	lm	INTJ
ejpam-3900	4	29	,	,	PUNCT
ejpam-3900	4	30	r[n	r[n	VERB
ejpam-3900	4	31	,	,	PUNCT
ejpam-3900	4	32	k]q	k]q	NOUN
ejpam-3900	4	33	is	be	AUX
ejpam-3900	4	34	defined	define	VERB
ejpam-3900	4	35	using	use	VERB
ejpam-3900	4	36	the	the	DET
ejpam-3900	4	37	triangular	triangular	NOUN
ejpam-3900	4	38	recurrence	recurrence	NOUN
ejpam-3900	4	39	relation	relation	NOUN
ejpam-3900	4	40	.	.	PUNCT
ejpam-3900	5	1	several	several	ADJ
ejpam-3900	5	2	fundamental	fundamental	ADJ
ejpam-3900	5	3	properties	property	NOUN
ejpam-3900	5	4	for	for	ADP
ejpam-3900	5	5	the	the	DET
ejpam-3900	5	6	q	q	NOUN
ejpam-3900	5	7	-	-	PUNCT
ejpam-3900	5	8	analogue	analogue	NOUN
ejpam-3900	5	9	are	be	AUX
ejpam-3900	5	10	established	establish	VERB
ejpam-3900	5	11	such	such	ADJ
ejpam-3900	5	12	as	as	ADP
ejpam-3900	5	13	vertical	vertical	ADJ
ejpam-3900	5	14	and	and	CCONJ
ejpam-3900	5	15	horizontal	horizontal	ADJ
ejpam-3900	5	16	recurrence	recurrence	NOUN
ejpam-3900	5	17	relations	relation	NOUN
ejpam-3900	5	18	,	,	PUNCT
ejpam-3900	5	19	horizontal	horizontal	ADJ
ejpam-3900	5	20	and	and	CCONJ
ejpam-3900	5	21	exponential	exponential	ADJ
ejpam-3900	5	22	generating	generating	NOUN
ejpam-3900	5	23	functions	function	NOUN
ejpam-3900	5	24	.	.	PUNCT
ejpam-3900	6	1	moreover	moreover	ADV
ejpam-3900	6	2	,	,	PUNCT
ejpam-3900	6	3	an	an	DET
ejpam-3900	6	4	explicit	explicit	ADJ
ejpam-3900	6	5	formula	formula	NOUN
ejpam-3900	6	6	for	for	ADP
ejpam-3900	6	7	(	(	PUNCT
ejpam-3900	6	8	q	q	NOUN
ejpam-3900	6	9	,	,	PUNCT
ejpam-3900	6	10	r)whitney	r)whitney	ADJ
ejpam-3900	6	11	-	-	ADJ
ejpam-3900	6	12	lah	lah	ADJ
ejpam-3900	6	13	number	number	NOUN
ejpam-3900	6	14	is	be	AUX
ejpam-3900	6	15	derived	derive	VERB
ejpam-3900	6	16	using	use	VERB
ejpam-3900	6	17	the	the	DET
ejpam-3900	6	18	concept	concept	NOUN
ejpam-3900	6	19	of	of	ADP
ejpam-3900	6	20	q	q	ADJ
ejpam-3900	6	21	-	-	PUNCT
ejpam-3900	6	22	difference	difference	NOUN
ejpam-3900	6	23	operator	operator	NOUN
ejpam-3900	6	24	,	,	PUNCT
ejpam-3900	6	25	particularly	particularly	ADV
ejpam-3900	6	26	,	,	PUNCT
ejpam-3900	6	27	the	the	DET
ejpam-3900	6	28	qanalogue	qanalogue	NOUN
ejpam-3900	6	29	of	of	ADP
ejpam-3900	6	30	newton	newton	PROPN
ejpam-3900	6	31	’s	’s	PART
ejpam-3900	6	32	interpolation	interpolation	NOUN
ejpam-3900	6	33	formula	formula	NOUN
ejpam-3900	6	34	.	.	PUNCT
ejpam-3900	7	1	furthermore	furthermore	ADV
ejpam-3900	7	2	,	,	PUNCT
ejpam-3900	7	3	an	an	DET
ejpam-3900	7	4	explicit	explicit	ADJ
ejpam-3900	7	5	formula	formula	NOUN
ejpam-3900	7	6	for	for	ADP
ejpam-3900	7	7	the	the	DET
ejpam-3900	7	8	first	first	ADJ
ejpam-3900	7	9	form	form	NOUN
ejpam-3900	7	10	(	(	PUNCT
ejpam-3900	7	11	q	q	ADJ
ejpam-3900	7	12	,	,	PUNCT
ejpam-3900	7	13	r)-dowling	r)-dowle	VERB
ejpam-3900	7	14	numbers	number	NOUN
ejpam-3900	7	15	is	be	AUX
ejpam-3900	7	16	obtained	obtain	VERB
ejpam-3900	7	17	which	which	PRON
ejpam-3900	7	18	is	be	AUX
ejpam-3900	7	19	expressed	express	VERB
ejpam-3900	7	20	in	in	ADP
ejpam-3900	7	21	terms	term	NOUN
ejpam-3900	7	22	of	of	ADP
ejpam-3900	7	23	(	(	PUNCT
ejpam-3900	7	24	q	q	ADJ
ejpam-3900	7	25	,	,	PUNCT
ejpam-3900	7	26	r)-whitney	r)-whitney	ADJ
ejpam-3900	7	27	-	-	PUNCT
ejpam-3900	7	28	lah	lah	NOUN
ejpam-3900	7	29	numbers	number	NOUN
ejpam-3900	7	30	and	and	CCONJ
ejpam-3900	7	31	(	(	PUNCT
ejpam-3900	7	32	q	q	ADJ
ejpam-3900	7	33	,	,	PUNCT
ejpam-3900	7	34	r)-whitney	r)-whitney	NOUN
ejpam-3900	7	35	numbers	number	NOUN
ejpam-3900	7	36	of	of	ADP
ejpam-3900	7	37	the	the	DET
ejpam-3900	7	38	second	second	ADJ
ejpam-3900	7	39	kind	kind	NOUN
ejpam-3900	7	40	.	.	PUNCT
ejpam-3900	8	1	2020	2020	NUM
ejpam-3900	8	2	mathematics	mathematic	NOUN
ejpam-3900	8	3	subject	subject	NOUN
ejpam-3900	8	4	classifications	classification	NOUN
ejpam-3900	8	5	:	:	PUNCT
ejpam-3900	8	6	05a15	05a15	NUM
ejpam-3900	8	7	,	,	PUNCT
ejpam-3900	8	8	11b65	11b65	NUM
ejpam-3900	8	9	,	,	PUNCT
ejpam-3900	8	10	11b73	11b73	NUM
ejpam-3900	8	11	key	key	ADJ
ejpam-3900	8	12	words	word	NOUN
ejpam-3900	8	13	and	and	CCONJ
ejpam-3900	8	14	phrases	phrase	NOUN
ejpam-3900	8	15	:	:	PUNCT
ejpam-3900	8	16	r	r	X
ejpam-3900	8	17	-	-	PUNCT
ejpam-3900	8	18	whitney	whitney	NOUN
ejpam-3900	8	19	-	-	PUNCT
ejpam-3900	8	20	lah	lah	NOUN
ejpam-3900	8	21	numbers	number	NOUN
ejpam-3900	8	22	,	,	PUNCT
ejpam-3900	8	23	r	r	NOUN
ejpam-3900	8	24	-	-	PUNCT
ejpam-3900	8	25	whitney	whitney	NOUN
ejpam-3900	8	26	numbers	number	NOUN
ejpam-3900	8	27	,	,	PUNCT
ejpam-3900	8	28	r	r	NOUN
ejpam-3900	8	29	-	-	PUNCT
ejpam-3900	8	30	dowling	dowle	VERB
ejpam-3900	8	31	numbers	number	NOUN
ejpam-3900	8	32	,	,	PUNCT
ejpam-3900	8	33	generating	generate	VERB
ejpam-3900	8	34	function	function	NOUN
ejpam-3900	8	35	,	,	PUNCT
ejpam-3900	8	36	q	q	ADJ
ejpam-3900	8	37	-	-	PUNCT
ejpam-3900	8	38	exponential	exponential	ADJ
ejpam-3900	8	39	function	function	NOUN
ejpam-3900	8	40	,	,	PUNCT
ejpam-3900	8	41	q	q	ADJ
ejpam-3900	8	42	-	-	PUNCT
ejpam-3900	8	43	difference	difference	NOUN
ejpam-3900	8	44	operator	operator	NOUN
ejpam-3900	8	45	,	,	PUNCT
ejpam-3900	8	46	newton	newton	PROPN
ejpam-3900	8	47	’s	’s	PART
ejpam-3900	8	48	interpolation	interpolation	NOUN
ejpam-3900	8	49	formula	formula	NOUN
ejpam-3900	8	50	1	1	NUM
ejpam-3900	8	51	.	.	PUNCT
ejpam-3900	9	1	introduction	introduction	NOUN
ejpam-3900	9	2	the	the	DET
ejpam-3900	9	3	lah	lah	PROPN
ejpam-3900	9	4	numbers	number	NOUN
ejpam-3900	9	5	l(n	l(n	PROPN
ejpam-3900	9	6	,	,	PUNCT
ejpam-3900	9	7	k	k	NOUN
ejpam-3900	9	8	)	)	PUNCT
ejpam-3900	9	9	are	be	AUX
ejpam-3900	9	10	the	the	DET
ejpam-3900	9	11	connection	connection	NOUN
ejpam-3900	9	12	constants	constant	NOUN
ejpam-3900	9	13	between	between	ADP
ejpam-3900	9	14	the	the	DET
ejpam-3900	9	15	rising	rise	VERB
ejpam-3900	9	16	factorial	factorial	NOUN
ejpam-3900	9	17	and	and	CCONJ
ejpam-3900	9	18	falling	fall	VERB
ejpam-3900	9	19	factorial	factorial	ADJ
ejpam-3900	9	20	polynomial	polynomial	ADJ
ejpam-3900	9	21	bases	basis	NOUN
ejpam-3900	9	22	and	and	CCONJ
ejpam-3900	9	23	count	count	VERB
ejpam-3900	9	24	partitions	partition	NOUN
ejpam-3900	9	25	of	of	ADP
ejpam-3900	9	26	n	n	DET
ejpam-3900	9	27	distinct	distinct	ADJ
ejpam-3900	9	28	objects	object	NOUN
ejpam-3900	9	29	into	into	ADP
ejpam-3900	9	30	k	k	PROPN
ejpam-3900	9	31	blocks	block	NOUN
ejpam-3900	9	32	,	,	PUNCT
ejpam-3900	9	33	where	where	SCONJ
ejpam-3900	9	34	objects	object	NOUN
ejpam-3900	9	35	within	within	ADP
ejpam-3900	9	36	a	a	DET
ejpam-3900	9	37	block	block	NOUN
ejpam-3900	9	38	are	be	AUX
ejpam-3900	9	39	ordered	order	VERB
ejpam-3900	9	40	(	(	PUNCT
ejpam-3900	9	41	termed	term	VERB
ejpam-3900	9	42	laguerre	laguerre	NOUN
ejpam-3900	9	43	configurations	configuration	NOUN
ejpam-3900	9	44	)	)	PUNCT
ejpam-3900	10	1	[	[	X
ejpam-3900	10	2	8	8	NUM
ejpam-3900	10	3	]	]	PUNCT
ejpam-3900	10	4	.	.	PUNCT
ejpam-3900	11	1	the	the	DET
ejpam-3900	11	2	classical	classical	ADJ
ejpam-3900	11	3	(	(	PUNCT
ejpam-3900	11	4	signless	signless	ADJ
ejpam-3900	11	5	)	)	PUNCT
ejpam-3900	11	6	lah	lah	PROPN
ejpam-3900	11	7	numbers	number	NOUN
ejpam-3900	11	8	l(n	l(n	PROPN
ejpam-3900	11	9	,	,	PUNCT
ejpam-3900	11	10	k	k	NOUN
ejpam-3900	11	11	)	)	PUNCT
ejpam-3900	11	12	=	=	SYM
ejpam-3900	11	13	n	n	X
ejpam-3900	11	14	!	!	PUNCT
ejpam-3900	12	1	k	k	X
ejpam-3900	12	2	!	!	PUNCT
ejpam-3900	13	1	(	(	PUNCT
ejpam-3900	13	2	n−1	n−1	PROPN
ejpam-3900	13	3	k−1	k−1	PROPN
ejpam-3900	13	4	)	)	PUNCT
ejpam-3900	13	5	may	may	AUX
ejpam-3900	13	6	be	be	AUX
ejpam-3900	13	7	expressed	express	VERB
ejpam-3900	13	8	in	in	ADP
ejpam-3900	13	9	terms	term	NOUN
ejpam-3900	13	10	of	of	ADP
ejpam-3900	13	11	the	the	DET
ejpam-3900	13	12	stirling	stirling	NOUN
ejpam-3900	13	13	numbers	number	NOUN
ejpam-3900	13	14	s(n	s(n	PROPN
ejpam-3900	13	15	,	,	PUNCT
ejpam-3900	13	16	k	k	NOUN
ejpam-3900	13	17	)	)	PUNCT
ejpam-3900	13	18	and	and	CCONJ
ejpam-3900	13	19	s(n	s(n	PROPN
ejpam-3900	13	20	,	,	PUNCT
ejpam-3900	13	21	k	k	NOUN
ejpam-3900	13	22	)	)	PUNCT
ejpam-3900	13	23	of	of	ADP
ejpam-3900	13	24	the	the	DET
ejpam-3900	13	25	first	first	ADJ
ejpam-3900	13	26	and	and	CCONJ
ejpam-3900	13	27	second	second	ADJ
ejpam-3900	13	28	kind	kind	NOUN
ejpam-3900	13	29	,	,	PUNCT
ejpam-3900	13	30	respectively	respectively	ADV
ejpam-3900	13	31	:	:	PUNCT
ejpam-3900	13	32	l(n	l(n	NOUN
ejpam-3900	13	33	,	,	PUNCT
ejpam-3900	13	34	k	k	NOUN
ejpam-3900	13	35	)	)	PUNCT
ejpam-3900	13	36	=	=	SYM
ejpam-3900	14	1	n∑	n∑	PROPN
ejpam-3900	14	2	j	j	PROPN
ejpam-3900	14	3	=	=	PROPN
ejpam-3900	14	4	k	k	PROPN
ejpam-3900	14	5	s(n	s(n	PROPN
ejpam-3900	14	6	,	,	PUNCT
ejpam-3900	14	7	j)s(j	j)s(j	PROPN
ejpam-3900	14	8	,	,	PUNCT
ejpam-3900	14	9	k	k	NOUN
ejpam-3900	14	10	)	)	PUNCT
ejpam-3900	14	11	.	.	PUNCT
ejpam-3900	15	1	(	(	PUNCT
ejpam-3900	15	2	1	1	X
ejpam-3900	15	3	)	)	PUNCT
ejpam-3900	15	4	∗corresponding	∗corresponde	VERB
ejpam-3900	15	5	author	author	NOUN
ejpam-3900	15	6	.	.	PUNCT
ejpam-3900	16	1	doi	doi	NOUN
ejpam-3900	16	2	:	:	PUNCT
ejpam-3900	16	3	https://doi.org/10.29020/nybg.ejpam.v14i1.3900	https://doi.org/10.29020/nybg.ejpam.v14i1.3900	ADJ
ejpam-3900	16	4	email	email	NOUN
ejpam-3900	16	5	addresses	address	VERB
ejpam-3900	16	6	:	:	PUNCT
ejpam-3900	16	7	rcorcino@yahoo.com	rcorcino@yahoo.com	X
ejpam-3900	16	8	(	(	PUNCT
ejpam-3900	16	9	r.	r.	PROPN
ejpam-3900	16	10	corcino	corcino	PROPN
ejpam-3900	16	11	)	)	PUNCT
ejpam-3900	16	12	,	,	PUNCT
ejpam-3900	16	13	ontolanj@cnu.edu.ph	ontolanj@cnu.edu.ph	PROPN
ejpam-3900	16	14	(	(	PUNCT
ejpam-3900	16	15	j.	j.	PROPN
ejpam-3900	16	16	ontolan	ontolan	PROPN
ejpam-3900	16	17	)	)	PUNCT
ejpam-3900	16	18	,	,	PUNCT
ejpam-3900	16	19	mariarowena.lobrigas@gmail.com	mariarowena.lobrigas@gmail.com	X
ejpam-3900	16	20	(	(	PUNCT
ejpam-3900	16	21	m.	m.	NOUN
ejpam-3900	16	22	lobrigas	lobrigas	PROPN
ejpam-3900	16	23	)	)	PUNCT
ejpam-3900	16	24	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3900	17	1	65	65	NUM
ejpam-3900	17	2	c	c	X
ejpam-3900	17	3	©	©	PROPN
ejpam-3900	17	4	2021	2021	NUM
ejpam-3900	17	5	ejpam	ejpam	VERB
ejpam-3900	17	6	all	all	DET
ejpam-3900	17	7	rights	right	NOUN
ejpam-3900	17	8	reserved	reserve	VERB
ejpam-3900	17	9	.	.	PUNCT
ejpam-3900	18	1	r.	r.	PROPN
ejpam-3900	18	2	corcino	corcino	PROPN
ejpam-3900	18	3	,	,	PUNCT
ejpam-3900	18	4	j.	j.	PROPN
ejpam-3900	18	5	ontolan	ontolan	PROPN
ejpam-3900	18	6	,	,	PUNCT
ejpam-3900	18	7	m.	m.	NOUN
ejpam-3900	18	8	lobrigas	lobrigas	PROPN
ejpam-3900	18	9	/	/	SYM
ejpam-3900	18	10	eur	eur	PROPN
ejpam-3900	18	11	.	.	PUNCT
ejpam-3900	19	1	j.	j.	PROPN
ejpam-3900	19	2	pure	pure	PROPN
ejpam-3900	19	3	appl	appl	PROPN
ejpam-3900	19	4	.	.	PROPN
ejpam-3900	19	5	math	math	PROPN
ejpam-3900	19	6	,	,	PUNCT
ejpam-3900	19	7	14	14	NUM
ejpam-3900	19	8	(	(	PUNCT
ejpam-3900	19	9	1	1	NUM
ejpam-3900	19	10	)	)	PUNCT
ejpam-3900	19	11	(	(	PUNCT
ejpam-3900	19	12	2021	2021	NUM
ejpam-3900	19	13	)	)	PUNCT
ejpam-3900	19	14	,	,	PUNCT
ejpam-3900	19	15	65	65	NUM
ejpam-3900	19	16	-	-	SYM
ejpam-3900	19	17	81	81	NUM
ejpam-3900	19	18	66	66	NUM
ejpam-3900	19	19	cheon	cheon	NOUN
ejpam-3900	19	20	and	and	CCONJ
ejpam-3900	19	21	jung	jung	PROPN
ejpam-3900	20	1	[	[	X
ejpam-3900	20	2	1	1	X
ejpam-3900	20	3	]	]	PUNCT
ejpam-3900	20	4	defined	define	VERB
ejpam-3900	20	5	the	the	DET
ejpam-3900	20	6	r	r	PROPN
ejpam-3900	20	7	-	-	PUNCT
ejpam-3900	20	8	whitney	whitney	NOUN
ejpam-3900	20	9	-	-	PUNCT
ejpam-3900	20	10	lah	lah	PROPN
ejpam-3900	20	11	numbers	number	NOUN
ejpam-3900	20	12	lm	lm	ADP
ejpam-3900	20	13	,	,	PUNCT
ejpam-3900	20	14	r(n	r(n	PROPN
ejpam-3900	20	15	,	,	PUNCT
ejpam-3900	20	16	k	k	NOUN
ejpam-3900	20	17	)	)	PUNCT
ejpam-3900	20	18	in	in	ADP
ejpam-3900	20	19	terms	term	NOUN
ejpam-3900	20	20	of	of	ADP
ejpam-3900	20	21	the	the	DET
ejpam-3900	20	22	rwhitney	rwhitney	NOUN
ejpam-3900	20	23	numbers	number	NOUN
ejpam-3900	20	24	of	of	ADP
ejpam-3900	20	25	the	the	DET
ejpam-3900	20	26	first	first	ADJ
ejpam-3900	20	27	kind	kind	NOUN
ejpam-3900	20	28	wm	wm	PROPN
ejpam-3900	20	29	,	,	PUNCT
ejpam-3900	20	30	r(n	r(n	PROPN
ejpam-3900	20	31	,	,	PUNCT
ejpam-3900	20	32	k	k	NOUN
ejpam-3900	20	33	)	)	PUNCT
ejpam-3900	20	34	and	and	CCONJ
ejpam-3900	20	35	second	second	ADJ
ejpam-3900	20	36	kind	kind	NOUN
ejpam-3900	20	37	wm	wm	PROPN
ejpam-3900	20	38	,	,	PUNCT
ejpam-3900	20	39	r(n	r(n	PROPN
ejpam-3900	20	40	,	,	PUNCT
ejpam-3900	20	41	k	k	NOUN
ejpam-3900	20	42	)	)	PUNCT
ejpam-3900	20	43	lm	lm	PROPN
ejpam-3900	20	44	,	,	PUNCT
ejpam-3900	20	45	r(n	r(n	PROPN
ejpam-3900	20	46	,	,	PUNCT
ejpam-3900	20	47	k	k	NOUN
ejpam-3900	20	48	)	)	PUNCT
ejpam-3900	20	49	=	=	SYM
ejpam-3900	21	1	n∑	n∑	PROPN
ejpam-3900	21	2	j	j	PROPN
ejpam-3900	21	3	=	=	PROPN
ejpam-3900	21	4	k	k	PROPN
ejpam-3900	21	5	wm	wm	PROPN
ejpam-3900	21	6	,	,	PUNCT
ejpam-3900	21	7	r(n	r(n	PROPN
ejpam-3900	21	8	,	,	PUNCT
ejpam-3900	21	9	j)wm	j)wm	PROPN
ejpam-3900	21	10	,	,	PUNCT
ejpam-3900	21	11	r(j	r(j	PROPN
ejpam-3900	21	12	,	,	PUNCT
ejpam-3900	21	13	k	k	PROPN
ejpam-3900	21	14	)	)	PUNCT
ejpam-3900	21	15	,	,	PUNCT
ejpam-3900	21	16	(	(	PUNCT
ejpam-3900	21	17	2	2	X
ejpam-3900	21	18	)	)	PUNCT
ejpam-3900	21	19	which	which	PRON
ejpam-3900	21	20	generalizes	generalize	VERB
ejpam-3900	21	21	the	the	DET
ejpam-3900	21	22	identity	identity	NOUN
ejpam-3900	21	23	for	for	ADP
ejpam-3900	21	24	the	the	DET
ejpam-3900	21	25	lah	lah	PROPN
ejpam-3900	21	26	numbers	number	NOUN
ejpam-3900	21	27	in	in	ADP
ejpam-3900	21	28	terms	term	NOUN
ejpam-3900	21	29	of	of	ADP
ejpam-3900	21	30	the	the	DET
ejpam-3900	21	31	stirling	stirling	NOUN
ejpam-3900	21	32	numbers	number	NOUN
ejpam-3900	21	33	of	of	ADP
ejpam-3900	21	34	the	the	DET
ejpam-3900	21	35	first	first	ADJ
ejpam-3900	21	36	kind	kind	NOUN
ejpam-3900	21	37	s(n	s(n	PROPN
ejpam-3900	21	38	,	,	PUNCT
ejpam-3900	21	39	k	k	NOUN
ejpam-3900	21	40	)	)	PUNCT
ejpam-3900	21	41	and	and	CCONJ
ejpam-3900	21	42	second	second	ADJ
ejpam-3900	21	43	kind	kind	NOUN
ejpam-3900	21	44	s(n	s(n	PROPN
ejpam-3900	21	45	,	,	PUNCT
ejpam-3900	21	46	k	k	NOUN
ejpam-3900	21	47	)	)	PUNCT
ejpam-3900	21	48	.	.	PUNCT
ejpam-3900	22	1	the	the	DET
ejpam-3900	22	2	importance	importance	NOUN
ejpam-3900	22	3	of	of	ADP
ejpam-3900	22	4	a	a	DET
ejpam-3900	22	5	q	q	NOUN
ejpam-3900	22	6	-	-	PUNCT
ejpam-3900	22	7	analogue	analogue	NOUN
ejpam-3900	22	8	is	be	AUX
ejpam-3900	22	9	related	relate	VERB
ejpam-3900	22	10	to	to	ADP
ejpam-3900	22	11	a	a	DET
ejpam-3900	22	12	mathematical	mathematical	ADJ
ejpam-3900	22	13	expression	expression	NOUN
ejpam-3900	22	14	parameterized	parameterize	VERB
ejpam-3900	22	15	by	by	ADP
ejpam-3900	22	16	a	a	DET
ejpam-3900	22	17	quantity	quantity	NOUN
ejpam-3900	22	18	q	q	NOUN
ejpam-3900	22	19	that	that	PRON
ejpam-3900	22	20	generalizes	generalize	VERB
ejpam-3900	22	21	a	a	DET
ejpam-3900	22	22	known	know	VERB
ejpam-3900	22	23	expression	expression	NOUN
ejpam-3900	22	24	and	and	CCONJ
ejpam-3900	22	25	reduces	reduce	VERB
ejpam-3900	22	26	to	to	ADP
ejpam-3900	22	27	the	the	DET
ejpam-3900	22	28	known	know	VERB
ejpam-3900	22	29	expression	expression	NOUN
ejpam-3900	22	30	in	in	ADP
ejpam-3900	22	31	the	the	DET
ejpam-3900	22	32	limit	limit	NOUN
ejpam-3900	22	33	,	,	PUNCT
ejpam-3900	22	34	as	as	ADP
ejpam-3900	22	35	q	q	NOUN
ejpam-3900	22	36	approaches	approach	VERB
ejpam-3900	22	37	1	1	NUM
ejpam-3900	22	38	.	.	PUNCT
ejpam-3900	22	39	corcino	corcino	NOUN
ejpam-3900	22	40	et	et	PROPN
ejpam-3900	22	41	al[5	al[5	PROPN
ejpam-3900	22	42	]	]	PUNCT
ejpam-3900	22	43	established	establish	VERB
ejpam-3900	22	44	a	a	DET
ejpam-3900	22	45	q	q	NOUN
ejpam-3900	22	46	-	-	PUNCT
ejpam-3900	22	47	analogue	analogue	NOUN
ejpam-3900	22	48	of	of	ADP
ejpam-3900	22	49	sn	sn	PROPN
ejpam-3900	22	50	,	,	PUNCT
ejpam-3900	22	51	k(a	k(a	PROPN
ejpam-3900	22	52	)	)	PUNCT
ejpam-3900	22	53	denoted	denote	VERB
ejpam-3900	22	54	by	by	ADP
ejpam-3900	22	55	σ[n	σ[n	NOUN
ejpam-3900	22	56	,	,	PUNCT
ejpam-3900	22	57	k]β	k]β	PROPN
ejpam-3900	22	58	,	,	PUNCT
ejpam-3900	22	59	rq	rq	INTJ
ejpam-3900	22	60	,	,	PUNCT
ejpam-3900	22	61	given	give	VERB
ejpam-3900	22	62	by	by	ADP
ejpam-3900	22	63	σ[n	σ[n	NOUN
ejpam-3900	22	64	,	,	PUNCT
ejpam-3900	22	65	k]β	k]β	NOUN
ejpam-3900	22	66	,	,	PUNCT
ejpam-3900	22	67	rq	rq	VERB
ejpam-3900	22	68	=	=	PUNCT
ejpam-3900	22	69	σ[n−	σ[n−	NOUN
ejpam-3900	22	70	1	1	NUM
ejpam-3900	22	71	,	,	PUNCT
ejpam-3900	22	72	k	k	PROPN
ejpam-3900	23	1	−	−	PROPN
ejpam-3900	23	2	1]β	1]β	NOUN
ejpam-3900	23	3	,	,	PUNCT
ejpam-3900	23	4	rq	rq	X
ejpam-3900	23	5	+	+	X
ejpam-3900	24	1	(	(	PUNCT
ejpam-3900	24	2	[	[	X
ejpam-3900	24	3	kβ]q	kβ]q	NOUN
ejpam-3900	24	4	+	+	CCONJ
ejpam-3900	24	5	[	[	X
ejpam-3900	24	6	r]q)σ[n−	r]q)σ[n−	NOUN
ejpam-3900	24	7	1	1	NUM
ejpam-3900	24	8	,	,	PUNCT
ejpam-3900	24	9	k]β	k]β	NOUN
ejpam-3900	24	10	,	,	PUNCT
ejpam-3900	24	11	rq	rq	X
ejpam-3900	24	12	and	and	CCONJ
ejpam-3900	24	13	obtained	obtain	VERB
ejpam-3900	24	14	some	some	DET
ejpam-3900	24	15	properties	property	NOUN
ejpam-3900	24	16	including	include	VERB
ejpam-3900	24	17	vertical	vertical	ADJ
ejpam-3900	24	18	and	and	CCONJ
ejpam-3900	24	19	horizontal	horizontal	ADJ
ejpam-3900	24	20	recurrence	recurrence	NOUN
ejpam-3900	24	21	relation	relation	PROPN
ejpam-3900	24	22	,	,	PUNCT
ejpam-3900	24	23	horizontal	horizontal	ADJ
ejpam-3900	24	24	generating	generating	NOUN
ejpam-3900	24	25	function	function	NOUN
ejpam-3900	24	26	,	,	PUNCT
ejpam-3900	24	27	explicit	explicit	ADJ
ejpam-3900	24	28	formula	formula	NOUN
ejpam-3900	24	29	,	,	PUNCT
ejpam-3900	24	30	as	as	ADV
ejpam-3900	24	31	well	well	ADV
ejpam-3900	24	32	as	as	ADP
ejpam-3900	24	33	exponential	exponential	ADJ
ejpam-3900	24	34	generating	generating	NOUN
ejpam-3900	24	35	function	function	NOUN
ejpam-3900	24	36	,	,	PUNCT
ejpam-3900	24	37	rational	rational	ADJ
ejpam-3900	24	38	generating	generating	NOUN
ejpam-3900	24	39	function	function	NOUN
ejpam-3900	24	40	,	,	PUNCT
ejpam-3900	24	41	and	and	CCONJ
ejpam-3900	24	42	explicit	explicit	ADJ
ejpam-3900	24	43	formula	formula	NOUN
ejpam-3900	24	44	in	in	ADP
ejpam-3900	24	45	homogeneous	homogeneous	ADJ
ejpam-3900	24	46	symmetric	symmetric	ADJ
ejpam-3900	24	47	form	form	NOUN
ejpam-3900	24	48	.	.	PUNCT
ejpam-3900	25	1	it	it	PRON
ejpam-3900	25	2	is	be	AUX
ejpam-3900	25	3	well	well	ADV
ejpam-3900	25	4	-	-	PUNCT
ejpam-3900	25	5	known	know	VERB
ejpam-3900	25	6	that	that	SCONJ
ejpam-3900	25	7	the	the	DET
ejpam-3900	25	8	rucinski	rucinski	ADJ
ejpam-3900	25	9	-	-	PUNCT
ejpam-3900	25	10	voigt	voigt	NOUN
ejpam-3900	25	11	numbers	number	NOUN
ejpam-3900	25	12	are	be	AUX
ejpam-3900	25	13	also	also	ADV
ejpam-3900	25	14	known	know	VERB
ejpam-3900	25	15	as	as	ADP
ejpam-3900	25	16	r	r	NOUN
ejpam-3900	25	17	-	-	PUNCT
ejpam-3900	25	18	whitney	whitney	NOUN
ejpam-3900	25	19	numbers	number	NOUN
ejpam-3900	25	20	of	of	ADP
ejpam-3900	25	21	the	the	DET
ejpam-3900	25	22	second	second	ADJ
ejpam-3900	25	23	kind	kind	NOUN
ejpam-3900	25	24	,	,	PUNCT
ejpam-3900	25	25	denoted	denote	VERB
ejpam-3900	25	26	by	by	ADP
ejpam-3900	25	27	wm	wm	PROPN
ejpam-3900	25	28	,	,	PUNCT
ejpam-3900	25	29	r(n	r(n	PROPN
ejpam-3900	25	30	,	,	PUNCT
ejpam-3900	25	31	k	k	NOUN
ejpam-3900	25	32	)	)	PUNCT
ejpam-3900	25	33	by	by	ADP
ejpam-3900	25	34	mező	mező	PROPN
ejpam-3900	26	1	[	[	X
ejpam-3900	26	2	10	10	NUM
ejpam-3900	26	3	]	]	PUNCT
ejpam-3900	26	4	.	.	PUNCT
ejpam-3900	27	1	corcino	corcino	NOUN
ejpam-3900	27	2	and	and	CCONJ
ejpam-3900	27	3	montero	montero	NOUN
ejpam-3900	28	1	[	[	X
ejpam-3900	28	2	5	5	NUM
ejpam-3900	28	3	]	]	PUNCT
ejpam-3900	28	4	defined	define	VERB
ejpam-3900	28	5	a	a	DET
ejpam-3900	28	6	q	q	NOUN
ejpam-3900	28	7	-	-	PUNCT
ejpam-3900	28	8	analogue	analogue	NOUN
ejpam-3900	28	9	of	of	ADP
ejpam-3900	28	10	r	r	NOUN
ejpam-3900	28	11	-	-	PUNCT
ejpam-3900	28	12	whitney	whitney	NOUN
ejpam-3900	28	13	numbers	number	NOUN
ejpam-3900	28	14	of	of	ADP
ejpam-3900	28	15	the	the	DET
ejpam-3900	28	16	second	second	ADJ
ejpam-3900	28	17	kind	kind	NOUN
ejpam-3900	28	18	which	which	PRON
ejpam-3900	28	19	are	be	AUX
ejpam-3900	28	20	exactly	exactly	ADV
ejpam-3900	28	21	the	the	DET
ejpam-3900	28	22	same	same	ADJ
ejpam-3900	28	23	numbers	number	NOUN
ejpam-3900	28	24	with	with	ADP
ejpam-3900	28	25	the	the	DET
ejpam-3900	28	26	rucinski	rucinski	ADJ
ejpam-3900	28	27	-	-	PUNCT
ejpam-3900	28	28	voigt	voigt	NOUN
ejpam-3900	28	29	numbers	number	NOUN
ejpam-3900	28	30	,	,	PUNCT
ejpam-3900	28	31	in	in	ADP
ejpam-3900	28	32	a	a	DET
ejpam-3900	28	33	form	form	NOUN
ejpam-3900	28	34	of	of	ADP
ejpam-3900	28	35	triangular	triangular	NOUN
ejpam-3900	28	36	recurrence	recurrence	NOUN
ejpam-3900	28	37	relation	relation	NOUN
ejpam-3900	28	38	.	.	PUNCT
ejpam-3900	29	1	on	on	ADP
ejpam-3900	29	2	the	the	DET
ejpam-3900	29	3	other	other	ADJ
ejpam-3900	29	4	hand	hand	NOUN
ejpam-3900	29	5	,	,	PUNCT
ejpam-3900	29	6	cheon	cheon	NOUN
ejpam-3900	29	7	and	and	CCONJ
ejpam-3900	29	8	jung	jung	PROPN
ejpam-3900	30	1	[	[	X
ejpam-3900	30	2	1	1	X
ejpam-3900	30	3	]	]	PUNCT
ejpam-3900	30	4	defined	define	VERB
ejpam-3900	30	5	the	the	DET
ejpam-3900	30	6	r	r	PROPN
ejpam-3900	30	7	-	-	PUNCT
ejpam-3900	30	8	whitney	whitney	NOUN
ejpam-3900	30	9	-	-	PUNCT
ejpam-3900	30	10	lah	lah	PROPN
ejpam-3900	30	11	numbers	number	NOUN
ejpam-3900	30	12	,	,	PUNCT
ejpam-3900	30	13	denoted	denote	VERB
ejpam-3900	30	14	by	by	ADP
ejpam-3900	30	15	lm	lm	NOUN
ejpam-3900	30	16	,	,	PUNCT
ejpam-3900	30	17	r(n	r(n	PROPN
ejpam-3900	30	18	,	,	PUNCT
ejpam-3900	30	19	k	k	NOUN
ejpam-3900	30	20	)	)	PUNCT
ejpam-3900	30	21	,	,	PUNCT
ejpam-3900	30	22	in	in	ADP
ejpam-3900	30	23	terms	term	NOUN
ejpam-3900	30	24	of	of	ADP
ejpam-3900	30	25	the	the	DET
ejpam-3900	30	26	r	r	NOUN
ejpam-3900	30	27	-	-	PUNCT
ejpam-3900	30	28	whitney	whitney	NOUN
ejpam-3900	30	29	numbers	number	NOUN
ejpam-3900	30	30	of	of	ADP
ejpam-3900	30	31	the	the	DET
ejpam-3900	30	32	first	first	ADJ
ejpam-3900	30	33	kind	kind	NOUN
ejpam-3900	30	34	wm	wm	PROPN
ejpam-3900	30	35	,	,	PUNCT
ejpam-3900	30	36	r(n	r(n	PROPN
ejpam-3900	30	37	,	,	PUNCT
ejpam-3900	30	38	k	k	NOUN
ejpam-3900	30	39	)	)	PUNCT
ejpam-3900	30	40	and	and	CCONJ
ejpam-3900	30	41	the	the	DET
ejpam-3900	30	42	second	second	ADJ
ejpam-3900	30	43	kind	kind	NOUN
ejpam-3900	30	44	wm	wm	PROPN
ejpam-3900	30	45	,	,	PUNCT
ejpam-3900	30	46	r(n	r(n	PROPN
ejpam-3900	30	47	,	,	PUNCT
ejpam-3900	30	48	k	k	NOUN
ejpam-3900	30	49	)	)	PUNCT
ejpam-3900	30	50	lm	lm	PROPN
ejpam-3900	30	51	,	,	PUNCT
ejpam-3900	30	52	r(n	r(n	PROPN
ejpam-3900	30	53	,	,	PUNCT
ejpam-3900	30	54	k	k	NOUN
ejpam-3900	30	55	)	)	PUNCT
ejpam-3900	30	56	=	=	SYM
ejpam-3900	31	1	n∑	n∑	PROPN
ejpam-3900	31	2	j	j	PROPN
ejpam-3900	31	3	=	=	PROPN
ejpam-3900	31	4	k	k	PROPN
ejpam-3900	31	5	wm	wm	PROPN
ejpam-3900	31	6	,	,	PUNCT
ejpam-3900	31	7	r(n	r(n	PROPN
ejpam-3900	31	8	,	,	PUNCT
ejpam-3900	31	9	j)wm	j)wm	PROPN
ejpam-3900	31	10	,	,	PUNCT
ejpam-3900	31	11	r(j	r(j	PROPN
ejpam-3900	31	12	,	,	PUNCT
ejpam-3900	31	13	k	k	PROPN
ejpam-3900	31	14	)	)	PUNCT
ejpam-3900	31	15	,	,	PUNCT
ejpam-3900	31	16	which	which	PRON
ejpam-3900	31	17	generalizes	generalize	VERB
ejpam-3900	31	18	the	the	DET
ejpam-3900	31	19	identity	identity	NOUN
ejpam-3900	31	20	for	for	ADP
ejpam-3900	31	21	the	the	DET
ejpam-3900	31	22	lah	lah	PROPN
ejpam-3900	31	23	numbers	number	NOUN
ejpam-3900	31	24	in	in	ADP
ejpam-3900	31	25	terms	term	NOUN
ejpam-3900	31	26	of	of	ADP
ejpam-3900	31	27	the	the	DET
ejpam-3900	31	28	stirling	stirling	NOUN
ejpam-3900	31	29	numbers	number	NOUN
ejpam-3900	31	30	of	of	ADP
ejpam-3900	31	31	the	the	DET
ejpam-3900	31	32	first	first	ADJ
ejpam-3900	31	33	kind	kind	NOUN
ejpam-3900	31	34	and	and	CCONJ
ejpam-3900	31	35	the	the	DET
ejpam-3900	31	36	second	second	ADJ
ejpam-3900	31	37	kind	kind	NOUN
ejpam-3900	31	38	(	(	PUNCT
ejpam-3900	31	39	−1)nl(n	−1)nl(n	ADJ
ejpam-3900	31	40	,	,	PUNCT
ejpam-3900	31	41	k	k	NOUN
ejpam-3900	31	42	)	)	PUNCT
ejpam-3900	31	43	=	=	SYM
ejpam-3900	31	44	n∑	n∑	PROPN
ejpam-3900	31	45	j	j	PROPN
ejpam-3900	31	46	=	=	X
ejpam-3900	31	47	k	k	PROPN
ejpam-3900	31	48	(	(	PUNCT
ejpam-3900	31	49	−1)js(n	−1)js(n	PROPN
ejpam-3900	31	50	,	,	PUNCT
ejpam-3900	31	51	j)s(j	j)s(j	PROPN
ejpam-3900	31	52	,	,	PUNCT
ejpam-3900	31	53	k	k	NOUN
ejpam-3900	31	54	)	)	PUNCT
ejpam-3900	31	55	.	.	PUNCT
ejpam-3900	32	1	other	other	ADJ
ejpam-3900	32	2	properties	property	NOUN
ejpam-3900	32	3	for	for	ADP
ejpam-3900	32	4	lm	lm	PROPN
ejpam-3900	32	5	,	,	PUNCT
ejpam-3900	32	6	r(n	r(n	PROPN
ejpam-3900	32	7	,	,	PUNCT
ejpam-3900	32	8	k	k	NOUN
ejpam-3900	32	9	)	)	PUNCT
ejpam-3900	32	10	were	be	AUX
ejpam-3900	32	11	established	establish	VERB
ejpam-3900	32	12	by	by	ADP
ejpam-3900	32	13	means	mean	NOUN
ejpam-3900	32	14	of	of	ADP
ejpam-3900	32	15	its	its	PRON
ejpam-3900	32	16	horizontal	horizontal	ADJ
ejpam-3900	32	17	generating	generating	NOUN
ejpam-3900	32	18	function	function	NOUN
ejpam-3900	32	19	:	:	PUNCT
ejpam-3900	33	1	〈	〈	PROPN
ejpam-3900	33	2	x+	x+	X
ejpam-3900	33	3	2r|m〉n	2r|m〉n	NOUN
ejpam-3900	33	4	=	=	SYM
ejpam-3900	33	5	n∑	n∑	PROPN
ejpam-3900	33	6	k=0	k=0	PROPN
ejpam-3900	33	7	lm	lm	PROPN
ejpam-3900	33	8	,	,	PUNCT
ejpam-3900	33	9	r(n	r(n	PROPN
ejpam-3900	33	10	,	,	PUNCT
ejpam-3900	33	11	k)(x|m)k	k)(x|m)k	NOUN
ejpam-3900	33	12	,	,	PUNCT
ejpam-3900	33	13	where	where	SCONJ
ejpam-3900	33	14	〈	〈	PROPN
ejpam-3900	33	15	x+	x+	X
ejpam-3900	33	16	2r|m〉n	2r|m〉n	NOUN
ejpam-3900	33	17	=	=	SYM
ejpam-3900	33	18	{	{	PUNCT
ejpam-3900	33	19	(	(	PUNCT
ejpam-3900	33	20	x+	x+	PROPN
ejpam-3900	33	21	2r	2r	NUM
ejpam-3900	33	22	)	)	PUNCT
ejpam-3900	33	23	.	.	PUNCT
ejpam-3900	33	24	.	.	PUNCT
ejpam-3900	33	25	.	.	PUNCT
ejpam-3900	34	1	(	(	PUNCT
ejpam-3900	34	2	x+	x+	NUM
ejpam-3900	34	3	2r	2r	NUM
ejpam-3900	34	4	+	+	CCONJ
ejpam-3900	34	5	(	(	PUNCT
ejpam-3900	34	6	n−	n−	NOUN
ejpam-3900	34	7	1)m	1)m	NUM
ejpam-3900	34	8	)	)	PUNCT
ejpam-3900	34	9	,	,	PUNCT
ejpam-3900	34	10	n	n	X
ejpam-3900	34	11	≥	≥	NOUN
ejpam-3900	34	12	1	1	NUM
ejpam-3900	34	13	0	0	NUM
ejpam-3900	34	14	,	,	PUNCT
ejpam-3900	34	15	n	n	NOUN
ejpam-3900	34	16	=	=	SYM
ejpam-3900	34	17	0	0	NUM
ejpam-3900	34	18	,	,	PUNCT
ejpam-3900	34	19	r.	r.	PROPN
ejpam-3900	34	20	corcino	corcino	PROPN
ejpam-3900	34	21	,	,	PUNCT
ejpam-3900	34	22	j.	j.	PROPN
ejpam-3900	34	23	ontolan	ontolan	PROPN
ejpam-3900	34	24	,	,	PUNCT
ejpam-3900	34	25	m.	m.	NOUN
ejpam-3900	34	26	lobrigas	lobrigas	PROPN
ejpam-3900	34	27	/	/	SYM
ejpam-3900	34	28	eur	eur	PROPN
ejpam-3900	34	29	.	.	PUNCT
ejpam-3900	35	1	j.	j.	PROPN
ejpam-3900	35	2	pure	pure	PROPN
ejpam-3900	35	3	appl	appl	PROPN
ejpam-3900	35	4	.	.	PROPN
ejpam-3900	35	5	math	math	PROPN
ejpam-3900	35	6	,	,	PUNCT
ejpam-3900	35	7	14	14	NUM
ejpam-3900	35	8	(	(	PUNCT
ejpam-3900	35	9	1	1	NUM
ejpam-3900	35	10	)	)	PUNCT
ejpam-3900	35	11	(	(	PUNCT
ejpam-3900	35	12	2021	2021	NUM
ejpam-3900	35	13	)	)	PUNCT
ejpam-3900	35	14	,	,	PUNCT
ejpam-3900	35	15	65	65	NUM
ejpam-3900	35	16	-	-	SYM
ejpam-3900	35	17	81	81	NUM
ejpam-3900	35	18	67	67	NUM
ejpam-3900	35	19	and	and	CCONJ
ejpam-3900	35	20	the	the	DET
ejpam-3900	35	21	triangular	triangular	NOUN
ejpam-3900	35	22	recurrence	recurrence	NOUN
ejpam-3900	35	23	relation	relation	NOUN
ejpam-3900	35	24	lm	lm	PROPN
ejpam-3900	35	25	,	,	PUNCT
ejpam-3900	35	26	r(n	r(n	PROPN
ejpam-3900	35	27	,	,	PUNCT
ejpam-3900	35	28	k	k	NOUN
ejpam-3900	35	29	)	)	PUNCT
ejpam-3900	35	30	=	=	SYM
ejpam-3900	35	31	lm	lm	PROPN
ejpam-3900	35	32	,	,	PUNCT
ejpam-3900	35	33	r(n−	r(n−	NOUN
ejpam-3900	35	34	1	1	NUM
ejpam-3900	35	35	,	,	PUNCT
ejpam-3900	35	36	k	k	PROPN
ejpam-3900	35	37	−	−	PROPN
ejpam-3900	35	38	1	1	NUM
ejpam-3900	35	39	)	)	PUNCT
ejpam-3900	35	40	+	+	CCONJ
ejpam-3900	35	41	(	(	PUNCT
ejpam-3900	35	42	2r	2r	NUM
ejpam-3900	35	43	+	+	CCONJ
ejpam-3900	35	44	(	(	PUNCT
ejpam-3900	35	45	n+	n+	NUM
ejpam-3900	35	46	k	k	NOUN
ejpam-3900	36	1	−	−	PROPN
ejpam-3900	36	2	1)m)lm	1)m)lm	NUM
ejpam-3900	36	3	,	,	PUNCT
ejpam-3900	36	4	r(n−	r(n−	NOUN
ejpam-3900	36	5	1	1	NUM
ejpam-3900	36	6	,	,	PUNCT
ejpam-3900	36	7	k	k	NOUN
ejpam-3900	36	8	)	)	PUNCT
ejpam-3900	36	9	,	,	PUNCT
ejpam-3900	36	10	with	with	ADP
ejpam-3900	36	11	lm	lm	PROPN
ejpam-3900	36	12	,	,	PUNCT
ejpam-3900	36	13	r(n	r(n	PROPN
ejpam-3900	36	14	,	,	PUNCT
ejpam-3900	36	15	n	n	CCONJ
ejpam-3900	36	16	)	)	PUNCT
ejpam-3900	36	17	=	=	SYM
ejpam-3900	36	18	1	1	NUM
ejpam-3900	36	19	for	for	ADP
ejpam-3900	36	20	n	n	PRON
ejpam-3900	36	21	≥	≥	NOUN
ejpam-3900	36	22	0	0	NUM
ejpam-3900	36	23	and	and	CCONJ
ejpam-3900	36	24	lm	lm	INTJ
ejpam-3900	36	25	,	,	PUNCT
ejpam-3900	36	26	r(n	r(n	PROPN
ejpam-3900	36	27	,	,	PUNCT
ejpam-3900	36	28	n	n	CCONJ
ejpam-3900	36	29	)	)	PUNCT
ejpam-3900	36	30	=	=	SYM
ejpam-3900	36	31	0	0	NUM
ejpam-3900	36	32	for	for	ADP
ejpam-3900	36	33	n	n	X
ejpam-3900	36	34	<	<	X
ejpam-3900	36	35	k	k	X
ejpam-3900	36	36	,	,	PUNCT
ejpam-3900	36	37	or	or	CCONJ
ejpam-3900	36	38	n	n	CCONJ
ejpam-3900	36	39	,	,	PUNCT
ejpam-3900	36	40	k	k	X
ejpam-3900	36	41	<	<	X
ejpam-3900	36	42	0	0	X
ejpam-3900	36	43	.	.	PUNCT
ejpam-3900	37	1	we	we	PRON
ejpam-3900	37	2	can	can	AUX
ejpam-3900	37	3	use	use	VERB
ejpam-3900	37	4	the	the	DET
ejpam-3900	37	5	triangular	triangular	NOUN
ejpam-3900	37	6	recurrence	recurrence	NOUN
ejpam-3900	37	7	relation	relation	NOUN
ejpam-3900	37	8	to	to	PART
ejpam-3900	37	9	generate	generate	VERB
ejpam-3900	37	10	the	the	DET
ejpam-3900	37	11	first	first	ADJ
ejpam-3900	37	12	values	value	NOUN
ejpam-3900	37	13	of	of	ADP
ejpam-3900	37	14	lm	lm	PROPN
ejpam-3900	37	15	,	,	PUNCT
ejpam-3900	37	16	r(n	r(n	PROPN
ejpam-3900	37	17	,	,	PUNCT
ejpam-3900	37	18	k	k	NOUN
ejpam-3900	37	19	)	)	PUNCT
ejpam-3900	37	20	.	.	PUNCT
ejpam-3900	38	1	cillar	cillar	NOUN
ejpam-3900	38	2	and	and	CCONJ
ejpam-3900	38	3	corcino	corcino	NOUN
ejpam-3900	39	1	[	[	X
ejpam-3900	39	2	2	2	NUM
ejpam-3900	39	3	]	]	PUNCT
ejpam-3900	39	4	defined	define	VERB
ejpam-3900	39	5	the	the	DET
ejpam-3900	39	6	q	q	NOUN
ejpam-3900	39	7	-	-	PUNCT
ejpam-3900	39	8	analogue	analogue	NOUN
ejpam-3900	39	9	of	of	ADP
ejpam-3900	39	10	r	r	NOUN
ejpam-3900	39	11	-	-	PUNCT
ejpam-3900	39	12	whitney	whitney	NOUN
ejpam-3900	39	13	-	-	PUNCT
ejpam-3900	39	14	lah	lah	PROPN
ejpam-3900	39	15	numbers	number	NOUN
ejpam-3900	39	16	which	which	PRON
ejpam-3900	39	17	is	be	AUX
ejpam-3900	39	18	parallel	parallel	ADJ
ejpam-3900	39	19	to	to	ADP
ejpam-3900	39	20	cheon	cheon	PROPN
ejpam-3900	39	21	and	and	CCONJ
ejpam-3900	39	22	jung	jung	PROPN
ejpam-3900	39	23	’s	’s	PART
ejpam-3900	39	24	definition	definition	NOUN
ejpam-3900	39	25	of	of	ADP
ejpam-3900	39	26	r	r	PROPN
ejpam-3900	39	27	-	-	PUNCT
ejpam-3900	39	28	whitney	whitney	NOUN
ejpam-3900	39	29	-	-	PUNCT
ejpam-3900	39	30	lah	lah	PROPN
ejpam-3900	39	31	numbers	number	NOUN
ejpam-3900	39	32	lβ	lβ	ADP
ejpam-3900	39	33	,	,	PUNCT
ejpam-3900	39	34	r[n	r[n	NOUN
ejpam-3900	39	35	,	,	PUNCT
ejpam-3900	39	36	k]q	k]q	NOUN
ejpam-3900	39	37	=	=	SYM
ejpam-3900	40	1	n∑	n∑	PROPN
ejpam-3900	40	2	j	j	PROPN
ejpam-3900	41	1	=	=	PROPN
ejpam-3900	41	2	k	k	PROPN
ejpam-3900	41	3	φβ	φβ	PROPN
ejpam-3900	41	4	,	,	PUNCT
ejpam-3900	41	5	r[n	r[n	NOUN
ejpam-3900	41	6	,	,	PUNCT
ejpam-3900	41	7	j]qσ[j	j]qσ[j	ADJ
ejpam-3900	41	8	,	,	PUNCT
ejpam-3900	41	9	k]β	k]β	NOUN
ejpam-3900	41	10	,	,	PUNCT
ejpam-3900	41	11	rq	rq	NOUN
ejpam-3900	41	12	.	.	PUNCT
ejpam-3900	42	1	where	where	SCONJ
ejpam-3900	42	2	φβ	φβ	X
ejpam-3900	42	3	,	,	PUNCT
ejpam-3900	42	4	r[n	r[n	NOUN
ejpam-3900	42	5	,	,	PUNCT
ejpam-3900	42	6	j]q	j]q	NOUN
ejpam-3900	42	7	and	and	CCONJ
ejpam-3900	42	8	σ[j	σ[j	PROPN
ejpam-3900	42	9	,	,	PUNCT
ejpam-3900	42	10	k]β	k]β	PROPN
ejpam-3900	42	11	,	,	PUNCT
ejpam-3900	42	12	rq	rq	VERB
ejpam-3900	42	13	is	be	AUX
ejpam-3900	42	14	equivalent	equivalent	ADJ
ejpam-3900	42	15	to	to	ADP
ejpam-3900	42	16	wβ	wβ	ADP
ejpam-3900	42	17	,	,	PUNCT
ejpam-3900	42	18	r[n	r[n	NOUN
ejpam-3900	42	19	,	,	PUNCT
ejpam-3900	42	20	j]q	j]q	NOUN
ejpam-3900	42	21	and	and	CCONJ
ejpam-3900	42	22	wβ	wβ	ADP
ejpam-3900	42	23	,	,	PUNCT
ejpam-3900	42	24	r[n	r[n	NOUN
ejpam-3900	42	25	,	,	PUNCT
ejpam-3900	42	26	j]q	j]q	PROPN
ejpam-3900	42	27	,	,	PUNCT
ejpam-3900	42	28	respectively	respectively	ADV
ejpam-3900	42	29	.	.	PUNCT
ejpam-3900	43	1	they	they	PRON
ejpam-3900	43	2	also	also	ADV
ejpam-3900	43	3	obtained	obtain	VERB
ejpam-3900	43	4	some	some	DET
ejpam-3900	43	5	combinatorial	combinatorial	ADJ
ejpam-3900	43	6	properties	property	NOUN
ejpam-3900	43	7	.	.	PUNCT
ejpam-3900	44	1	their	their	PRON
ejpam-3900	44	2	results	result	NOUN
ejpam-3900	44	3	are	be	AUX
ejpam-3900	44	4	as	as	SCONJ
ejpam-3900	44	5	follows	follow	VERB
ejpam-3900	44	6	:	:	PUNCT
ejpam-3900	44	7	(	(	PUNCT
ejpam-3900	44	8	i	i	NOUN
ejpam-3900	44	9	)	)	PUNCT
ejpam-3900	44	10	horizontal	horizontal	ADJ
ejpam-3900	44	11	generating	generating	NOUN
ejpam-3900	44	12	function	function	NOUN
ejpam-3900	44	13	:	:	PUNCT
ejpam-3900	45	1	〈	〈	PROPN
ejpam-3900	45	2	t+	t+	NOUN
ejpam-3900	45	3	2[r]q|[β]q〉n	2[r]q|[β]q〉n	PRON
ejpam-3900	45	4	=	=	SYM
ejpam-3900	45	5	n∑	n∑	PROPN
ejpam-3900	45	6	k=0	k=0	PROPN
ejpam-3900	45	7	lβ	lβ	PROPN
ejpam-3900	45	8	,	,	PUNCT
ejpam-3900	45	9	r[n	r[n	PROPN
ejpam-3900	45	10	,	,	PUNCT
ejpam-3900	45	11	k]q(t|[β]q)k	k]q(t|[β]q)k	NOUN
ejpam-3900	45	12	where	where	SCONJ
ejpam-3900	45	13	〈	〈	PROPN
ejpam-3900	45	14	t+	t+	NOUN
ejpam-3900	45	15	2[r]q|[β]q〉n	2[r]q|[β]q〉n	PRON
ejpam-3900	45	16	=	=	SYM
ejpam-3900	45	17	{	{	PUNCT
ejpam-3900	45	18	πn−1	πn−1	PROPN
ejpam-3900	45	19	i=0	i=0	PROPN
ejpam-3900	45	20	(	(	PUNCT
ejpam-3900	45	21	t+	t+	NOUN
ejpam-3900	45	22	2[r]q	2[r]q	NOUN
ejpam-3900	45	23	+	+	CCONJ
ejpam-3900	45	24	[	[	X
ejpam-3900	45	25	iβ]q	iβ]q	ADJ
ejpam-3900	45	26	)	)	PUNCT
ejpam-3900	45	27	,	,	PUNCT
ejpam-3900	45	28	n	n	CCONJ
ejpam-3900	45	29	>	>	X
ejpam-3900	45	30	0	0	NUM
ejpam-3900	45	31	,	,	PUNCT
ejpam-3900	45	32	1	1	NUM
ejpam-3900	45	33	,	,	PUNCT
ejpam-3900	45	34	n	n	NOUN
ejpam-3900	45	35	=	=	SYM
ejpam-3900	45	36	0	0	PROPN
ejpam-3900	45	37	.	.	PUNCT
ejpam-3900	45	38	(	(	PUNCT
ejpam-3900	45	39	ii	ii	NOUN
ejpam-3900	45	40	)	)	PUNCT
ejpam-3900	45	41	recurrence	recurrence	NOUN
ejpam-3900	45	42	relation	relation	PROPN
ejpam-3900	45	43	:	:	PUNCT
ejpam-3900	45	44	lβ	lβ	PROPN
ejpam-3900	45	45	,	,	PUNCT
ejpam-3900	45	46	r[n	r[n	NOUN
ejpam-3900	45	47	,	,	PUNCT
ejpam-3900	45	48	k]q	k]q	NOUN
ejpam-3900	45	49	=	=	SYM
ejpam-3900	45	50	lβ	lβ	PROPN
ejpam-3900	45	51	,	,	PUNCT
ejpam-3900	45	52	r[n−	r[n−	ADJ
ejpam-3900	45	53	1	1	NUM
ejpam-3900	45	54	,	,	PUNCT
ejpam-3900	45	55	k	k	PROPN
ejpam-3900	45	56	−	−	PROPN
ejpam-3900	46	1	1]q	1]q	PROPN
ejpam-3900	47	1	+	+	CCONJ
ejpam-3900	47	2	(	(	PUNCT
ejpam-3900	47	3	2[r]q	2[r]q	NUM
ejpam-3900	47	4	+	+	CCONJ
ejpam-3900	48	1	[	[	PUNCT
ejpam-3900	48	2	kβ]q	kβ]q	NOUN
ejpam-3900	48	3	+	+	CCONJ
ejpam-3900	48	4	[	[	X
ejpam-3900	48	5	(	(	PUNCT
ejpam-3900	48	6	n−	n−	NOUN
ejpam-3900	48	7	1)β]q)lβ	1)β]q)lβ	NUM
ejpam-3900	48	8	,	,	PUNCT
ejpam-3900	48	9	r[n−	r[n−	NOUN
ejpam-3900	48	10	1	1	NUM
ejpam-3900	48	11	,	,	PUNCT
ejpam-3900	48	12	k]q	k]q	PROPN
ejpam-3900	48	13	,	,	PUNCT
ejpam-3900	48	14	with	with	ADP
ejpam-3900	48	15	lβ	lβ	PROPN
ejpam-3900	48	16	,	,	PUNCT
ejpam-3900	48	17	r[0	r[0	PROPN
ejpam-3900	48	18	,	,	PUNCT
ejpam-3900	48	19	0]q	0]q	NOUN
ejpam-3900	48	20	=	=	SYM
ejpam-3900	48	21	1	1	NUM
ejpam-3900	48	22	and	and	CCONJ
ejpam-3900	48	23	lβ	lβ	PROPN
ejpam-3900	48	24	,	,	PUNCT
ejpam-3900	48	25	r[n	r[n	NOUN
ejpam-3900	48	26	,	,	PUNCT
ejpam-3900	48	27	k]q	k]q	NOUN
ejpam-3900	48	28	=	=	NOUN
ejpam-3900	48	29	0	0	NUM
ejpam-3900	48	30	for	for	ADP
ejpam-3900	48	31	n	n	X
ejpam-3900	48	32	<	<	X
ejpam-3900	48	33	k	k	PROPN
ejpam-3900	48	34	or	or	CCONJ
ejpam-3900	48	35	n	n	CCONJ
ejpam-3900	48	36	,	,	PUNCT
ejpam-3900	48	37	k	k	X
ejpam-3900	48	38	<	<	X
ejpam-3900	48	39	0	0	X
ejpam-3900	48	40	.	.	PUNCT
ejpam-3900	49	1	recently	recently	ADV
ejpam-3900	49	2	,	,	PUNCT
ejpam-3900	49	3	a	a	DET
ejpam-3900	49	4	q	q	NOUN
ejpam-3900	49	5	-	-	PUNCT
ejpam-3900	49	6	analogue	analogue	NOUN
ejpam-3900	49	7	of	of	ADP
ejpam-3900	49	8	r	r	NOUN
ejpam-3900	49	9	-	-	PUNCT
ejpam-3900	49	10	whitney	whitney	NOUN
ejpam-3900	49	11	numbers	number	NOUN
ejpam-3900	49	12	of	of	ADP
ejpam-3900	49	13	the	the	DET
ejpam-3900	49	14	second	second	ADJ
ejpam-3900	49	15	kind	kind	NOUN
ejpam-3900	49	16	wm	wm	PROPN
ejpam-3900	49	17	,	,	PUNCT
ejpam-3900	49	18	r[n	r[n	NOUN
ejpam-3900	49	19	,	,	PUNCT
ejpam-3900	49	20	k]q	k]q	PROPN
ejpam-3900	49	21	,	,	PUNCT
ejpam-3900	49	22	also	also	ADV
ejpam-3900	49	23	known	know	VERB
ejpam-3900	49	24	as	as	ADP
ejpam-3900	49	25	(	(	PUNCT
ejpam-3900	49	26	q	q	ADJ
ejpam-3900	49	27	,	,	PUNCT
ejpam-3900	49	28	r)-whitney	r)-whitney	ADJ
ejpam-3900	49	29	number	number	NOUN
ejpam-3900	49	30	of	of	ADP
ejpam-3900	49	31	the	the	DET
ejpam-3900	49	32	second	second	ADJ
ejpam-3900	49	33	kind	kind	NOUN
ejpam-3900	49	34	,	,	PUNCT
ejpam-3900	49	35	was	be	AUX
ejpam-3900	49	36	introduced	introduce	VERB
ejpam-3900	49	37	in	in	ADP
ejpam-3900	49	38	[	[	X
ejpam-3900	49	39	3	3	NUM
ejpam-3900	49	40	,	,	PUNCT
ejpam-3900	49	41	6	6	NUM
ejpam-3900	49	42	]	]	PUNCT
ejpam-3900	49	43	by	by	ADP
ejpam-3900	49	44	means	mean	NOUN
ejpam-3900	49	45	of	of	ADP
ejpam-3900	49	46	the	the	DET
ejpam-3900	49	47	following	follow	VERB
ejpam-3900	49	48	triangular	triangular	NOUN
ejpam-3900	49	49	recurrence	recurrence	NOUN
ejpam-3900	49	50	relation	relation	NOUN
ejpam-3900	49	51	:	:	PUNCT
ejpam-3900	49	52	wm	wm	PROPN
ejpam-3900	49	53	,	,	PUNCT
ejpam-3900	49	54	r[n	r[n	NOUN
ejpam-3900	49	55	,	,	PUNCT
ejpam-3900	49	56	k]q	k]q	NOUN
ejpam-3900	49	57	=	=	SYM
ejpam-3900	49	58	qm(k−1)−rwm	qm(k−1)−rwm	PROPN
ejpam-3900	49	59	,	,	PUNCT
ejpam-3900	49	60	r[n−	r[n−	PROPN
ejpam-3900	49	61	1	1	NUM
ejpam-3900	49	62	,	,	PUNCT
ejpam-3900	49	63	k	k	PROPN
ejpam-3900	49	64	−	−	PROPN
ejpam-3900	50	1	1]q	1]q	PROPN
ejpam-3900	51	1	+	+	NUM
ejpam-3900	52	1	[	[	X
ejpam-3900	52	2	mk	mk	X
ejpam-3900	52	3	−	−	PROPN
ejpam-3900	52	4	r]qwm	r]qwm	NOUN
ejpam-3900	52	5	,	,	PUNCT
ejpam-3900	52	6	r[n−	r[n−	PROPN
ejpam-3900	52	7	1	1	NUM
ejpam-3900	52	8	,	,	PUNCT
ejpam-3900	52	9	k]q	k]q	PROPN
ejpam-3900	52	10	.	.	PUNCT
ejpam-3900	53	1	(	(	PUNCT
ejpam-3900	53	2	3	3	X
ejpam-3900	53	3	)	)	PUNCT
ejpam-3900	53	4	from	from	ADP
ejpam-3900	53	5	this	this	DET
ejpam-3900	53	6	definition	definition	NOUN
ejpam-3900	53	7	,	,	PUNCT
ejpam-3900	53	8	two	two	NUM
ejpam-3900	53	9	more	more	ADJ
ejpam-3900	53	10	forms	form	NOUN
ejpam-3900	53	11	of	of	ADP
ejpam-3900	53	12	the	the	DET
ejpam-3900	53	13	q	q	NOUN
ejpam-3900	53	14	-	-	PUNCT
ejpam-3900	53	15	analogue	analogue	NOUN
ejpam-3900	53	16	were	be	AUX
ejpam-3900	53	17	defined	define	VERB
ejpam-3900	53	18	in	in	ADP
ejpam-3900	53	19	[	[	X
ejpam-3900	53	20	3	3	NUM
ejpam-3900	53	21	,	,	PUNCT
ejpam-3900	53	22	6	6	NUM
ejpam-3900	53	23	]	]	PUNCT
ejpam-3900	53	24	as	as	ADP
ejpam-3900	53	25	w	w	PROPN
ejpam-3900	53	26	∗m	∗m	NOUN
ejpam-3900	53	27	,	,	PUNCT
ejpam-3900	53	28	r[n	r[n	NOUN
ejpam-3900	53	29	,	,	PUNCT
ejpam-3900	53	30	k]q	k]q	ADV
ejpam-3900	53	31	:	:	PUNCT
ejpam-3900	53	32	=	=	SYM
ejpam-3900	53	33	q−kr−m(k2)wm	q−kr−m(k2)wm	NOUN
ejpam-3900	53	34	,	,	PUNCT
ejpam-3900	53	35	r[n	r[n	NOUN
ejpam-3900	53	36	,	,	PUNCT
ejpam-3900	53	37	k]q	k]q	X
ejpam-3900	53	38	(	(	PUNCT
ejpam-3900	53	39	4	4	NUM
ejpam-3900	53	40	)	)	PUNCT
ejpam-3900	53	41	w̃m	w̃m	PROPN
ejpam-3900	53	42	,	,	PUNCT
ejpam-3900	53	43	r[n	r[n	NOUN
ejpam-3900	53	44	,	,	PUNCT
ejpam-3900	53	45	k]q	k]q	ADV
ejpam-3900	53	46	:	:	PUNCT
ejpam-3900	53	47	=	=	NUM
ejpam-3900	53	48	qkrw	qkrw	ADJ
ejpam-3900	53	49	∗m	∗m	NOUN
ejpam-3900	53	50	,	,	PUNCT
ejpam-3900	53	51	r[n	r[n	NOUN
ejpam-3900	53	52	,	,	PUNCT
ejpam-3900	53	53	k]q	k]q	NOUN
ejpam-3900	53	54	=	=	SYM
ejpam-3900	53	55	q−m(k2)wm	q−m(k2)wm	NOUN
ejpam-3900	53	56	,	,	PUNCT
ejpam-3900	53	57	r[n	r[n	NOUN
ejpam-3900	53	58	,	,	PUNCT
ejpam-3900	53	59	k]q	k]q	PROPN
ejpam-3900	53	60	,	,	PUNCT
ejpam-3900	53	61	(	(	PUNCT
ejpam-3900	53	62	5	5	NUM
ejpam-3900	53	63	)	)	PUNCT
ejpam-3900	53	64	where	where	SCONJ
ejpam-3900	53	65	w	w	ADP
ejpam-3900	53	66	∗m	∗m	NOUN
ejpam-3900	53	67	,	,	PUNCT
ejpam-3900	53	68	r[n	r[n	NOUN
ejpam-3900	53	69	,	,	PUNCT
ejpam-3900	53	70	k]q	k]q	NOUN
ejpam-3900	53	71	and	and	CCONJ
ejpam-3900	53	72	w̃m	w̃m	PROPN
ejpam-3900	53	73	,	,	PUNCT
ejpam-3900	53	74	r[n	r[n	NOUN
ejpam-3900	53	75	,	,	PUNCT
ejpam-3900	53	76	k]q	k]q	NOUN
ejpam-3900	53	77	denote	denote	VERB
ejpam-3900	53	78	the	the	DET
ejpam-3900	53	79	second	second	ADJ
ejpam-3900	53	80	and	and	CCONJ
ejpam-3900	53	81	third	third	ADJ
ejpam-3900	53	82	forms	form	NOUN
ejpam-3900	53	83	of	of	ADP
ejpam-3900	53	84	the	the	DET
ejpam-3900	53	85	q	q	NOUN
ejpam-3900	53	86	-	-	PUNCT
ejpam-3900	53	87	analogue	analogue	NOUN
ejpam-3900	53	88	,	,	PUNCT
ejpam-3900	53	89	respectively	respectively	ADV
ejpam-3900	53	90	.	.	PUNCT
ejpam-3900	54	1	corresponding	correspond	VERB
ejpam-3900	54	2	to	to	ADP
ejpam-3900	54	3	the	the	DET
ejpam-3900	54	4	q	q	NOUN
ejpam-3900	54	5	-	-	PUNCT
ejpam-3900	54	6	analogues	analogue	NOUN
ejpam-3900	54	7	in	in	ADP
ejpam-3900	54	8	equations	equation	NOUN
ejpam-3900	54	9	(	(	PUNCT
ejpam-3900	54	10	3	3	NUM
ejpam-3900	54	11	)	)	PUNCT
ejpam-3900	54	12	,	,	PUNCT
ejpam-3900	54	13	(	(	PUNCT
ejpam-3900	54	14	4	4	NUM
ejpam-3900	54	15	)	)	PUNCT
ejpam-3900	54	16	and	and	CCONJ
ejpam-3900	54	17	(	(	PUNCT
ejpam-3900	54	18	5	5	NUM
ejpam-3900	54	19	)	)	PUNCT
ejpam-3900	54	20	,	,	PUNCT
ejpam-3900	54	21	three	three	NUM
ejpam-3900	54	22	forms	form	NOUN
ejpam-3900	54	23	r.	r.	PROPN
ejpam-3900	54	24	corcino	corcino	PROPN
ejpam-3900	54	25	,	,	PUNCT
ejpam-3900	54	26	j.	j.	PROPN
ejpam-3900	54	27	ontolan	ontolan	PROPN
ejpam-3900	54	28	,	,	PUNCT
ejpam-3900	54	29	m.	m.	NOUN
ejpam-3900	54	30	lobrigas	lobrigas	PROPN
ejpam-3900	54	31	/	/	SYM
ejpam-3900	54	32	eur	eur	PROPN
ejpam-3900	54	33	.	.	PUNCT
ejpam-3900	55	1	j.	j.	PROPN
ejpam-3900	55	2	pure	pure	PROPN
ejpam-3900	55	3	appl	appl	PROPN
ejpam-3900	55	4	.	.	PROPN
ejpam-3900	55	5	math	math	PROPN
ejpam-3900	55	6	,	,	PUNCT
ejpam-3900	55	7	14	14	NUM
ejpam-3900	55	8	(	(	PUNCT
ejpam-3900	55	9	1	1	NUM
ejpam-3900	55	10	)	)	PUNCT
ejpam-3900	55	11	(	(	PUNCT
ejpam-3900	55	12	2021	2021	NUM
ejpam-3900	55	13	)	)	PUNCT
ejpam-3900	55	14	,	,	PUNCT
ejpam-3900	55	15	65	65	NUM
ejpam-3900	55	16	-	-	SYM
ejpam-3900	55	17	81	81	NUM
ejpam-3900	55	18	68	68	NUM
ejpam-3900	55	19	of	of	ADP
ejpam-3900	55	20	q	q	NOUN
ejpam-3900	55	21	-	-	PUNCT
ejpam-3900	55	22	analogues	analogue	NOUN
ejpam-3900	55	23	for	for	ADP
ejpam-3900	55	24	r	r	NOUN
ejpam-3900	55	25	-	-	PUNCT
ejpam-3900	55	26	dowling	dowle	VERB
ejpam-3900	55	27	numbers	number	NOUN
ejpam-3900	55	28	(	(	PUNCT
ejpam-3900	55	29	also	also	ADV
ejpam-3900	55	30	known	know	VERB
ejpam-3900	55	31	as	as	ADP
ejpam-3900	55	32	(	(	PUNCT
ejpam-3900	55	33	q	q	ADJ
ejpam-3900	55	34	,	,	PUNCT
ejpam-3900	55	35	r)-dowling	r)-dowling	ADJ
ejpam-3900	55	36	numbers	number	NOUN
ejpam-3900	55	37	)	)	PUNCT
ejpam-3900	55	38	were	be	AUX
ejpam-3900	55	39	also	also	ADV
ejpam-3900	55	40	defined	define	VERB
ejpam-3900	55	41	as	as	SCONJ
ejpam-3900	55	42	follows	follow	VERB
ejpam-3900	55	43	:	:	PUNCT
ejpam-3900	56	1	dm	dm	NUM
ejpam-3900	56	2	,	,	PUNCT
ejpam-3900	56	3	r[n]q	r[n]q	NOUN
ejpam-3900	56	4	:	:	PUNCT
ejpam-3900	57	1	=	=	SYM
ejpam-3900	57	2	n∑	n∑	PROPN
ejpam-3900	57	3	k=0	k=0	PROPN
ejpam-3900	57	4	wm	wm	PROPN
ejpam-3900	57	5	,	,	PUNCT
ejpam-3900	57	6	r[n	r[n	NOUN
ejpam-3900	57	7	,	,	PUNCT
ejpam-3900	57	8	k]q	k]q	X
ejpam-3900	57	9	(	(	PUNCT
ejpam-3900	57	10	6	6	NUM
ejpam-3900	57	11	)	)	PUNCT
ejpam-3900	57	12	d∗m	d∗m	NOUN
ejpam-3900	57	13	,	,	PUNCT
ejpam-3900	57	14	r[n]q	r[n]q	NOUN
ejpam-3900	57	15	:	:	PUNCT
ejpam-3900	58	1	=	=	SYM
ejpam-3900	58	2	n∑	n∑	PROPN
ejpam-3900	58	3	k=0	k=0	PROPN
ejpam-3900	58	4	w	w	ADP
ejpam-3900	58	5	∗m	∗m	PROPN
ejpam-3900	58	6	,	,	PUNCT
ejpam-3900	58	7	r[n	r[n	NOUN
ejpam-3900	58	8	,	,	PUNCT
ejpam-3900	58	9	k]q	k]q	X
ejpam-3900	58	10	(	(	PUNCT
ejpam-3900	58	11	7	7	NUM
ejpam-3900	58	12	)	)	PUNCT
ejpam-3900	58	13	d̃m	d̃m	PROPN
ejpam-3900	58	14	,	,	PUNCT
ejpam-3900	58	15	r[n]q	r[n]q	VERB
ejpam-3900	58	16	:	:	PUNCT
ejpam-3900	58	17	=	=	SYM
ejpam-3900	58	18	n∑	n∑	PROPN
ejpam-3900	58	19	k=0	k=0	PROPN
ejpam-3900	58	20	w̃m	w̃m	PROPN
ejpam-3900	58	21	,	,	PUNCT
ejpam-3900	58	22	r[n	r[n	NOUN
ejpam-3900	58	23	,	,	PUNCT
ejpam-3900	58	24	k]q	k]q	PROPN
ejpam-3900	58	25	.	.	PUNCT
ejpam-3900	59	1	(	(	PUNCT
ejpam-3900	59	2	8)	8)	NUM
ejpam-3900	59	3	the	the	DET
ejpam-3900	59	4	focus	focus	NOUN
ejpam-3900	59	5	in	in	ADP
ejpam-3900	59	6	this	this	DET
ejpam-3900	59	7	paper	paper	NOUN
ejpam-3900	59	8	is	be	AUX
ejpam-3900	59	9	on	on	ADP
ejpam-3900	59	10	the	the	DET
ejpam-3900	59	11	first	first	ADJ
ejpam-3900	59	12	form	form	NOUN
ejpam-3900	59	13	of	of	ADP
ejpam-3900	59	14	the	the	DET
ejpam-3900	59	15	q	q	NOUN
ejpam-3900	59	16	-	-	NOUN
ejpam-3900	59	17	analogue	analogue	NOUN
ejpam-3900	59	18	.	.	PUNCT
ejpam-3900	60	1	the	the	DET
ejpam-3900	60	2	following	follow	VERB
ejpam-3900	60	3	results	result	NOUN
ejpam-3900	60	4	are	be	AUX
ejpam-3900	60	5	obtained	obtain	VERB
ejpam-3900	60	6	for	for	ADP
ejpam-3900	60	7	the	the	DET
ejpam-3900	60	8	first	first	ADJ
ejpam-3900	60	9	form	form	NOUN
ejpam-3900	60	10	(	(	PUNCT
ejpam-3900	60	11	q	q	X
ejpam-3900	60	12	,	,	PUNCT
ejpam-3900	60	13	r)-whitney	r)-whitney	NOUN
ejpam-3900	60	14	numbers	number	NOUN
ejpam-3900	60	15	of	of	ADP
ejpam-3900	60	16	the	the	DET
ejpam-3900	60	17	second	second	ADJ
ejpam-3900	60	18	kind	kind	NOUN
ejpam-3900	60	19	:	:	PUNCT
ejpam-3900	60	20	(	(	PUNCT
ejpam-3900	60	21	i	i	NOUN
ejpam-3900	60	22	)	)	PUNCT
ejpam-3900	60	23	vertical	vertical	ADJ
ejpam-3900	60	24	and	and	CCONJ
ejpam-3900	60	25	horizontal	horizontal	ADJ
ejpam-3900	60	26	recurrence	recurrence	NOUN
ejpam-3900	60	27	relations	relations	PROPN
ejpam-3900	60	28	wm	wm	PROPN
ejpam-3900	60	29	,	,	PUNCT
ejpam-3900	60	30	r[n+	r[n+	NOUN
ejpam-3900	60	31	1	1	NUM
ejpam-3900	60	32	,	,	PUNCT
ejpam-3900	60	33	k	k	PROPN
ejpam-3900	60	34	+	+	PROPN
ejpam-3900	61	1	1]q	1]q	NUM
ejpam-3900	61	2	=	=	SYM
ejpam-3900	61	3	qmk+r	qmk+r	PROPN
ejpam-3900	61	4	n∑	n∑	PROPN
ejpam-3900	61	5	j	j	PROPN
ejpam-3900	62	1	=	=	PROPN
ejpam-3900	62	2	k	k	PROPN
ejpam-3900	63	1	[	[	X
ejpam-3900	63	2	m(k	m(k	PROPN
ejpam-3900	63	3	+	+	CCONJ
ejpam-3900	63	4	1	1	NUM
ejpam-3900	63	5	)	)	PUNCT
ejpam-3900	63	6	+	+	NUM
ejpam-3900	63	7	r]n−jq	r]n−jq	VERB
ejpam-3900	63	8	wm	wm	PROPN
ejpam-3900	63	9	,	,	PUNCT
ejpam-3900	63	10	r[j	r[j	NOUN
ejpam-3900	63	11	,	,	PUNCT
ejpam-3900	63	12	k]q	k]q	X
ejpam-3900	63	13	(	(	PUNCT
ejpam-3900	63	14	9	9	NUM
ejpam-3900	63	15	)	)	PUNCT
ejpam-3900	63	16	wm	wm	PROPN
ejpam-3900	63	17	,	,	PUNCT
ejpam-3900	63	18	r[n	r[n	NOUN
ejpam-3900	63	19	,	,	PUNCT
ejpam-3900	63	20	k]q	k]q	PROPN
ejpam-3900	63	21	=	=	PUNCT
ejpam-3900	63	22	n−k∑	n−k∑	NOUN
ejpam-3900	63	23	j=0	j=0	PROPN
ejpam-3900	63	24	(	(	PUNCT
ejpam-3900	63	25	−1)jq−r−m(k+j	−1)jq−r−m(k+j	PROPN
ejpam-3900	63	26	)	)	PUNCT
ejpam-3900	63	27	rk+j+1,q	rk+j+1,q	PROPN
ejpam-3900	63	28	rk+1,q	rk+1,q	PROPN
ejpam-3900	63	29	wm	wm	PROPN
ejpam-3900	63	30	,	,	PUNCT
ejpam-3900	63	31	r[n+	r[n+	NOUN
ejpam-3900	63	32	1	1	NUM
ejpam-3900	63	33	,	,	PUNCT
ejpam-3900	63	34	k	k	PROPN
ejpam-3900	63	35	+	+	NUM
ejpam-3900	63	36	j	j	PROPN
ejpam-3900	63	37	+	+	CCONJ
ejpam-3900	63	38	1]q	1]q	NUM
ejpam-3900	63	39	(	(	PUNCT
ejpam-3900	63	40	10	10	NUM
ejpam-3900	63	41	)	)	PUNCT
ejpam-3900	63	42	respectively	respectively	ADV
ejpam-3900	63	43	,	,	PUNCT
ejpam-3900	63	44	where	where	SCONJ
ejpam-3900	63	45	ri	ri	NOUN
ejpam-3900	63	46	,	,	PUNCT
ejpam-3900	63	47	q	q	NOUN
ejpam-3900	63	48	=	=	SYM
ejpam-3900	63	49	i−1∏	i−1∏	PROPN
ejpam-3900	63	50	h=1	h=1	PUNCT
ejpam-3900	63	51	q−r−mh+m[mh+	q−r−mh+m[mh+	NOUN
ejpam-3900	63	52	r]q	r]q	VERB
ejpam-3900	63	53	with	with	ADP
ejpam-3900	63	54	initial	initial	ADJ
ejpam-3900	63	55	value	value	NOUN
ejpam-3900	63	56	wm	wm	PROPN
ejpam-3900	63	57	,	,	PUNCT
ejpam-3900	63	58	r[0	r[0	PROPN
ejpam-3900	63	59	,	,	PUNCT
ejpam-3900	63	60	0]q	0]q	NOUN
ejpam-3900	63	61	=	=	SYM
ejpam-3900	64	1	1	1	X
ejpam-3900	64	2	.	.	PUNCT
ejpam-3900	64	3	(	(	PUNCT
ejpam-3900	64	4	ii	ii	NOUN
ejpam-3900	64	5	)	)	PUNCT
ejpam-3900	64	6	horizontal	horizontal	ADJ
ejpam-3900	64	7	generating	generating	NOUN
ejpam-3900	64	8	function	function	NOUN
ejpam-3900	64	9	n∑	n∑	PROPN
ejpam-3900	64	10	k=0	k=0	PROPN
ejpam-3900	64	11	wm	wm	PROPN
ejpam-3900	64	12	,	,	PUNCT
ejpam-3900	64	13	r[n	r[n	NOUN
ejpam-3900	64	14	,	,	PUNCT
ejpam-3900	64	15	k]q[t−	k]q[t−	NOUN
ejpam-3900	64	16	r|m]k	r|m]k	NUM
ejpam-3900	64	17	,	,	PUNCT
ejpam-3900	64	18	q	q	NOUN
ejpam-3900	65	1	=	=	PUNCT
ejpam-3900	66	1	[	[	X
ejpam-3900	66	2	t]nq	t]nq	NOUN
ejpam-3900	66	3	.	.	PUNCT
ejpam-3900	67	1	(	(	PUNCT
ejpam-3900	67	2	11	11	NUM
ejpam-3900	67	3	)	)	PUNCT
ejpam-3900	67	4	(	(	PUNCT
ejpam-3900	67	5	iii	iii	NOUN
ejpam-3900	67	6	)	)	PUNCT
ejpam-3900	67	7	explicit	explicit	ADJ
ejpam-3900	67	8	formula	formula	NOUN
ejpam-3900	67	9	wm	wm	PROPN
ejpam-3900	67	10	,	,	PUNCT
ejpam-3900	67	11	r[n	r[n	NOUN
ejpam-3900	67	12	,	,	PUNCT
ejpam-3900	67	13	k]q	k]q	NOUN
ejpam-3900	67	14	=	=	SYM
ejpam-3900	67	15	1	1	NUM
ejpam-3900	68	1	[	[	X
ejpam-3900	68	2	k]qm	k]qm	X
ejpam-3900	68	3	!	!	PUNCT
ejpam-3900	69	1	[	[	X
ejpam-3900	69	2	m]kq	m]kq	PROPN
ejpam-3900	69	3	k∑	k∑	VERB
ejpam-3900	69	4	j=0	j=0	PROPN
ejpam-3900	69	5	(	(	PUNCT
ejpam-3900	69	6	−1)k−jqm(k−j	−1)k−jqm(k−j	NUM
ejpam-3900	69	7	2	2	NUM
ejpam-3900	69	8	)	)	PUNCT
ejpam-3900	69	9	[	[	PUNCT
ejpam-3900	69	10	k	k	PROPN
ejpam-3900	69	11	j	j	PROPN
ejpam-3900	69	12	]	]	PUNCT
ejpam-3900	69	13	qm	qm	PROPN
ejpam-3900	70	1	[	[	X
ejpam-3900	70	2	jm+	jm+	X
ejpam-3900	70	3	r]nq	r]nq	NOUN
ejpam-3900	70	4	.	.	PUNCT
ejpam-3900	71	1	(	(	PUNCT
ejpam-3900	71	2	12	12	NUM
ejpam-3900	71	3	)	)	PUNCT
ejpam-3900	71	4	(	(	PUNCT
ejpam-3900	71	5	iv	iv	X
ejpam-3900	71	6	)	)	PUNCT
ejpam-3900	71	7	exponential	exponential	NOUN
ejpam-3900	71	8	generating	generating	NOUN
ejpam-3900	71	9	function	function	NOUN
ejpam-3900	71	10	∑	∑	PROPN
ejpam-3900	71	11	n≥0	n≥0	PROPN
ejpam-3900	71	12	wm	wm	PROPN
ejpam-3900	71	13	,	,	PUNCT
ejpam-3900	71	14	r[n	r[n	NOUN
ejpam-3900	71	15	,	,	PUNCT
ejpam-3900	71	16	k]q	k]q	VERB
ejpam-3900	72	1	[	[	X
ejpam-3900	72	2	t]nq	t]nq	NOUN
ejpam-3900	72	3	[	[	X
ejpam-3900	72	4	n]q	n]q	X
ejpam-3900	72	5	!	!	PUNCT
ejpam-3900	73	1	=	=	SYM
ejpam-3900	73	2	1	1	NUM
ejpam-3900	74	1	[	[	X
ejpam-3900	74	2	k]qm	k]qm	X
ejpam-3900	74	3	!	!	PUNCT
ejpam-3900	75	1	[	[	X
ejpam-3900	75	2	m]kq	m]kq	X
ejpam-3900	75	3	[	[	X
ejpam-3900	75	4	∆qm	∆qm	X
ejpam-3900	75	5	,	,	PUNCT
ejpam-3900	75	6	mkeq([x+	mkeq([x+	ADJ
ejpam-3900	75	7	jm+	jm+	NOUN
ejpam-3900	75	8	r]q[t]q)]x=0	r]q[t]q)]x=0	VERB
ejpam-3900	75	9	.	.	PUNCT
ejpam-3900	76	1	(	(	PUNCT
ejpam-3900	76	2	13	13	NUM
ejpam-3900	76	3	)	)	PUNCT
ejpam-3900	76	4	r.	r.	PROPN
ejpam-3900	76	5	corcino	corcino	PROPN
ejpam-3900	76	6	,	,	PUNCT
ejpam-3900	76	7	j.	j.	PROPN
ejpam-3900	76	8	ontolan	ontolan	PROPN
ejpam-3900	76	9	,	,	PUNCT
ejpam-3900	76	10	m.	m.	NOUN
ejpam-3900	76	11	lobrigas	lobrigas	PROPN
ejpam-3900	76	12	/	/	SYM
ejpam-3900	76	13	eur	eur	PROPN
ejpam-3900	76	14	.	.	PUNCT
ejpam-3900	77	1	j.	j.	PROPN
ejpam-3900	77	2	pure	pure	PROPN
ejpam-3900	77	3	appl	appl	PROPN
ejpam-3900	77	4	.	.	PROPN
ejpam-3900	77	5	math	math	PROPN
ejpam-3900	77	6	,	,	PUNCT
ejpam-3900	77	7	14	14	NUM
ejpam-3900	77	8	(	(	PUNCT
ejpam-3900	77	9	1	1	NUM
ejpam-3900	77	10	)	)	PUNCT
ejpam-3900	77	11	(	(	PUNCT
ejpam-3900	77	12	2021	2021	NUM
ejpam-3900	77	13	)	)	PUNCT
ejpam-3900	77	14	,	,	PUNCT
ejpam-3900	77	15	65	65	NUM
ejpam-3900	77	16	-	-	SYM
ejpam-3900	77	17	81	81	NUM
ejpam-3900	77	18	69	69	NUM
ejpam-3900	77	19	(	(	PUNCT
ejpam-3900	77	20	v	v	NOUN
ejpam-3900	77	21	)	)	PUNCT
ejpam-3900	77	22	rational	rational	ADJ
ejpam-3900	77	23	generating	generating	NOUN
ejpam-3900	77	24	function	function	NOUN
ejpam-3900	77	25	ψk(t	ψk(t	NOUN
ejpam-3900	77	26	)	)	PUNCT
ejpam-3900	78	1	=	=	PUNCT
ejpam-3900	78	2	∑	∑	PROPN
ejpam-3900	78	3	n≥k	n≥k	PROPN
ejpam-3900	78	4	wm	wm	PROPN
ejpam-3900	78	5	,	,	PUNCT
ejpam-3900	78	6	r[n	r[n	NOUN
ejpam-3900	78	7	,	,	PUNCT
ejpam-3900	78	8	k]q[t	k]q[t	X
ejpam-3900	78	9	]	]	X
ejpam-3900	78	10	n	n	PRON
ejpam-3900	78	11	q	q	NOUN
ejpam-3900	78	12	=	=	SYM
ejpam-3900	78	13	qm(k2)+kr[t]kq∏k	qm(k2)+kr[t]kq∏k	PROPN
ejpam-3900	78	14	j=0(1−	j=0(1−	PROPN
ejpam-3900	78	15	[	[	X
ejpam-3900	78	16	mj	mj	X
ejpam-3900	78	17	+	+	NUM
ejpam-3900	78	18	r]q[t]q	r]q[t]q	NUM
ejpam-3900	78	19	)	)	PUNCT
ejpam-3900	78	20	.	.	PUNCT
ejpam-3900	79	1	(	(	PUNCT
ejpam-3900	79	2	14	14	NUM
ejpam-3900	79	3	)	)	PUNCT
ejpam-3900	79	4	the	the	DET
ejpam-3900	79	5	purpose	purpose	NOUN
ejpam-3900	79	6	of	of	ADP
ejpam-3900	79	7	introducing	introduce	VERB
ejpam-3900	79	8	these	these	DET
ejpam-3900	79	9	new	new	ADJ
ejpam-3900	79	10	q	q	NOUN
ejpam-3900	79	11	-	-	PUNCT
ejpam-3900	79	12	analogues	analogue	NOUN
ejpam-3900	79	13	of	of	ADP
ejpam-3900	79	14	r	r	NOUN
ejpam-3900	79	15	-	-	PUNCT
ejpam-3900	79	16	whitney	whitney	NOUN
ejpam-3900	79	17	and	and	CCONJ
ejpam-3900	79	18	r	r	NOUN
ejpam-3900	79	19	-	-	PUNCT
ejpam-3900	79	20	dowling	dowle	VERB
ejpam-3900	79	21	numbers	number	NOUN
ejpam-3900	79	22	is	be	AUX
ejpam-3900	79	23	to	to	PART
ejpam-3900	79	24	address	address	VERB
ejpam-3900	79	25	the	the	DET
ejpam-3900	79	26	conjecture	conjecture	NOUN
ejpam-3900	79	27	in	in	ADP
ejpam-3900	79	28	the	the	DET
ejpam-3900	79	29	paper	paper	NOUN
ejpam-3900	79	30	of	of	ADP
ejpam-3900	79	31	corcino	corcino	NOUN
ejpam-3900	79	32	-	-	PUNCT
ejpam-3900	79	33	corcino	corcino	NOUN
ejpam-3900	79	34	[	[	X
ejpam-3900	79	35	4	4	NUM
ejpam-3900	79	36	]	]	PUNCT
ejpam-3900	79	37	.	.	PUNCT
ejpam-3900	80	1	that	that	PRON
ejpam-3900	80	2	is	be	AUX
ejpam-3900	80	3	,	,	PUNCT
ejpam-3900	80	4	to	to	PART
ejpam-3900	80	5	establish	establish	VERB
ejpam-3900	80	6	the	the	DET
ejpam-3900	80	7	hankel	hankel	NOUN
ejpam-3900	80	8	transform	transform	NOUN
ejpam-3900	80	9	of	of	ADP
ejpam-3900	80	10	the	the	DET
ejpam-3900	80	11	q	q	NOUN
ejpam-3900	80	12	-	-	PUNCT
ejpam-3900	80	13	analogue	analogue	NOUN
ejpam-3900	80	14	of	of	ADP
ejpam-3900	80	15	(	(	PUNCT
ejpam-3900	80	16	r	r	NOUN
ejpam-3900	80	17	,	,	PUNCT
ejpam-3900	80	18	β)-stirling	β)-stirle	VERB
ejpam-3900	80	19	numbers	number	NOUN
ejpam-3900	80	20	,	,	PUNCT
ejpam-3900	80	21	which	which	PRON
ejpam-3900	80	22	are	be	AUX
ejpam-3900	80	23	exactly	exactly	ADV
ejpam-3900	80	24	the	the	DET
ejpam-3900	80	25	r	r	NOUN
ejpam-3900	80	26	-	-	PUNCT
ejpam-3900	80	27	dowling	dowle	VERB
ejpam-3900	80	28	numbers	number	NOUN
ejpam-3900	80	29	.	.	PUNCT
ejpam-3900	81	1	in	in	ADP
ejpam-3900	81	2	establishing	establish	VERB
ejpam-3900	81	3	the	the	DET
ejpam-3900	81	4	hankel	hankel	NOUN
ejpam-3900	81	5	transforms	transform	VERB
ejpam-3900	81	6	of	of	ADP
ejpam-3900	81	7	these	these	DET
ejpam-3900	81	8	three	three	NUM
ejpam-3900	81	9	forms	form	NOUN
ejpam-3900	81	10	of	of	ADP
ejpam-3900	81	11	(	(	PUNCT
ejpam-3900	81	12	q	q	INTJ
ejpam-3900	81	13	,	,	PUNCT
ejpam-3900	81	14	r)dowling	r)dowle	VERB
ejpam-3900	81	15	numbers	number	NOUN
ejpam-3900	81	16	,	,	PUNCT
ejpam-3900	81	17	the	the	DET
ejpam-3900	81	18	hankel	hankel	NOUN
ejpam-3900	81	19	transform	transform	NOUN
ejpam-3900	81	20	of	of	ADP
ejpam-3900	81	21	the	the	DET
ejpam-3900	81	22	third	third	ADJ
ejpam-3900	81	23	form	form	NOUN
ejpam-3900	81	24	was	be	AUX
ejpam-3900	81	25	the	the	DET
ejpam-3900	81	26	first	first	ADJ
ejpam-3900	81	27	one	one	NUM
ejpam-3900	81	28	being	be	AUX
ejpam-3900	81	29	established	establish	VERB
ejpam-3900	81	30	and	and	CCONJ
ejpam-3900	81	31	followed	follow	VERB
ejpam-3900	81	32	by	by	ADP
ejpam-3900	81	33	the	the	DET
ejpam-3900	81	34	second	second	ADJ
ejpam-3900	81	35	form	form	NOUN
ejpam-3900	81	36	.	.	PUNCT
ejpam-3900	82	1	for	for	ADP
ejpam-3900	82	2	the	the	DET
ejpam-3900	82	3	first	first	ADJ
ejpam-3900	82	4	form	form	NOUN
ejpam-3900	82	5	,	,	PUNCT
ejpam-3900	82	6	it	it	PRON
ejpam-3900	82	7	is	be	AUX
ejpam-3900	82	8	still	still	ADV
ejpam-3900	82	9	on	on	ADP
ejpam-3900	82	10	the	the	DET
ejpam-3900	82	11	process	process	NOUN
ejpam-3900	82	12	of	of	ADP
ejpam-3900	82	13	constructing	construct	VERB
ejpam-3900	82	14	the	the	DET
ejpam-3900	82	15	method	method	NOUN
ejpam-3900	82	16	that	that	PRON
ejpam-3900	82	17	can	can	AUX
ejpam-3900	82	18	possibly	possibly	ADV
ejpam-3900	82	19	be	be	AUX
ejpam-3900	82	20	used	use	VERB
ejpam-3900	82	21	to	to	PART
ejpam-3900	82	22	derive	derive	VERB
ejpam-3900	82	23	it	it	PRON
ejpam-3900	82	24	.	.	PUNCT
ejpam-3900	83	1	in	in	ADP
ejpam-3900	83	2	this	this	DET
ejpam-3900	83	3	paper	paper	NOUN
ejpam-3900	83	4	,	,	PUNCT
ejpam-3900	83	5	(	(	PUNCT
ejpam-3900	83	6	q	q	ADJ
ejpam-3900	83	7	,	,	PUNCT
ejpam-3900	83	8	r)-whitney	r)-whitney	ADJ
ejpam-3900	83	9	-	-	PUNCT
ejpam-3900	83	10	lah	lah	NOUN
ejpam-3900	83	11	numbers	number	NOUN
ejpam-3900	83	12	will	will	AUX
ejpam-3900	83	13	be	be	AUX
ejpam-3900	83	14	introduced	introduce	VERB
ejpam-3900	83	15	and	and	CCONJ
ejpam-3900	83	16	properties	property	NOUN
ejpam-3900	83	17	of	of	ADP
ejpam-3900	83	18	these	these	DET
ejpam-3900	83	19	number	number	NOUN
ejpam-3900	83	20	will	will	AUX
ejpam-3900	83	21	be	be	AUX
ejpam-3900	83	22	establshed	establshe	VERB
ejpam-3900	83	23	using	use	VERB
ejpam-3900	83	24	the	the	DET
ejpam-3900	83	25	approach	approach	NOUN
ejpam-3900	83	26	employed	employ	VERB
ejpam-3900	83	27	in	in	ADP
ejpam-3900	83	28	[	[	X
ejpam-3900	83	29	6	6	NUM
ejpam-3900	83	30	]	]	PUNCT
ejpam-3900	83	31	.	.	PUNCT
ejpam-3900	84	1	the	the	DET
ejpam-3900	84	2	method	method	NOUN
ejpam-3900	84	3	used	use	VERB
ejpam-3900	84	4	in	in	ADP
ejpam-3900	84	5	the	the	DET
ejpam-3900	84	6	paper	paper	NOUN
ejpam-3900	84	7	of	of	ADP
ejpam-3900	84	8	cillar	cillar	NOUN
ejpam-3900	84	9	and	and	CCONJ
ejpam-3900	84	10	corcino	corcino	NOUN
ejpam-3900	84	11	[	[	X
ejpam-3900	84	12	2	2	NUM
ejpam-3900	84	13	]	]	PUNCT
ejpam-3900	84	14	will	will	AUX
ejpam-3900	84	15	also	also	ADV
ejpam-3900	84	16	be	be	AUX
ejpam-3900	84	17	used	use	VERB
ejpam-3900	84	18	to	to	PART
ejpam-3900	84	19	obtain	obtain	VERB
ejpam-3900	84	20	the	the	DET
ejpam-3900	84	21	properties	property	NOUN
ejpam-3900	84	22	of	of	ADP
ejpam-3900	84	23	the	the	DET
ejpam-3900	84	24	(	(	PUNCT
ejpam-3900	84	25	q	q	NOUN
ejpam-3900	84	26	,	,	PUNCT
ejpam-3900	84	27	r)whitney	r)whitney	ADJ
ejpam-3900	84	28	-	-	PUNCT
ejpam-3900	84	29	lah	lah	ADJ
ejpam-3900	84	30	numbers	number	NOUN
ejpam-3900	84	31	.	.	PUNCT
ejpam-3900	85	1	moreover	moreover	ADV
ejpam-3900	85	2	,	,	PUNCT
ejpam-3900	85	3	this	this	DET
ejpam-3900	85	4	paper	paper	NOUN
ejpam-3900	85	5	is	be	AUX
ejpam-3900	85	6	concluded	conclude	VERB
ejpam-3900	85	7	by	by	ADP
ejpam-3900	85	8	deriving	derive	VERB
ejpam-3900	85	9	an	an	DET
ejpam-3900	85	10	explicit	explicit	ADJ
ejpam-3900	85	11	formula	formula	NOUN
ejpam-3900	85	12	for	for	ADP
ejpam-3900	85	13	the	the	DET
ejpam-3900	85	14	first	first	ADJ
ejpam-3900	85	15	form	form	NOUN
ejpam-3900	85	16	(	(	PUNCT
ejpam-3900	85	17	q	q	ADJ
ejpam-3900	85	18	,	,	PUNCT
ejpam-3900	85	19	r)-dowling	r)-dowle	VERB
ejpam-3900	85	20	numbers	number	NOUN
ejpam-3900	85	21	expressed	express	VERB
ejpam-3900	85	22	in	in	ADP
ejpam-3900	85	23	terms	term	NOUN
ejpam-3900	85	24	of	of	ADP
ejpam-3900	85	25	(	(	PUNCT
ejpam-3900	85	26	q	q	ADJ
ejpam-3900	85	27	,	,	PUNCT
ejpam-3900	85	28	r)-whitney	r)-whitney	ADJ
ejpam-3900	85	29	-	-	PUNCT
ejpam-3900	85	30	lah	lah	NOUN
ejpam-3900	85	31	numbers	number	NOUN
ejpam-3900	85	32	and	and	CCONJ
ejpam-3900	85	33	(	(	PUNCT
ejpam-3900	85	34	q	q	ADJ
ejpam-3900	85	35	,	,	PUNCT
ejpam-3900	85	36	r)-whitney	r)-whitney	NOUN
ejpam-3900	85	37	numbers	number	NOUN
ejpam-3900	85	38	of	of	ADP
ejpam-3900	85	39	the	the	DET
ejpam-3900	85	40	second	second	ADJ
ejpam-3900	85	41	kind	kind	NOUN
ejpam-3900	85	42	.	.	PUNCT
ejpam-3900	86	1	2	2	X
ejpam-3900	86	2	.	.	X
ejpam-3900	86	3	(	(	PUNCT
ejpam-3900	86	4	q	q	NOUN
ejpam-3900	86	5	,	,	PUNCT
ejpam-3900	86	6	r)-whitney	r)-whitney	ADJ
ejpam-3900	86	7	-	-	PUNCT
ejpam-3900	86	8	lah	lah	NOUN
ejpam-3900	86	9	numbers	number	NOUN
ejpam-3900	86	10	and	and	CCONJ
ejpam-3900	86	11	their	their	PRON
ejpam-3900	86	12	recurrence	recurrence	NOUN
ejpam-3900	86	13	relations	relation	VERB
ejpam-3900	86	14	the	the	DET
ejpam-3900	86	15	definition	definition	NOUN
ejpam-3900	86	16	of	of	ADP
ejpam-3900	86	17	the	the	DET
ejpam-3900	86	18	q	q	NOUN
ejpam-3900	86	19	-	-	PUNCT
ejpam-3900	86	20	analogue	analogue	NOUN
ejpam-3900	86	21	of	of	ADP
ejpam-3900	86	22	r	r	NOUN
ejpam-3900	86	23	-	-	PUNCT
ejpam-3900	86	24	whitney	whitney	NOUN
ejpam-3900	86	25	-	-	PUNCT
ejpam-3900	86	26	lah	lah	NOUN
ejpam-3900	86	27	numbers	number	NOUN
ejpam-3900	86	28	,	,	PUNCT
ejpam-3900	86	29	also	also	ADV
ejpam-3900	86	30	known	know	VERB
ejpam-3900	86	31	as	as	ADP
ejpam-3900	86	32	the	the	DET
ejpam-3900	86	33	(	(	PUNCT
ejpam-3900	86	34	q	q	NOUN
ejpam-3900	86	35	,	,	PUNCT
ejpam-3900	86	36	r)whitney	r)whitney	ADJ
ejpam-3900	86	37	-	-	PUNCT
ejpam-3900	86	38	lah	lah	ADJ
ejpam-3900	86	39	numbers	number	NOUN
ejpam-3900	86	40	,	,	PUNCT
ejpam-3900	86	41	is	be	AUX
ejpam-3900	86	42	given	give	VERB
ejpam-3900	86	43	as	as	SCONJ
ejpam-3900	86	44	follows	follow	VERB
ejpam-3900	86	45	.	.	PUNCT
ejpam-3900	87	1	definition	definition	NOUN
ejpam-3900	87	2	2.1	2.1	NUM
ejpam-3900	87	3	.	.	PUNCT
ejpam-3900	88	1	the	the	DET
ejpam-3900	88	2	(	(	PUNCT
ejpam-3900	88	3	q	q	ADJ
ejpam-3900	88	4	,	,	PUNCT
ejpam-3900	88	5	r)-whitney	r)-whitney	ADJ
ejpam-3900	88	6	-	-	PUNCT
ejpam-3900	88	7	lah	lah	NOUN
ejpam-3900	88	8	numbers	number	NOUN
ejpam-3900	88	9	lm	lm	ADP
ejpam-3900	88	10	,	,	PUNCT
ejpam-3900	88	11	r[n	r[n	VERB
ejpam-3900	88	12	,	,	PUNCT
ejpam-3900	88	13	k]q	k]q	NOUN
ejpam-3900	88	14	are	be	AUX
ejpam-3900	88	15	defined	define	VERB
ejpam-3900	88	16	by	by	ADP
ejpam-3900	88	17	lm	lm	INTJ
ejpam-3900	88	18	,	,	PUNCT
ejpam-3900	88	19	r[n	r[n	NOUN
ejpam-3900	88	20	,	,	PUNCT
ejpam-3900	88	21	k]q	k]q	NOUN
ejpam-3900	88	22	=	=	SYM
ejpam-3900	88	23	q2r+m(k−1)+m(n−1)lm	q2r+m(k−1)+m(n−1)lm	NOUN
ejpam-3900	88	24	,	,	PUNCT
ejpam-3900	88	25	r[n−	r[n−	ADJ
ejpam-3900	88	26	1	1	NUM
ejpam-3900	88	27	,	,	PUNCT
ejpam-3900	88	28	k−	k−	NOUN
ejpam-3900	88	29	1]q	1]q	PROPN
ejpam-3900	89	1	+	+	CCONJ
ejpam-3900	90	1	[	[	X
ejpam-3900	90	2	2r+	2r+	NUM
ejpam-3900	90	3	km+	km+	NOUN
ejpam-3900	90	4	(	(	PUNCT
ejpam-3900	90	5	n−	n−	NOUN
ejpam-3900	90	6	1)m]qlm	1)m]qlm	NUM
ejpam-3900	90	7	,	,	PUNCT
ejpam-3900	90	8	r[n−	r[n−	ADJ
ejpam-3900	90	9	1	1	NUM
ejpam-3900	90	10	,	,	PUNCT
ejpam-3900	90	11	k]q	k]q	PROPN
ejpam-3900	90	12	,	,	PUNCT
ejpam-3900	90	13	(	(	PUNCT
ejpam-3900	90	14	15	15	NUM
ejpam-3900	90	15	)	)	PUNCT
ejpam-3900	90	16	with	with	ADP
ejpam-3900	90	17	lm	lm	PROPN
ejpam-3900	90	18	,	,	PUNCT
ejpam-3900	90	19	r[n	r[n	NOUN
ejpam-3900	90	20	,	,	PUNCT
ejpam-3900	90	21	k]q	k]q	NOUN
ejpam-3900	90	22	=	=	PUNCT
ejpam-3900	90	23	{	{	PUNCT
ejpam-3900	90	24	0	0	NUM
ejpam-3900	90	25	if	if	SCONJ
ejpam-3900	90	26	n	n	CCONJ
ejpam-3900	90	27	<	<	X
ejpam-3900	90	28	k	k	PROPN
ejpam-3900	90	29	or	or	CCONJ
ejpam-3900	90	30	n	n	CCONJ
ejpam-3900	90	31	,	,	PUNCT
ejpam-3900	90	32	k	k	X
ejpam-3900	90	33	<	<	X
ejpam-3900	90	34	0	0	NUM
ejpam-3900	90	35	,	,	PUNCT
ejpam-3900	90	36	1	1	NUM
ejpam-3900	90	37	if	if	SCONJ
ejpam-3900	90	38	n	n	NOUN
ejpam-3900	90	39	=	=	SYM
ejpam-3900	90	40	k	k	PROPN
ejpam-3900	90	41	and	and	CCONJ
ejpam-3900	90	42	n	n	PRON
ejpam-3900	90	43	≥	≥	NOUN
ejpam-3900	90	44	0	0	NUM
ejpam-3900	90	45	.	.	PUNCT
ejpam-3900	91	1	and	and	CCONJ
ejpam-3900	91	2	[	[	X
ejpam-3900	91	3	t−	t−	PROPN
ejpam-3900	91	4	k]q	k]q	NOUN
ejpam-3900	91	5	=	=	SYM
ejpam-3900	91	6	1	1	NUM
ejpam-3900	91	7	qk	qk	NOUN
ejpam-3900	91	8	(	(	PUNCT
ejpam-3900	91	9	[	[	X
ejpam-3900	91	10	t]q	t]q	NOUN
ejpam-3900	91	11	−	−	NOUN
ejpam-3900	92	1	[	[	X
ejpam-3900	92	2	k]q	k]q	NOUN
ejpam-3900	92	3	)	)	PUNCT
ejpam-3900	92	4	.	.	PUNCT
ejpam-3900	93	1	remark	remark	PROPN
ejpam-3900	93	2	2.2	2.2	NUM
ejpam-3900	93	3	.	.	PUNCT
ejpam-3900	94	1	when	when	SCONJ
ejpam-3900	94	2	q	q	X
ejpam-3900	94	3	→	→	SYM
ejpam-3900	94	4	1	1	NUM
ejpam-3900	94	5	,	,	PUNCT
ejpam-3900	94	6	we	we	PRON
ejpam-3900	94	7	obtain	obtain	VERB
ejpam-3900	94	8	the	the	DET
ejpam-3900	94	9	triangular	triangular	NOUN
ejpam-3900	94	10	recurrence	recurrence	NOUN
ejpam-3900	94	11	relation	relation	NOUN
ejpam-3900	94	12	of	of	ADP
ejpam-3900	94	13	r	r	PROPN
ejpam-3900	94	14	-	-	PUNCT
ejpam-3900	94	15	whitney	whitney	NOUN
ejpam-3900	94	16	-	-	PUNCT
ejpam-3900	94	17	lah	lah	PROPN
ejpam-3900	94	18	numbers	number	NOUN
ejpam-3900	94	19	,	,	PUNCT
ejpam-3900	94	20	lm	lm	INTJ
ejpam-3900	94	21	,	,	PUNCT
ejpam-3900	94	22	r(n	r(n	PROPN
ejpam-3900	94	23	,	,	PUNCT
ejpam-3900	94	24	k	k	NOUN
ejpam-3900	94	25	)	)	PUNCT
ejpam-3900	94	26	,	,	PUNCT
ejpam-3900	94	27	defined	define	VERB
ejpam-3900	94	28	by	by	ADP
ejpam-3900	94	29	cheon	cheon	PROPN
ejpam-3900	94	30	and	and	CCONJ
ejpam-3900	94	31	jung	jung	PROPN
ejpam-3900	95	1	[	[	X
ejpam-3900	95	2	1	1	NUM
ejpam-3900	95	3	]	]	PUNCT
ejpam-3900	95	4	:	:	PUNCT
ejpam-3900	95	5	lm	lm	INTJ
ejpam-3900	95	6	,	,	PUNCT
ejpam-3900	95	7	r(n	r(n	PROPN
ejpam-3900	95	8	,	,	PUNCT
ejpam-3900	95	9	k	k	NOUN
ejpam-3900	95	10	)	)	PUNCT
ejpam-3900	95	11	=	=	SYM
ejpam-3900	95	12	lm	lm	PROPN
ejpam-3900	95	13	,	,	PUNCT
ejpam-3900	95	14	r(n−	r(n−	NOUN
ejpam-3900	95	15	1	1	NUM
ejpam-3900	95	16	,	,	PUNCT
ejpam-3900	95	17	k	k	PROPN
ejpam-3900	95	18	−	−	PROPN
ejpam-3900	95	19	1	1	NUM
ejpam-3900	95	20	)	)	PUNCT
ejpam-3900	95	21	+	+	CCONJ
ejpam-3900	95	22	(	(	PUNCT
ejpam-3900	95	23	2r	2r	NUM
ejpam-3900	95	24	+	+	CCONJ
ejpam-3900	95	25	km+	km+	PROPN
ejpam-3900	95	26	(	(	PUNCT
ejpam-3900	95	27	n−	n−	NOUN
ejpam-3900	95	28	1)m)lm	1)m)lm	NUM
ejpam-3900	95	29	,	,	PUNCT
ejpam-3900	95	30	r(n−	r(n−	NOUN
ejpam-3900	95	31	1	1	NUM
ejpam-3900	95	32	,	,	PUNCT
ejpam-3900	95	33	k	k	NOUN
ejpam-3900	95	34	)	)	PUNCT
ejpam-3900	95	35	with	with	ADP
ejpam-3900	95	36	lm	lm	PROPN
ejpam-3900	95	37	,	,	PUNCT
ejpam-3900	95	38	r(n	r(n	PROPN
ejpam-3900	95	39	,	,	PUNCT
ejpam-3900	95	40	k	k	NOUN
ejpam-3900	95	41	)	)	PUNCT
ejpam-3900	95	42	=	=	SYM
ejpam-3900	95	43	1	1	NUM
ejpam-3900	95	44	for	for	ADP
ejpam-3900	95	45	n	n	PRON
ejpam-3900	95	46	≥	≥	NOUN
ejpam-3900	95	47	0	0	NUM
ejpam-3900	95	48	and	and	CCONJ
ejpam-3900	95	49	n	n	NOUN
ejpam-3900	95	50	=	=	SYM
ejpam-3900	95	51	k	k	NOUN
ejpam-3900	95	52	,	,	PUNCT
ejpam-3900	95	53	and	and	CCONJ
ejpam-3900	95	54	lm	lm	INTJ
ejpam-3900	95	55	,	,	PUNCT
ejpam-3900	95	56	r(n	r(n	PROPN
ejpam-3900	95	57	,	,	PUNCT
ejpam-3900	95	58	k	k	NOUN
ejpam-3900	95	59	)	)	PUNCT
ejpam-3900	95	60	=	=	SYM
ejpam-3900	95	61	0	0	NUM
ejpam-3900	95	62	for	for	ADP
ejpam-3900	95	63	n	n	X
ejpam-3900	95	64	<	<	X
ejpam-3900	95	65	k	k	PROPN
ejpam-3900	95	66	or	or	CCONJ
ejpam-3900	95	67	n	n	CCONJ
ejpam-3900	95	68	,	,	PUNCT
ejpam-3900	95	69	k	k	X
ejpam-3900	95	70	<	<	X
ejpam-3900	95	71	0	0	X
ejpam-3900	95	72	.	.	PUNCT
ejpam-3900	95	73	r.	r.	PROPN
ejpam-3900	95	74	corcino	corcino	PROPN
ejpam-3900	95	75	,	,	PUNCT
ejpam-3900	95	76	j.	j.	PROPN
ejpam-3900	95	77	ontolan	ontolan	PROPN
ejpam-3900	95	78	,	,	PUNCT
ejpam-3900	95	79	m.	m.	NOUN
ejpam-3900	95	80	lobrigas	lobrigas	PROPN
ejpam-3900	95	81	/	/	SYM
ejpam-3900	95	82	eur	eur	PROPN
ejpam-3900	95	83	.	.	PUNCT
ejpam-3900	96	1	j.	j.	PROPN
ejpam-3900	96	2	pure	pure	PROPN
ejpam-3900	96	3	appl	appl	PROPN
ejpam-3900	96	4	.	.	PROPN
ejpam-3900	96	5	math	math	PROPN
ejpam-3900	96	6	,	,	PUNCT
ejpam-3900	96	7	14	14	NUM
ejpam-3900	96	8	(	(	PUNCT
ejpam-3900	96	9	1	1	NUM
ejpam-3900	96	10	)	)	PUNCT
ejpam-3900	96	11	(	(	PUNCT
ejpam-3900	96	12	2021	2021	NUM
ejpam-3900	96	13	)	)	PUNCT
ejpam-3900	96	14	,	,	PUNCT
ejpam-3900	96	15	65	65	NUM
ejpam-3900	96	16	-	-	SYM
ejpam-3900	96	17	81	81	NUM
ejpam-3900	96	18	70	70	NUM
ejpam-3900	96	19	remark	remark	NOUN
ejpam-3900	96	20	2.3	2.3	NUM
ejpam-3900	96	21	.	.	PUNCT
ejpam-3900	97	1	it	it	PRON
ejpam-3900	97	2	can	can	AUX
ejpam-3900	97	3	easily	easily	ADV
ejpam-3900	97	4	be	be	AUX
ejpam-3900	97	5	verified	verify	VERB
ejpam-3900	97	6	that	that	SCONJ
ejpam-3900	97	7	lm	lm	PROPN
ejpam-3900	97	8	,	,	PUNCT
ejpam-3900	97	9	r[n	r[n	NOUN
ejpam-3900	97	10	,	,	PUNCT
ejpam-3900	97	11	0	0	NUM
ejpam-3900	97	12	]	]	PUNCT
ejpam-3900	97	13	=	=	PUNCT
ejpam-3900	98	1	[	[	X
ejpam-3900	98	2	2r	2r	NUM
ejpam-3900	98	3	+	+	CCONJ
ejpam-3900	98	4	(	(	PUNCT
ejpam-3900	98	5	n−	n−	NOUN
ejpam-3900	98	6	1)m]nq	1)m]nq	NUM
ejpam-3900	98	7	.	.	PUNCT
ejpam-3900	99	1	by	by	ADP
ejpam-3900	99	2	making	make	VERB
ejpam-3900	99	3	use	use	NOUN
ejpam-3900	99	4	of	of	ADP
ejpam-3900	99	5	(	(	PUNCT
ejpam-3900	99	6	15	15	NUM
ejpam-3900	99	7	)	)	PUNCT
ejpam-3900	99	8	,	,	PUNCT
ejpam-3900	99	9	we	we	PRON
ejpam-3900	99	10	can	can	AUX
ejpam-3900	99	11	easily	easily	ADV
ejpam-3900	99	12	obtain	obtain	VERB
ejpam-3900	99	13	the	the	DET
ejpam-3900	99	14	following	follow	VERB
ejpam-3900	99	15	two	two	NUM
ejpam-3900	99	16	other	other	ADJ
ejpam-3900	99	17	forms	form	NOUN
ejpam-3900	99	18	of	of	ADP
ejpam-3900	99	19	recurrence	recurrence	NOUN
ejpam-3900	99	20	relations	relation	NOUN
ejpam-3900	99	21	and	and	CCONJ
ejpam-3900	99	22	generating	generate	VERB
ejpam-3900	99	23	function	function	NOUN
ejpam-3900	99	24	.	.	PUNCT
ejpam-3900	100	1	theorem	theorem	VERB
ejpam-3900	100	2	2.4	2.4	NUM
ejpam-3900	100	3	.	.	PUNCT
ejpam-3900	101	1	a	a	DET
ejpam-3900	101	2	q	q	NOUN
ejpam-3900	101	3	-	-	PUNCT
ejpam-3900	101	4	analogue	analogue	NOUN
ejpam-3900	101	5	of	of	ADP
ejpam-3900	101	6	r	r	NOUN
ejpam-3900	101	7	-	-	PUNCT
ejpam-3900	101	8	whitney	whitney	NOUN
ejpam-3900	101	9	-	-	PUNCT
ejpam-3900	101	10	lah	lah	PROPN
ejpam-3900	101	11	numbers	number	NOUN
ejpam-3900	101	12	,	,	PUNCT
ejpam-3900	101	13	lm	lm	INTJ
ejpam-3900	101	14	,	,	PUNCT
ejpam-3900	101	15	r[n	r[n	NOUN
ejpam-3900	101	16	,	,	PUNCT
ejpam-3900	101	17	k]q	k]q	PROPN
ejpam-3900	101	18	,	,	PUNCT
ejpam-3900	101	19	satisfies	satisfy	VERB
ejpam-3900	101	20	the	the	DET
ejpam-3900	101	21	following	follow	VERB
ejpam-3900	101	22	vertical	vertical	ADJ
ejpam-3900	101	23	recurrence	recurrence	NOUN
ejpam-3900	101	24	relations	relation	NOUN
ejpam-3900	101	25	,	,	PUNCT
ejpam-3900	101	26	lm	lm	PROPN
ejpam-3900	101	27	,	,	PUNCT
ejpam-3900	101	28	r[n+	r[n+	NOUN
ejpam-3900	101	29	1	1	NUM
ejpam-3900	101	30	,	,	PUNCT
ejpam-3900	101	31	k	k	PROPN
ejpam-3900	102	1	+	+	PROPN
ejpam-3900	102	2	1]q	1]q	NUM
ejpam-3900	102	3	=	=	SYM
ejpam-3900	102	4	n∑	n∑	PROPN
ejpam-3900	102	5	j	j	PROPN
ejpam-3900	102	6	=	=	PROPN
ejpam-3900	102	7	k	k	PROPN
ejpam-3900	102	8	q[2r+mk+m(n−j	q[2r+mk+m(n−j	PROPN
ejpam-3900	102	9	)	)	PUNCT
ejpam-3900	102	10	]	]	PUNCT
ejpam-3900	103	1	(	(	PUNCT
ejpam-3900	103	2	k∏	k∏	PROPN
ejpam-3900	103	3	i=0	i=0	PROPN
ejpam-3900	103	4	[	[	X
ejpam-3900	103	5	2r	2r	NUM
ejpam-3900	103	6	+	+	CCONJ
ejpam-3900	103	7	(	(	PUNCT
ejpam-3900	103	8	k	k	X
ejpam-3900	103	9	+	+	NUM
ejpam-3900	103	10	1)m+	1)m+	NUM
ejpam-3900	103	11	(	(	PUNCT
ejpam-3900	103	12	n−	n−	NOUN
ejpam-3900	103	13	i)m]q	i)m]q	X
ejpam-3900	103	14	)	)	PUNCT
ejpam-3900	103	15	lm	lm	PROPN
ejpam-3900	103	16	,	,	PUNCT
ejpam-3900	103	17	r[j	r[j	NOUN
ejpam-3900	103	18	,	,	PUNCT
ejpam-3900	103	19	k]q	k]q	VERB
ejpam-3900	103	20	with	with	ADP
ejpam-3900	103	21	initial	initial	ADJ
ejpam-3900	103	22	value	value	NOUN
ejpam-3900	103	23	lm	lm	PROPN
ejpam-3900	103	24	,	,	PUNCT
ejpam-3900	103	25	r[0	r[0	PROPN
ejpam-3900	103	26	,	,	PUNCT
ejpam-3900	103	27	0]q	0]q	NOUN
ejpam-3900	104	1	=	=	SYM
ejpam-3900	104	2	1	1	X
ejpam-3900	104	3	.	.	PUNCT
ejpam-3900	105	1	proof	proof	NOUN
ejpam-3900	105	2	.	.	PUNCT
ejpam-3900	106	1	we	we	PRON
ejpam-3900	106	2	replace	replace	VERB
ejpam-3900	106	3	n	n	ADV
ejpam-3900	106	4	by	by	ADP
ejpam-3900	106	5	n+	n+	ADP
ejpam-3900	106	6	1	1	NUM
ejpam-3900	106	7	and	and	CCONJ
ejpam-3900	106	8	k	k	X
ejpam-3900	106	9	by	by	ADP
ejpam-3900	106	10	k	k	PROPN
ejpam-3900	107	1	+	+	PROPN
ejpam-3900	107	2	1	1	NUM
ejpam-3900	107	3	,	,	PUNCT
ejpam-3900	107	4	then	then	ADV
ejpam-3900	107	5	using	use	VERB
ejpam-3900	107	6	(	(	PUNCT
ejpam-3900	107	7	15	15	NUM
ejpam-3900	107	8	)	)	PUNCT
ejpam-3900	107	9	,	,	PUNCT
ejpam-3900	107	10	we	we	PRON
ejpam-3900	107	11	have	have	VERB
ejpam-3900	107	12	lm	lm	PROPN
ejpam-3900	107	13	,	,	PUNCT
ejpam-3900	107	14	r[n+	r[n+	NOUN
ejpam-3900	107	15	1	1	NUM
ejpam-3900	107	16	,	,	PUNCT
ejpam-3900	107	17	k	k	PROPN
ejpam-3900	108	1	+	+	PROPN
ejpam-3900	108	2	1]q	1]q	NUM
ejpam-3900	108	3	=	=	SYM
ejpam-3900	108	4	q2r+mk+mnlm	q2r+mk+mnlm	PROPN
ejpam-3900	108	5	,	,	PUNCT
ejpam-3900	108	6	r[n	r[n	NOUN
ejpam-3900	108	7	,	,	PUNCT
ejpam-3900	108	8	k]q	k]q	ADJ
ejpam-3900	108	9	+	+	CCONJ
ejpam-3900	109	1	[	[	X
ejpam-3900	109	2	2r	2r	NUM
ejpam-3900	110	1	+	+	CCONJ
ejpam-3900	110	2	(	(	PUNCT
ejpam-3900	110	3	k	k	X
ejpam-3900	110	4	+	+	NUM
ejpam-3900	110	5	1)m+	1)m+	NUM
ejpam-3900	110	6	(	(	PUNCT
ejpam-3900	110	7	n)m]qlm	n)m]qlm	PROPN
ejpam-3900	110	8	,	,	PUNCT
ejpam-3900	110	9	r[n	r[n	NOUN
ejpam-3900	110	10	,	,	PUNCT
ejpam-3900	110	11	k	k	PROPN
ejpam-3900	110	12	+	+	PROPN
ejpam-3900	110	13	1]q	1]q	NUM
ejpam-3900	110	14	.	.	PUNCT
ejpam-3900	111	1	using	use	VERB
ejpam-3900	111	2	iteration	iteration	NOUN
ejpam-3900	111	3	method	method	NOUN
ejpam-3900	111	4	on	on	ADP
ejpam-3900	111	5	(	(	PUNCT
ejpam-3900	111	6	15	15	NUM
ejpam-3900	111	7	)	)	PUNCT
ejpam-3900	111	8	we	we	PRON
ejpam-3900	111	9	have	have	AUX
ejpam-3900	111	10	,	,	PUNCT
ejpam-3900	111	11	lm	lm	INTJ
ejpam-3900	111	12	,	,	PUNCT
ejpam-3900	111	13	r[n+	r[n+	NOUN
ejpam-3900	111	14	1	1	NUM
ejpam-3900	111	15	,	,	PUNCT
ejpam-3900	111	16	k	k	PROPN
ejpam-3900	111	17	+	+	PROPN
ejpam-3900	111	18	1]q	1]q	NUM
ejpam-3900	111	19	=	=	SYM
ejpam-3900	111	20	q2r+mk+mnlm	q2r+mk+mnlm	PROPN
ejpam-3900	111	21	,	,	PUNCT
ejpam-3900	111	22	r[n	r[n	NOUN
ejpam-3900	111	23	,	,	PUNCT
ejpam-3900	111	24	k]q	k]q	ADJ
ejpam-3900	111	25	+	+	CCONJ
ejpam-3900	112	1	[	[	X
ejpam-3900	112	2	2r	2r	NUM
ejpam-3900	112	3	+	+	CCONJ
ejpam-3900	112	4	(	(	PUNCT
ejpam-3900	112	5	k	k	X
ejpam-3900	112	6	+	+	PROPN
ejpam-3900	112	7	1)m+	1)m+	NUM
ejpam-3900	112	8	nm]q	nm]q	PROPN
ejpam-3900	112	9	{	{	PUNCT
ejpam-3900	112	10	q2r+mk+m(n−1)lm	q2r+mk+m(n−1)lm	NOUN
ejpam-3900	112	11	,	,	PUNCT
ejpam-3900	112	12	r[n−	r[n−	NOUN
ejpam-3900	112	13	1	1	NUM
ejpam-3900	112	14	,	,	PUNCT
ejpam-3900	112	15	k]q	k]q	VERB
ejpam-3900	112	16	+	+	PUNCT
ejpam-3900	113	1	[	[	X
ejpam-3900	113	2	2r	2r	NUM
ejpam-3900	114	1	+	+	CCONJ
ejpam-3900	114	2	(	(	PUNCT
ejpam-3900	114	3	k	k	X
ejpam-3900	114	4	+	+	NUM
ejpam-3900	114	5	1)m+	1)m+	NUM
ejpam-3900	114	6	(	(	PUNCT
ejpam-3900	114	7	n−	n−	NOUN
ejpam-3900	114	8	1)m]qlm	1)m]qlm	NUM
ejpam-3900	114	9	,	,	PUNCT
ejpam-3900	114	10	r[n−	r[n−	PROPN
ejpam-3900	114	11	1	1	NUM
ejpam-3900	114	12	,	,	PUNCT
ejpam-3900	114	13	k	k	PROPN
ejpam-3900	114	14	+	+	PROPN
ejpam-3900	114	15	1]q	1]q	NUM
ejpam-3900	114	16	}	}	PUNCT
ejpam-3900	114	17	=	=	SYM
ejpam-3900	114	18	q2r+mk+mnlm	q2r+mk+mnlm	PROPN
ejpam-3900	114	19	,	,	PUNCT
ejpam-3900	114	20	r[n	r[n	NOUN
ejpam-3900	114	21	,	,	PUNCT
ejpam-3900	114	22	k]q	k]q	ADV
ejpam-3900	114	23	+	+	CCONJ
ejpam-3900	114	24	q2r+mk+m(n−1)[2r	q2r+mk+m(n−1)[2r	PROPN
ejpam-3900	115	1	+	+	CCONJ
ejpam-3900	115	2	(	(	PUNCT
ejpam-3900	115	3	k	k	X
ejpam-3900	115	4	+	+	NUM
ejpam-3900	115	5	1)m+	1)m+	NUM
ejpam-3900	115	6	nm]qlm	nm]qlm	NOUN
ejpam-3900	115	7	,	,	PUNCT
ejpam-3900	115	8	r[n−	r[n−	NOUN
ejpam-3900	115	9	1	1	NUM
ejpam-3900	115	10	,	,	PUNCT
ejpam-3900	115	11	k]q	k]q	VERB
ejpam-3900	115	12	+	+	CCONJ
ejpam-3900	115	13	q2r+mk+m(n−2)[2r	q2r+mk+m(n−2)[2r	ADV
ejpam-3900	115	14	+	+	CCONJ
ejpam-3900	115	15	(	(	PUNCT
ejpam-3900	115	16	k	k	X
ejpam-3900	115	17	+	+	NUM
ejpam-3900	115	18	1)m+	1)m+	NUM
ejpam-3900	115	19	nm]q[2r	nm]q[2r	NOUN
ejpam-3900	116	1	+	+	CCONJ
ejpam-3900	116	2	(	(	PUNCT
ejpam-3900	116	3	k	k	X
ejpam-3900	116	4	+	+	NUM
ejpam-3900	116	5	1)m+	1)m+	NUM
ejpam-3900	116	6	(	(	PUNCT
ejpam-3900	116	7	n−	n−	NOUN
ejpam-3900	116	8	1)m]qlm	1)m]qlm	NUM
ejpam-3900	116	9	,	,	PUNCT
ejpam-3900	116	10	r[n−	r[n−	NOUN
ejpam-3900	116	11	2	2	NUM
ejpam-3900	116	12	,	,	PUNCT
ejpam-3900	116	13	k]q	k]q	ADV
ejpam-3900	116	14	+	+	PUNCT
ejpam-3900	116	15	.	.	PUNCT
ejpam-3900	116	16	.	.	PUNCT
ejpam-3900	117	1	.+	.+	NOUN
ejpam-3900	117	2	q2r+mk+m(k+1){[2r	q2r+mk+m(k+1){[2r	VERB
ejpam-3900	118	1	+	+	CCONJ
ejpam-3900	118	2	(	(	PUNCT
ejpam-3900	118	3	k	k	X
ejpam-3900	118	4	+	+	NUM
ejpam-3900	118	5	1)m+	1)m+	NUM
ejpam-3900	118	6	nm]q[2r	nm]q[2r	NOUN
ejpam-3900	119	1	+	+	CCONJ
ejpam-3900	119	2	(	(	PUNCT
ejpam-3900	119	3	k	k	X
ejpam-3900	119	4	+	+	NUM
ejpam-3900	119	5	1)m+	1)m+	NUM
ejpam-3900	119	6	(	(	PUNCT
ejpam-3900	119	7	n−	n−	NOUN
ejpam-3900	119	8	1)m]q	1)m]q	PROPN
ejpam-3900	119	9	.	.	PUNCT
ejpam-3900	119	10	.	.	PUNCT
ejpam-3900	119	11	.	.	PUNCT
ejpam-3900	120	1	[	[	X
ejpam-3900	120	2	2r	2r	NUM
ejpam-3900	121	1	+	+	CCONJ
ejpam-3900	121	2	(	(	PUNCT
ejpam-3900	121	3	k	k	X
ejpam-3900	121	4	+	+	NUM
ejpam-3900	121	5	1)m+	1)m+	NUM
ejpam-3900	121	6	(	(	PUNCT
ejpam-3900	121	7	n−	n−	NOUN
ejpam-3900	121	8	k)m]q}lm	k)m]q}lm	NUM
ejpam-3900	121	9	,	,	PUNCT
ejpam-3900	121	10	r[k	r[k	NOUN
ejpam-3900	121	11	+	+	PROPN
ejpam-3900	121	12	1	1	NUM
ejpam-3900	121	13	,	,	PUNCT
ejpam-3900	121	14	k	k	PROPN
ejpam-3900	122	1	+	+	PROPN
ejpam-3900	122	2	1]q	1]q	NUM
ejpam-3900	122	3	.	.	PUNCT
ejpam-3900	123	1	using	use	VERB
ejpam-3900	123	2	the	the	DET
ejpam-3900	123	3	fact	fact	NOUN
ejpam-3900	123	4	that	that	SCONJ
ejpam-3900	123	5	lm	lm	ADP
ejpam-3900	123	6	,	,	PUNCT
ejpam-3900	123	7	r[k	r[k	NOUN
ejpam-3900	123	8	+	+	PROPN
ejpam-3900	123	9	1	1	NUM
ejpam-3900	123	10	,	,	PUNCT
ejpam-3900	123	11	k	k	PROPN
ejpam-3900	123	12	+	+	PROPN
ejpam-3900	123	13	1]q	1]q	NUM
ejpam-3900	123	14	=	=	SYM
ejpam-3900	123	15	lm	lm	PROPN
ejpam-3900	123	16	,	,	PUNCT
ejpam-3900	123	17	r[k	r[k	PROPN
ejpam-3900	123	18	,	,	PUNCT
ejpam-3900	123	19	k]q	k]q	AUX
ejpam-3900	123	20	we	we	PRON
ejpam-3900	123	21	have	have	AUX
ejpam-3900	123	22	,	,	PUNCT
ejpam-3900	123	23	lm	lm	INTJ
ejpam-3900	123	24	,	,	PUNCT
ejpam-3900	123	25	r[n+	r[n+	NOUN
ejpam-3900	123	26	1	1	NUM
ejpam-3900	123	27	,	,	PUNCT
ejpam-3900	123	28	k	k	PROPN
ejpam-3900	124	1	+	+	PROPN
ejpam-3900	124	2	1]q	1]q	NUM
ejpam-3900	124	3	=	=	SYM
ejpam-3900	124	4	n∑	n∑	PROPN
ejpam-3900	124	5	j	j	PROPN
ejpam-3900	124	6	=	=	PROPN
ejpam-3900	124	7	k	k	PROPN
ejpam-3900	124	8	q[2r+mk+m(n−j	q[2r+mk+m(n−j	PROPN
ejpam-3900	124	9	)	)	PUNCT
ejpam-3900	124	10	]	]	PUNCT
ejpam-3900	125	1	(	(	PUNCT
ejpam-3900	125	2	k∏	k∏	PROPN
ejpam-3900	125	3	i=0	i=0	PROPN
ejpam-3900	125	4	[	[	X
ejpam-3900	125	5	2r	2r	NUM
ejpam-3900	125	6	+	+	CCONJ
ejpam-3900	125	7	(	(	PUNCT
ejpam-3900	125	8	k	k	X
ejpam-3900	125	9	+	+	NUM
ejpam-3900	125	10	1)m+	1)m+	NUM
ejpam-3900	125	11	(	(	PUNCT
ejpam-3900	125	12	n−	n−	NOUN
ejpam-3900	125	13	i)m]q	i)m]q	X
ejpam-3900	125	14	)	)	PUNCT
ejpam-3900	125	15	lm	lm	PROPN
ejpam-3900	125	16	,	,	PUNCT
ejpam-3900	125	17	r[j	r[j	NOUN
ejpam-3900	125	18	,	,	PUNCT
ejpam-3900	125	19	k]q	k]q	PROPN
ejpam-3900	125	20	.	.	PUNCT
ejpam-3900	126	1	theorem	theorem	VERB
ejpam-3900	126	2	2.5	2.5	NUM
ejpam-3900	126	3	.	.	PUNCT
ejpam-3900	127	1	a	a	DET
ejpam-3900	127	2	q	q	ADJ
ejpam-3900	127	3	-	-	PUNCT
ejpam-3900	127	4	analogue	analogue	NOUN
ejpam-3900	127	5	lm	lm	PROPN
ejpam-3900	127	6	,	,	PUNCT
ejpam-3900	127	7	r[n	r[n	NOUN
ejpam-3900	127	8	,	,	PUNCT
ejpam-3900	127	9	k]q	k]q	VERB
ejpam-3900	127	10	satisfies	satisfy	VERB
ejpam-3900	127	11	the	the	DET
ejpam-3900	127	12	horizontal	horizontal	ADJ
ejpam-3900	127	13	recurrence	recurrence	PROPN
ejpam-3900	127	14	relation	relation	PROPN
ejpam-3900	127	15	lm	lm	PROPN
ejpam-3900	127	16	,	,	PUNCT
ejpam-3900	127	17	r[n	r[n	NOUN
ejpam-3900	127	18	,	,	PUNCT
ejpam-3900	127	19	k]q	k]q	PROPN
ejpam-3900	127	20	=	=	PUNCT
ejpam-3900	127	21	n−k∑	n−k∑	NOUN
ejpam-3900	127	22	j=0	j=0	PROPN
ejpam-3900	127	23	(	(	PUNCT
ejpam-3900	127	24	−1)j	−1)j	NOUN
ejpam-3900	127	25	q−2r−m(k+j)−nm	q−2r−m(k+j)−nm	PROPN
ejpam-3900	127	26	rk+j+1,q	rk+j+1,q	PROPN
ejpam-3900	127	27	rk+1,q	rk+1,q	PROPN
ejpam-3900	127	28	lm	lm	PROPN
ejpam-3900	127	29	,	,	PUNCT
ejpam-3900	127	30	r[n+	r[n+	NOUN
ejpam-3900	127	31	1	1	NUM
ejpam-3900	127	32	,	,	PUNCT
ejpam-3900	127	33	k	k	PROPN
ejpam-3900	128	1	+	+	NUM
ejpam-3900	128	2	j	j	PROPN
ejpam-3900	128	3	+	+	CCONJ
ejpam-3900	128	4	1]q	1]q	NUM
ejpam-3900	129	1	where	where	SCONJ
ejpam-3900	129	2	ri	ri	NOUN
ejpam-3900	129	3	,	,	PUNCT
ejpam-3900	129	4	q	q	NOUN
ejpam-3900	129	5	=	=	SYM
ejpam-3900	129	6	i−1∏	i−1∏	PROPN
ejpam-3900	129	7	h=1	h=1	PUNCT
ejpam-3900	129	8	q−2r−mh−nm+m[mh+	q−2r−mh−nm+m[mh+	PROPN
ejpam-3900	129	9	2r	2r	NUM
ejpam-3900	129	10	+	+	CCONJ
ejpam-3900	129	11	nm]q	nm]q	PROPN
ejpam-3900	129	12	with	with	ADP
ejpam-3900	129	13	initial	initial	ADJ
ejpam-3900	129	14	value	value	NOUN
ejpam-3900	129	15	lm	lm	PROPN
ejpam-3900	129	16	,	,	PUNCT
ejpam-3900	129	17	r[0	r[0	PROPN
ejpam-3900	129	18	,	,	PUNCT
ejpam-3900	129	19	0]q	0]q	NOUN
ejpam-3900	129	20	=	=	SYM
ejpam-3900	130	1	1	1	X
ejpam-3900	130	2	.	.	PUNCT
ejpam-3900	130	3	r.	r.	PROPN
ejpam-3900	130	4	corcino	corcino	PROPN
ejpam-3900	130	5	,	,	PUNCT
ejpam-3900	130	6	j.	j.	PROPN
ejpam-3900	130	7	ontolan	ontolan	PROPN
ejpam-3900	130	8	,	,	PUNCT
ejpam-3900	130	9	m.	m.	NOUN
ejpam-3900	130	10	lobrigas	lobrigas	PROPN
ejpam-3900	130	11	/	/	SYM
ejpam-3900	130	12	eur	eur	PROPN
ejpam-3900	130	13	.	.	PUNCT
ejpam-3900	131	1	j.	j.	PROPN
ejpam-3900	131	2	pure	pure	PROPN
ejpam-3900	131	3	appl	appl	PROPN
ejpam-3900	131	4	.	.	PROPN
ejpam-3900	131	5	math	math	PROPN
ejpam-3900	131	6	,	,	PUNCT
ejpam-3900	131	7	14	14	NUM
ejpam-3900	131	8	(	(	PUNCT
ejpam-3900	131	9	1	1	NUM
ejpam-3900	131	10	)	)	PUNCT
ejpam-3900	131	11	(	(	PUNCT
ejpam-3900	131	12	2021	2021	NUM
ejpam-3900	131	13	)	)	PUNCT
ejpam-3900	131	14	,	,	PUNCT
ejpam-3900	131	15	65	65	NUM
ejpam-3900	131	16	-	-	SYM
ejpam-3900	131	17	81	81	NUM
ejpam-3900	132	1	71	71	NUM
ejpam-3900	132	2	proof	proof	NOUN
ejpam-3900	132	3	.	.	PUNCT
ejpam-3900	133	1	using	use	VERB
ejpam-3900	133	2	iteration	iteration	NOUN
ejpam-3900	133	3	method	method	NOUN
ejpam-3900	133	4	on	on	ADP
ejpam-3900	133	5	(	(	PUNCT
ejpam-3900	133	6	15	15	NUM
ejpam-3900	133	7	)	)	PUNCT
ejpam-3900	133	8	we	we	PRON
ejpam-3900	133	9	have	have	AUX
ejpam-3900	133	10	,	,	PUNCT
ejpam-3900	133	11	rhs	rhs	PROPN
ejpam-3900	133	12	=	=	PROPN
ejpam-3900	133	13	n−k∑	n−k∑	NOUN
ejpam-3900	133	14	j=0	j=0	PROPN
ejpam-3900	133	15	(	(	PUNCT
ejpam-3900	133	16	−1)jq−2r−m(k+j)−nm	−1)jq−2r−m(k+j)−nm	PROPN
ejpam-3900	133	17	rk+j+1,q	rk+j+1,q	NUM
ejpam-3900	133	18	rk+1,q	rk+1,q	NOUN
ejpam-3900	133	19	{	{	PUNCT
ejpam-3900	133	20	q2r+m(k+j+1−1)+m(n+1−1)lm	q2r+m(k+j+1−1)+m(n+1−1)lm	X
ejpam-3900	133	21	,	,	PUNCT
ejpam-3900	133	22	r[n	r[n	PROPN
ejpam-3900	133	23	,	,	PUNCT
ejpam-3900	133	24	k	k	PROPN
ejpam-3900	134	1	+	+	CCONJ
ejpam-3900	134	2	j]q	j]q	ADJ
ejpam-3900	134	3	+	+	CCONJ
ejpam-3900	135	1	[	[	X
ejpam-3900	135	2	2r	2r	NUM
ejpam-3900	136	1	+	+	CCONJ
ejpam-3900	136	2	(	(	PUNCT
ejpam-3900	136	3	k	k	PROPN
ejpam-3900	136	4	+	+	CCONJ
ejpam-3900	136	5	j	j	PROPN
ejpam-3900	136	6	+	+	CCONJ
ejpam-3900	136	7	1)m+	1)m+	NUM
ejpam-3900	136	8	nm]qlm	nm]qlm	NOUN
ejpam-3900	136	9	,	,	PUNCT
ejpam-3900	136	10	r[n	r[n	NOUN
ejpam-3900	136	11	,	,	PUNCT
ejpam-3900	136	12	k	k	PROPN
ejpam-3900	137	1	+	+	NUM
ejpam-3900	137	2	j	j	PROPN
ejpam-3900	137	3	+	+	CCONJ
ejpam-3900	137	4	1]q	1]q	NUM
ejpam-3900	137	5	}	}	PUNCT
ejpam-3900	137	6	=	=	PUNCT
ejpam-3900	138	1	n−k∑	n−k∑	NOUN
ejpam-3900	138	2	j=0	j=0	PROPN
ejpam-3900	138	3	(	(	PUNCT
ejpam-3900	138	4	−1)j	−1)j	NOUN
ejpam-3900	138	5	rk+j+1,q	rk+j+1,q	NUM
ejpam-3900	138	6	rk+1,q	rk+1,q	PROPN
ejpam-3900	138	7	lm	lm	PROPN
ejpam-3900	138	8	,	,	PUNCT
ejpam-3900	138	9	r[n	r[n	NOUN
ejpam-3900	138	10	,	,	PUNCT
ejpam-3900	138	11	k	k	PROPN
ejpam-3900	138	12	+	+	CCONJ
ejpam-3900	138	13	j]q	j]q	ADJ
ejpam-3900	138	14	+	+	CCONJ
ejpam-3900	138	15	n−k+1∑	n−k+1∑	NOUN
ejpam-3900	138	16	j=1	j=1	NOUN
ejpam-3900	138	17	(	(	PUNCT
ejpam-3900	138	18	−1)j−1q−2r−m(k+j−1)−nm	−1)j−1q−2r−m(k+j−1)−nm	NUM
ejpam-3900	138	19	rk+j	rk+j	PROPN
ejpam-3900	138	20	,	,	PUNCT
ejpam-3900	138	21	q	q	NOUN
ejpam-3900	138	22	rk+1,q	rk+1,q	NOUN
ejpam-3900	138	23	[	[	X
ejpam-3900	138	24	2r	2r	NUM
ejpam-3900	139	1	+	+	CCONJ
ejpam-3900	140	1	(	(	PUNCT
ejpam-3900	140	2	k	k	X
ejpam-3900	140	3	+	+	PROPN
ejpam-3900	140	4	j)m+	j)m+	PROPN
ejpam-3900	140	5	nm]qlm	nm]qlm	PROPN
ejpam-3900	140	6	,	,	PUNCT
ejpam-3900	140	7	r[n	r[n	NOUN
ejpam-3900	140	8	,	,	PUNCT
ejpam-3900	140	9	k	k	PROPN
ejpam-3900	141	1	+	+	CCONJ
ejpam-3900	141	2	j]q	j]q	ADJ
ejpam-3900	141	3	=	=	PUNCT
ejpam-3900	141	4	n−k∑	n−k∑	NOUN
ejpam-3900	141	5	j=0	j=0	PROPN
ejpam-3900	141	6	(	(	PUNCT
ejpam-3900	141	7	−1)j	−1)j	NOUN
ejpam-3900	141	8	rk+j+1,q	rk+j+1,q	NUM
ejpam-3900	141	9	rk+1,q	rk+1,q	PROPN
ejpam-3900	141	10	lm	lm	PROPN
ejpam-3900	141	11	,	,	PUNCT
ejpam-3900	141	12	r[n	r[n	NOUN
ejpam-3900	141	13	,	,	PUNCT
ejpam-3900	141	14	k	k	PROPN
ejpam-3900	141	15	+	+	CCONJ
ejpam-3900	141	16	j]q	j]q	ADJ
ejpam-3900	141	17	+	+	CCONJ
ejpam-3900	141	18	n−k∑	n−k∑	NOUN
ejpam-3900	141	19	j=1	j=1	NOUN
ejpam-3900	141	20	(	(	PUNCT
ejpam-3900	141	21	−1)j−1q−2r−m(k+j−1)−nm	−1)j−1q−2r−m(k+j−1)−nm	NUM
ejpam-3900	141	22	∏k+j−1	∏k+j−1	NOUN
ejpam-3900	141	23	h=1	h=1	PUNCT
ejpam-3900	141	24	q−2r−mh−nm+m[mh+	q−2r−mh−nm+m[mh+	PROPN
ejpam-3900	141	25	2r	2r	NUM
ejpam-3900	141	26	+	+	NUM
ejpam-3900	141	27	nm]q∏k	nm]q∏k	NUM
ejpam-3900	141	28	h=1	h=1	NOUN
ejpam-3900	141	29	q	q	PUNCT
ejpam-3900	141	30	−2r−mh−nm+m[mh+	−2r−mh−nm+m[mh+	PROPN
ejpam-3900	141	31	2r	2r	NUM
ejpam-3900	141	32	+	+	CCONJ
ejpam-3900	141	33	nm]q	nm]q	PROPN
ejpam-3900	142	1	[	[	X
ejpam-3900	142	2	2r	2r	NUM
ejpam-3900	142	3	+	+	CCONJ
ejpam-3900	142	4	(	(	PUNCT
ejpam-3900	142	5	k	k	X
ejpam-3900	142	6	+	+	PROPN
ejpam-3900	142	7	j)m+	j)m+	PROPN
ejpam-3900	142	8	nm]qlm	nm]qlm	PROPN
ejpam-3900	142	9	,	,	PUNCT
ejpam-3900	142	10	r[n	r[n	NOUN
ejpam-3900	142	11	,	,	PUNCT
ejpam-3900	142	12	k	k	PROPN
ejpam-3900	142	13	+	+	PROPN
ejpam-3900	142	14	j]q	j]q	PROPN
ejpam-3900	142	15	.	.	PUNCT
ejpam-3900	143	1	note	note	VERB
ejpam-3900	143	2	that	that	PRON
ejpam-3900	143	3	k+j−1∏	k+j−1∏	NOUN
ejpam-3900	143	4	h=1	h=1	PUNCT
ejpam-3900	144	1	q−2r−mh−nm+m[mh+	q−2r−mh−nm+m[mh+	PROPN
ejpam-3900	144	2	2r	2r	NUM
ejpam-3900	144	3	+	+	CCONJ
ejpam-3900	144	4	nm]q	nm]q	PROPN
ejpam-3900	144	5	=	=	SYM
ejpam-3900	144	6	(	(	PUNCT
ejpam-3900	144	7	q−2r−m(1)−nm+m[m(1	q−2r−m(1)−nm+m[m(1	NOUN
ejpam-3900	144	8	)	)	PUNCT
ejpam-3900	145	1	+	+	NUM
ejpam-3900	145	2	2r	2r	NUM
ejpam-3900	145	3	+	+	CCONJ
ejpam-3900	145	4	nm]q	nm]q	PROPN
ejpam-3900	145	5	)	)	PUNCT
ejpam-3900	145	6	(	(	PUNCT
ejpam-3900	145	7	q−2r−m(2)−nm+m[m(2	q−2r−m(2)−nm+m[m(2	ADV
ejpam-3900	145	8	)	)	PUNCT
ejpam-3900	146	1	+	+	NUM
ejpam-3900	146	2	2r	2r	NUM
ejpam-3900	146	3	+	+	CCONJ
ejpam-3900	146	4	nm]q)(q	nm]q)(q	PROPN
ejpam-3900	146	5	−2r−m(3)−nm+m[m(3	−2r−m(3)−nm+m[m(3	NOUN
ejpam-3900	146	6	)	)	PUNCT
ejpam-3900	147	1	+	+	NUM
ejpam-3900	147	2	2r	2r	NUM
ejpam-3900	147	3	+	+	CCONJ
ejpam-3900	147	4	nm]q	nm]q	PROPN
ejpam-3900	147	5	)	)	PUNCT
ejpam-3900	147	6	.	.	PUNCT
ejpam-3900	147	7	.	.	PUNCT
ejpam-3900	147	8	.	.	PUNCT
ejpam-3900	148	1	(	(	PUNCT
ejpam-3900	148	2	q−2r−m(k+j−1)−nm+m[m(k	q−2r−m(k+j−1)−nm+m[m(k	VERB
ejpam-3900	148	3	+	+	CCONJ
ejpam-3900	149	1	j	j	PROPN
ejpam-3900	150	1	−	−	PROPN
ejpam-3900	150	2	1	1	NUM
ejpam-3900	150	3	)	)	PUNCT
ejpam-3900	150	4	+	+	NUM
ejpam-3900	150	5	2r	2r	NUM
ejpam-3900	150	6	+	+	CCONJ
ejpam-3900	150	7	nm]q	nm]q	PROPN
ejpam-3900	150	8	)	)	PUNCT
ejpam-3900	150	9	.	.	PUNCT
ejpam-3900	151	1	now	now	ADV
ejpam-3900	151	2	,	,	PUNCT
ejpam-3900	151	3	simplifying	simplify	VERB
ejpam-3900	151	4	the	the	DET
ejpam-3900	151	5	rhs	rh	NOUN
ejpam-3900	151	6	we	we	PRON
ejpam-3900	151	7	have	have	VERB
ejpam-3900	151	8	,	,	PUNCT
ejpam-3900	151	9	rhs	rhs	PROPN
ejpam-3900	151	10	=	=	PROPN
ejpam-3900	151	11	n−k∑	n−k∑	NOUN
ejpam-3900	151	12	j=0	j=0	PROPN
ejpam-3900	151	13	(	(	PUNCT
ejpam-3900	151	14	−1)j	−1)j	NOUN
ejpam-3900	151	15	rk+j+1,q	rk+j+1,q	NUM
ejpam-3900	151	16	rk+1,q	rk+1,q	PROPN
ejpam-3900	151	17	lm	lm	PROPN
ejpam-3900	151	18	,	,	PUNCT
ejpam-3900	151	19	r[n	r[n	NOUN
ejpam-3900	151	20	,	,	PUNCT
ejpam-3900	151	21	k	k	PROPN
ejpam-3900	152	1	+	+	CCONJ
ejpam-3900	152	2	j]q	j]q	ADJ
ejpam-3900	152	3	+	+	CCONJ
ejpam-3900	152	4	1∏k	1∏k	NUM
ejpam-3900	152	5	h=1	h=1	NOUN
ejpam-3900	152	6	q	q	PUNCT
ejpam-3900	152	7	−2r−mh−nm+m[mh+	−2r−mh−nm+m[mh+	PROPN
ejpam-3900	152	8	2r	2r	NUM
ejpam-3900	152	9	+	+	CCONJ
ejpam-3900	152	10	nm]q	nm]q	PROPN
ejpam-3900	152	11	=	=	SYM
ejpam-3900	152	12	n−k∑	n−k∑	NOUN
ejpam-3900	152	13	j=0	j=0	PROPN
ejpam-3900	152	14	(	(	PUNCT
ejpam-3900	152	15	−1)j	−1)j	NOUN
ejpam-3900	152	16	rk+j+1,q	rk+j+1,q	NUM
ejpam-3900	152	17	rk+1,q	rk+1,q	PROPN
ejpam-3900	152	18	lm	lm	PROPN
ejpam-3900	152	19	,	,	PUNCT
ejpam-3900	152	20	r[n	r[n	NOUN
ejpam-3900	152	21	,	,	PUNCT
ejpam-3900	152	22	k	k	PROPN
ejpam-3900	153	1	+	+	CCONJ
ejpam-3900	153	2	j]q	j]q	ADJ
ejpam-3900	153	3	+	+	CCONJ
ejpam-3900	153	4	1∏k	1∏k	NUM
ejpam-3900	153	5	h=1	h=1	NOUN
ejpam-3900	153	6	q	q	PUNCT
ejpam-3900	153	7	−2r−mh−nm+m[mh+	−2r−mh−nm+m[mh+	PROPN
ejpam-3900	153	8	2r	2r	NUM
ejpam-3900	153	9	+	+	CCONJ
ejpam-3900	153	10	nm]q	nm]q	PROPN
ejpam-3900	153	11	n−k∑	n−k∑	NOUN
ejpam-3900	153	12	j=1	j=1	PROPN
ejpam-3900	153	13	(	(	PUNCT
ejpam-3900	153	14	−1)j−1{(q−2r−m(1)−nm+m[m(1	−1)j−1{(q−2r−m(1)−nm+m[m(1	PROPN
ejpam-3900	153	15	)	)	PUNCT
ejpam-3900	154	1	+	+	NUM
ejpam-3900	154	2	2r	2r	NUM
ejpam-3900	154	3	+	+	CCONJ
ejpam-3900	154	4	nm]q)(q	nm]q)(q	PROPN
ejpam-3900	154	5	−2r−m(2)−nm+m[m(2	−2r−m(2)−nm+m[m(2	NOUN
ejpam-3900	154	6	)	)	PUNCT
ejpam-3900	155	1	+	+	NUM
ejpam-3900	155	2	2r	2r	NUM
ejpam-3900	155	3	+	+	CCONJ
ejpam-3900	155	4	nm]q	nm]q	PROPN
ejpam-3900	155	5	)	)	PUNCT
ejpam-3900	155	6	(	(	PUNCT
ejpam-3900	155	7	q−2r−m(3)−nm+m[m(3	q−2r−m(3)−nm+m[m(3	NOUN
ejpam-3900	155	8	)	)	PUNCT
ejpam-3900	155	9	+	+	SYM
ejpam-3900	155	10	2r	2r	NUM
ejpam-3900	155	11	+	+	CCONJ
ejpam-3900	155	12	nm]q	nm]q	PROPN
ejpam-3900	155	13	)	)	PUNCT
ejpam-3900	155	14	.	.	PUNCT
ejpam-3900	155	15	.	.	PUNCT
ejpam-3900	155	16	.	.	PUNCT
ejpam-3900	156	1	(	(	PUNCT
ejpam-3900	156	2	q	q	NOUN
ejpam-3900	156	3	−2r−m(k+j−1)−nm+m[m(k	−2r−m(k+j−1)−nm+m[m(k	NOUN
ejpam-3900	156	4	+	+	CCONJ
ejpam-3900	156	5	j	j	PROPN
ejpam-3900	156	6	−	−	PROPN
ejpam-3900	156	7	1	1	NUM
ejpam-3900	156	8	)	)	PUNCT
ejpam-3900	156	9	+	+	NUM
ejpam-3900	156	10	2r	2r	NUM
ejpam-3900	156	11	+	+	CCONJ
ejpam-3900	156	12	nm]q	nm]q	PROPN
ejpam-3900	156	13	)	)	PUNCT
ejpam-3900	156	14	}	}	PUNCT
ejpam-3900	157	1	q−2r−m(k+j)−nm+m[2r	q−2r−m(k+j)−nm+m[2r	ADV
ejpam-3900	158	1	+	+	CCONJ
ejpam-3900	158	2	(	(	PUNCT
ejpam-3900	158	3	k	k	X
ejpam-3900	158	4	+	+	PROPN
ejpam-3900	158	5	j)m+	j)m+	PROPN
ejpam-3900	158	6	nm]qlm	nm]qlm	PROPN
ejpam-3900	158	7	,	,	PUNCT
ejpam-3900	158	8	r[n	r[n	NOUN
ejpam-3900	158	9	,	,	PUNCT
ejpam-3900	158	10	k	k	PROPN
ejpam-3900	159	1	+	+	CCONJ
ejpam-3900	159	2	j]q	j]q	ADJ
ejpam-3900	159	3	=	=	PUNCT
ejpam-3900	159	4	n−k∑	n−k∑	NOUN
ejpam-3900	159	5	j=0	j=0	PROPN
ejpam-3900	159	6	(	(	PUNCT
ejpam-3900	159	7	−1)j	−1)j	NOUN
ejpam-3900	159	8	rk+j+1,q	rk+j+1,q	NUM
ejpam-3900	159	9	rk+1,q	rk+1,q	PROPN
ejpam-3900	159	10	lm	lm	PROPN
ejpam-3900	159	11	,	,	PUNCT
ejpam-3900	159	12	r[n	r[n	NOUN
ejpam-3900	159	13	,	,	PUNCT
ejpam-3900	159	14	k	k	PROPN
ejpam-3900	159	15	+	+	CCONJ
ejpam-3900	159	16	j]q	j]q	ADJ
ejpam-3900	159	17	+	+	CCONJ
ejpam-3900	159	18	n−k∑	n−k∑	NOUN
ejpam-3900	159	19	j=1	j=1	NOUN
ejpam-3900	159	20	(	(	PUNCT
ejpam-3900	159	21	−1)j−1	−1)j−1	PROPN
ejpam-3900	159	22	rk+j+1,q	rk+j+1,q	PROPN
ejpam-3900	159	23	rk+1,q	rk+1,q	PROPN
ejpam-3900	159	24	lm	lm	PROPN
ejpam-3900	159	25	,	,	PUNCT
ejpam-3900	159	26	r[n	r[n	NOUN
ejpam-3900	159	27	,	,	PUNCT
ejpam-3900	159	28	k	k	PROPN
ejpam-3900	159	29	+	+	CCONJ
ejpam-3900	159	30	j]q	j]q	ADJ
ejpam-3900	159	31	=	=	SYM
ejpam-3900	159	32	rk+1,q	rk+1,q	PROPN
ejpam-3900	159	33	rk+1,q	rk+1,q	PROPN
ejpam-3900	159	34	lm	lm	PROPN
ejpam-3900	159	35	,	,	PUNCT
ejpam-3900	159	36	r[n	r[n	NOUN
ejpam-3900	159	37	,	,	PUNCT
ejpam-3900	159	38	k]q	k]q	NOUN
ejpam-3900	159	39	=	=	SYM
ejpam-3900	159	40	lm	lm	PROPN
ejpam-3900	159	41	,	,	PUNCT
ejpam-3900	159	42	r[n	r[n	NOUN
ejpam-3900	159	43	,	,	PUNCT
ejpam-3900	159	44	k]q	k]q	PROPN
ejpam-3900	159	45	.	.	PUNCT
ejpam-3900	160	1	r.	r.	PROPN
ejpam-3900	160	2	corcino	corcino	PROPN
ejpam-3900	160	3	,	,	PUNCT
ejpam-3900	160	4	j.	j.	PROPN
ejpam-3900	160	5	ontolan	ontolan	PROPN
ejpam-3900	160	6	,	,	PUNCT
ejpam-3900	160	7	m.	m.	NOUN
ejpam-3900	160	8	lobrigas	lobrigas	PROPN
ejpam-3900	160	9	/	/	SYM
ejpam-3900	160	10	eur	eur	PROPN
ejpam-3900	160	11	.	.	PUNCT
ejpam-3900	161	1	j.	j.	PROPN
ejpam-3900	161	2	pure	pure	PROPN
ejpam-3900	161	3	appl	appl	PROPN
ejpam-3900	161	4	.	.	PROPN
ejpam-3900	161	5	math	math	PROPN
ejpam-3900	161	6	,	,	PUNCT
ejpam-3900	161	7	14	14	NUM
ejpam-3900	161	8	(	(	PUNCT
ejpam-3900	161	9	1	1	NUM
ejpam-3900	161	10	)	)	PUNCT
ejpam-3900	161	11	(	(	PUNCT
ejpam-3900	161	12	2021	2021	NUM
ejpam-3900	161	13	)	)	PUNCT
ejpam-3900	161	14	,	,	PUNCT
ejpam-3900	161	15	65	65	NUM
ejpam-3900	161	16	-	-	SYM
ejpam-3900	161	17	81	81	NUM
ejpam-3900	161	18	72	72	NUM
ejpam-3900	161	19	3	3	NUM
ejpam-3900	161	20	.	.	PUNCT
ejpam-3900	161	21	explicit	explicit	ADJ
ejpam-3900	161	22	formula	formula	NOUN
ejpam-3900	161	23	and	and	CCONJ
ejpam-3900	161	24	generating	generating	NOUN
ejpam-3900	161	25	functions	function	NOUN
ejpam-3900	161	26	the	the	DET
ejpam-3900	161	27	ordinary	ordinary	ADJ
ejpam-3900	161	28	generating	generating	NOUN
ejpam-3900	161	29	function	function	NOUN
ejpam-3900	161	30	for	for	ADP
ejpam-3900	161	31	the	the	DET
ejpam-3900	161	32	sequence	sequence	NOUN
ejpam-3900	161	33	(	(	PUNCT
ejpam-3900	161	34	ar	ar	NOUN
ejpam-3900	161	35	)	)	PUNCT
ejpam-3900	161	36	is	be	AUX
ejpam-3900	161	37	defined	define	VERB
ejpam-3900	161	38	to	to	PART
ejpam-3900	161	39	be	be	AUX
ejpam-3900	161	40	the	the	DET
ejpam-3900	161	41	power	power	NOUN
ejpam-3900	161	42	series	series	NOUN
ejpam-3900	161	43	a(x	a(x	PROPN
ejpam-3900	161	44	)	)	PUNCT
ejpam-3900	161	45	=	=	PUNCT
ejpam-3900	162	1	∞∑	∞∑	NUM
ejpam-3900	162	2	r=0	r=0	ADJ
ejpam-3900	162	3	arx	arx	PROPN
ejpam-3900	162	4	r.	r.	NOUN
ejpam-3900	162	5	it	it	PRON
ejpam-3900	162	6	is	be	AUX
ejpam-3900	162	7	a	a	DET
ejpam-3900	162	8	way	way	NOUN
ejpam-3900	162	9	of	of	ADP
ejpam-3900	162	10	uniting	unite	VERB
ejpam-3900	162	11	the	the	DET
ejpam-3900	162	12	power	power	NOUN
ejpam-3900	162	13	series	series	NOUN
ejpam-3900	162	14	in	in	ADP
ejpam-3900	162	15	compact	compact	ADJ
ejpam-3900	162	16	form	form	NOUN
ejpam-3900	162	17	which	which	PRON
ejpam-3900	162	18	describes	describe	VERB
ejpam-3900	162	19	the	the	DET
ejpam-3900	162	20	sequence	sequence	NOUN
ejpam-3900	162	21	as	as	ADP
ejpam-3900	162	22	coefficients	coefficient	NOUN
ejpam-3900	162	23	of	of	ADP
ejpam-3900	162	24	the	the	DET
ejpam-3900	162	25	variable	variable	NOUN
ejpam-3900	162	26	xr	xr	PROPN
ejpam-3900	162	27	determined	determine	VERB
ejpam-3900	162	28	by	by	ADP
ejpam-3900	162	29	its	its	PRON
ejpam-3900	162	30	power	power	NOUN
ejpam-3900	162	31	.	.	PUNCT
ejpam-3900	163	1	generating	generate	VERB
ejpam-3900	163	2	function	function	NOUN
ejpam-3900	163	3	is	be	AUX
ejpam-3900	163	4	useful	useful	ADJ
ejpam-3900	163	5	in	in	ADP
ejpam-3900	163	6	drawing	draw	VERB
ejpam-3900	163	7	combinatorial	combinatorial	ADJ
ejpam-3900	163	8	interpretation	interpretation	NOUN
ejpam-3900	163	9	of	of	ADP
ejpam-3900	163	10	a	a	DET
ejpam-3900	163	11	given	give	VERB
ejpam-3900	163	12	sequence	sequence	NOUN
ejpam-3900	163	13	of	of	ADP
ejpam-3900	163	14	numbers	number	NOUN
ejpam-3900	163	15	as	as	ADV
ejpam-3900	163	16	well	well	ADV
ejpam-3900	163	17	as	as	ADP
ejpam-3900	163	18	in	in	ADP
ejpam-3900	163	19	finding	find	VERB
ejpam-3900	163	20	asymptotic	asymptotic	ADJ
ejpam-3900	163	21	expansion	expansion	NOUN
ejpam-3900	163	22	of	of	ADP
ejpam-3900	163	23	a	a	DET
ejpam-3900	163	24	given	give	VERB
ejpam-3900	163	25	number	number	NOUN
ejpam-3900	163	26	.	.	PUNCT
ejpam-3900	164	1	motivated	motivate	VERB
ejpam-3900	164	2	by	by	ADP
ejpam-3900	164	3	the	the	DET
ejpam-3900	164	4	power	power	NOUN
ejpam-3900	164	5	series	series	PROPN
ejpam-3900	164	6	expansion	expansion	NOUN
ejpam-3900	164	7	of	of	ADP
ejpam-3900	164	8	the	the	DET
ejpam-3900	164	9	exponential	exponential	ADJ
ejpam-3900	164	10	function	function	NOUN
ejpam-3900	164	11	e(x	e(x	NUM
ejpam-3900	164	12	)	)	PUNCT
ejpam-3900	165	1	=	=	PUNCT
ejpam-3900	166	1	∞∑	∞∑	NUM
ejpam-3900	166	2	r=0	r=0	NUM
ejpam-3900	166	3	xr	xr	NOUN
ejpam-3900	166	4	r	r	PROPN
ejpam-3900	166	5	!	!	PROPN
ejpam-3900	166	6	,	,	PUNCT
ejpam-3900	166	7	a	a	DET
ejpam-3900	166	8	generating	generate	VERB
ejpam-3900	166	9	function	function	NOUN
ejpam-3900	166	10	that	that	PRON
ejpam-3900	166	11	expresses	express	VERB
ejpam-3900	166	12	the	the	DET
ejpam-3900	166	13	sequence	sequence	NOUN
ejpam-3900	166	14	of	of	ADP
ejpam-3900	166	15	numbers	number	NOUN
ejpam-3900	166	16	(	(	PUNCT
ejpam-3900	166	17	ar	ar	NOUN
ejpam-3900	166	18	)	)	PUNCT
ejpam-3900	166	19	as	as	ADP
ejpam-3900	166	20	coefficients	coefficient	NOUN
ejpam-3900	166	21	of	of	ADP
ejpam-3900	166	22	xr	xr	PROPN
ejpam-3900	166	23	r	r	PROPN
ejpam-3900	166	24	!	!	PROPN
ejpam-3900	166	25	,	,	PUNCT
ejpam-3900	166	26	say	say	INTJ
ejpam-3900	166	27	,	,	PUNCT
ejpam-3900	166	28	e(x	e(x	NUM
ejpam-3900	166	29	)	)	PUNCT
ejpam-3900	166	30	=	=	PUNCT
ejpam-3900	167	1	∞∑	∞∑	NUM
ejpam-3900	167	2	r=0	r=0	PROPN
ejpam-3900	167	3	ar	ar	NOUN
ejpam-3900	167	4	xr	xr	PROPN
ejpam-3900	167	5	r	r	PROPN
ejpam-3900	167	6	!	!	PROPN
ejpam-3900	167	7	,	,	PUNCT
ejpam-3900	167	8	is	be	AUX
ejpam-3900	167	9	called	call	VERB
ejpam-3900	167	10	an	an	DET
ejpam-3900	167	11	exponential	exponential	ADJ
ejpam-3900	167	12	generating	generating	NOUN
ejpam-3900	167	13	function	function	NOUN
ejpam-3900	167	14	for	for	ADP
ejpam-3900	167	15	(	(	PUNCT
ejpam-3900	167	16	ar	ar	NOUN
ejpam-3900	167	17	)	)	PUNCT
ejpam-3900	167	18	.	.	PUNCT
ejpam-3900	168	1	if	if	SCONJ
ejpam-3900	168	2	a	a	DET
ejpam-3900	168	3	number	number	NOUN
ejpam-3900	168	4	a(n	a(n	NOUN
ejpam-3900	168	5	,	,	PUNCT
ejpam-3900	168	6	k	k	NOUN
ejpam-3900	168	7	)	)	PUNCT
ejpam-3900	168	8	is	be	AUX
ejpam-3900	168	9	a	a	DET
ejpam-3900	168	10	function	function	NOUN
ejpam-3900	168	11	of	of	ADP
ejpam-3900	168	12	two	two	NUM
ejpam-3900	168	13	parameters	parameter	NOUN
ejpam-3900	168	14	n	n	CCONJ
ejpam-3900	168	15	and	and	CCONJ
ejpam-3900	168	16	k	k	NOUN
ejpam-3900	168	17	,	,	PUNCT
ejpam-3900	168	18	then	then	ADV
ejpam-3900	168	19	the	the	DET
ejpam-3900	168	20	generating	generate	VERB
ejpam-3900	168	21	function	function	NOUN
ejpam-3900	168	22	for	for	ADP
ejpam-3900	168	23	a(n	a(n	NOUN
ejpam-3900	168	24	,	,	PUNCT
ejpam-3900	168	25	k	k	NOUN
ejpam-3900	168	26	)	)	PUNCT
ejpam-3900	168	27	can	can	AUX
ejpam-3900	168	28	be	be	AUX
ejpam-3900	168	29	expressed	express	VERB
ejpam-3900	168	30	in	in	ADP
ejpam-3900	168	31	two	two	NUM
ejpam-3900	168	32	forms	form	NOUN
ejpam-3900	168	33	:	:	PUNCT
ejpam-3900	168	34	the	the	DET
ejpam-3900	168	35	horizontal	horizontal	ADJ
ejpam-3900	168	36	and	and	CCONJ
ejpam-3900	168	37	vertical	vertical	ADJ
ejpam-3900	168	38	generating	generating	NOUN
ejpam-3900	168	39	functions	function	NOUN
ejpam-3900	168	40	.	.	PUNCT
ejpam-3900	169	1	the	the	DET
ejpam-3900	169	2	following	follow	VERB
ejpam-3900	169	3	generating	generate	VERB
ejpam-3900	169	4	function	function	NOUN
ejpam-3900	169	5	is	be	AUX
ejpam-3900	169	6	the	the	DET
ejpam-3900	169	7	horizontal	horizontal	ADJ
ejpam-3900	169	8	generating	generating	NOUN
ejpam-3900	169	9	function	function	NOUN
ejpam-3900	169	10	for	for	ADP
ejpam-3900	169	11	lm	lm	PROPN
ejpam-3900	169	12	,	,	PUNCT
ejpam-3900	169	13	r[n	r[n	NOUN
ejpam-3900	169	14	,	,	PUNCT
ejpam-3900	169	15	k]q	k]q	NOUN
ejpam-3900	169	16	that	that	PRON
ejpam-3900	169	17	expresses	express	VERB
ejpam-3900	169	18	the	the	DET
ejpam-3900	169	19	values	value	NOUN
ejpam-3900	169	20	in	in	ADP
ejpam-3900	169	21	the	the	DET
ejpam-3900	169	22	nth	nth	NOUN
ejpam-3900	169	23	row	row	NOUN
ejpam-3900	169	24	of	of	ADP
ejpam-3900	169	25	the	the	DET
ejpam-3900	169	26	array	array	NOUN
ejpam-3900	169	27	of	of	ADP
ejpam-3900	169	28	numbers	number	NOUN
ejpam-3900	169	29	lm	lm	ADP
ejpam-3900	169	30	,	,	PUNCT
ejpam-3900	169	31	r[n	r[n	NOUN
ejpam-3900	169	32	,	,	PUNCT
ejpam-3900	169	33	k]q	k]q	X
ejpam-3900	169	34	(	(	PUNCT
ejpam-3900	169	35	i.e.	i.e.	X
ejpam-3900	169	36	,	,	PUNCT
ejpam-3900	169	37	fixing	fix	VERB
ejpam-3900	169	38	the	the	DET
ejpam-3900	169	39	value	value	NOUN
ejpam-3900	169	40	of	of	ADP
ejpam-3900	169	41	n	n	CCONJ
ejpam-3900	169	42	)	)	PUNCT
ejpam-3900	169	43	,	,	PUNCT
ejpam-3900	169	44	as	as	ADP
ejpam-3900	169	45	coefficients	coefficient	NOUN
ejpam-3900	169	46	of	of	ADP
ejpam-3900	169	47	the	the	DET
ejpam-3900	169	48	variable	variable	NOUN
ejpam-3900	169	49	[	[	X
ejpam-3900	169	50	t|m]k	t|m]k	PROPN
ejpam-3900	169	51	,	,	PUNCT
ejpam-3900	169	52	q.	q.	NOUN
ejpam-3900	169	53	this	this	PRON
ejpam-3900	169	54	is	be	AUX
ejpam-3900	169	55	necessary	necessary	ADJ
ejpam-3900	169	56	to	to	PART
ejpam-3900	169	57	obtain	obtain	VERB
ejpam-3900	169	58	the	the	DET
ejpam-3900	169	59	exponential	exponential	ADJ
ejpam-3900	169	60	generating	generating	NOUN
ejpam-3900	169	61	function	function	NOUN
ejpam-3900	169	62	and	and	CCONJ
ejpam-3900	169	63	explicit	explicit	ADJ
ejpam-3900	169	64	formula	formula	NOUN
ejpam-3900	169	65	of	of	ADP
ejpam-3900	169	66	lm	lm	PROPN
ejpam-3900	169	67	,	,	PUNCT
ejpam-3900	169	68	r[n	r[n	NOUN
ejpam-3900	169	69	,	,	PUNCT
ejpam-3900	169	70	k]q	k]q	PROPN
ejpam-3900	169	71	.	.	PUNCT
ejpam-3900	170	1	theorem	theorem	VERB
ejpam-3900	170	2	3.1	3.1	NUM
ejpam-3900	170	3	.	.	PUNCT
ejpam-3900	171	1	a	a	DET
ejpam-3900	171	2	horizontal	horizontal	ADJ
ejpam-3900	171	3	generating	generate	VERB
ejpam-3900	171	4	function	function	NOUN
ejpam-3900	171	5	of	of	ADP
ejpam-3900	171	6	lm	lm	PROPN
ejpam-3900	171	7	,	,	PUNCT
ejpam-3900	171	8	r[n	r[n	NOUN
ejpam-3900	171	9	,	,	PUNCT
ejpam-3900	171	10	k]q	k]q	NOUN
ejpam-3900	171	11	is	be	AUX
ejpam-3900	171	12	given	give	VERB
ejpam-3900	171	13	by	by	ADP
ejpam-3900	171	14	n∑	n∑	PROPN
ejpam-3900	171	15	k=0	k=0	PROPN
ejpam-3900	171	16	lm	lm	PROPN
ejpam-3900	171	17	,	,	PUNCT
ejpam-3900	171	18	r[n	r[n	NOUN
ejpam-3900	171	19	,	,	PUNCT
ejpam-3900	171	20	k]q	k]q	NOUN
ejpam-3900	172	1	[	[	X
ejpam-3900	172	2	t|m]k	t|m]k	NUM
ejpam-3900	172	3	,	,	PUNCT
ejpam-3900	172	4	q	q	NOUN
ejpam-3900	172	5	=	=	PUNCT
ejpam-3900	173	1	[	[	X
ejpam-3900	173	2	t+	t+	NOUN
ejpam-3900	173	3	2r|m]n	2r|m]n	NOUN
ejpam-3900	173	4	,	,	PUNCT
ejpam-3900	173	5	q	q	X
ejpam-3900	173	6	(	(	PUNCT
ejpam-3900	173	7	16	16	NUM
ejpam-3900	173	8	)	)	PUNCT
ejpam-3900	173	9	where	where	SCONJ
ejpam-3900	173	10	[	[	X
ejpam-3900	173	11	t+	t+	NOUN
ejpam-3900	173	12	2r|m]n	2r|m]n	NOUN
ejpam-3900	173	13	,	,	PUNCT
ejpam-3900	173	14	q	q	NOUN
ejpam-3900	173	15	=	=	PUNCT
ejpam-3900	173	16	{	{	PUNCT
ejpam-3900	173	17	∏n−1	∏n−1	PROPN
ejpam-3900	173	18	i=0	i=0	PROPN
ejpam-3900	174	1	[	[	X
ejpam-3900	174	2	t+	t+	NOUN
ejpam-3900	174	3	2r	2r	NUM
ejpam-3900	174	4	+	+	NUM
ejpam-3900	174	5	im]q	im]q	NOUN
ejpam-3900	174	6	,	,	PUNCT
ejpam-3900	174	7	if	if	SCONJ
ejpam-3900	174	8	n	n	PRON
ejpam-3900	174	9	≥	≥	NOUN
ejpam-3900	174	10	1	1	NUM
ejpam-3900	174	11	,	,	PUNCT
ejpam-3900	174	12	1	1	NUM
ejpam-3900	174	13	,	,	PUNCT
ejpam-3900	174	14	if	if	SCONJ
ejpam-3900	174	15	n	n	ADV
ejpam-3900	174	16	=	=	SYM
ejpam-3900	174	17	0	0	X
ejpam-3900	174	18	.	.	PUNCT
ejpam-3900	174	19	proof	proof	NOUN
ejpam-3900	174	20	.	.	PUNCT
ejpam-3900	175	1	to	to	PART
ejpam-3900	175	2	prove	prove	VERB
ejpam-3900	175	3	this	this	PRON
ejpam-3900	175	4	,	,	PUNCT
ejpam-3900	175	5	we	we	PRON
ejpam-3900	175	6	will	will	AUX
ejpam-3900	175	7	use	use	VERB
ejpam-3900	175	8	induction	induction	NOUN
ejpam-3900	175	9	.	.	PUNCT
ejpam-3900	176	1	we	we	PRON
ejpam-3900	176	2	now	now	ADV
ejpam-3900	176	3	verify	verify	VERB
ejpam-3900	176	4	that	that	SCONJ
ejpam-3900	176	5	(	(	PUNCT
ejpam-3900	176	6	16	16	NUM
ejpam-3900	176	7	)	)	PUNCT
ejpam-3900	176	8	holds	hold	VERB
ejpam-3900	176	9	when	when	SCONJ
ejpam-3900	176	10	n=0	n=0	NUM
ejpam-3900	176	11	.	.	PUNCT
ejpam-3900	177	1	lm	lm	ADJ
ejpam-3900	177	2	,	,	PUNCT
ejpam-3900	177	3	r[0	r[0	PROPN
ejpam-3900	177	4	,	,	PUNCT
ejpam-3900	177	5	0]q	0]q	PUNCT
ejpam-3900	178	1	[	[	X
ejpam-3900	178	2	t|m]0,q	t|m]0,q	X
ejpam-3900	178	3	=	=	SYM
ejpam-3900	178	4	1	1	NUM
ejpam-3900	178	5	·	·	SYM
ejpam-3900	178	6	1	1	NUM
ejpam-3900	178	7	=	=	SYM
ejpam-3900	178	8	1	1	NUM
ejpam-3900	178	9	=	=	SYM
ejpam-3900	179	1	[	[	X
ejpam-3900	179	2	t+	t+	NOUN
ejpam-3900	179	3	2r|m]0,q	2r|m]0,q	NUM
ejpam-3900	179	4	.	.	PUNCT
ejpam-3900	179	5	suppose	suppose	VERB
ejpam-3900	179	6	that	that	SCONJ
ejpam-3900	179	7	it	it	PRON
ejpam-3900	179	8	is	be	AUX
ejpam-3900	179	9	true	true	ADJ
ejpam-3900	179	10	for	for	ADP
ejpam-3900	179	11	some	some	PRON
ejpam-3900	179	12	n	n	NOUN
ejpam-3900	179	13	>	>	X
ejpam-3900	179	14	0	0	NUM
ejpam-3900	179	15	.	.	PUNCT
ejpam-3900	180	1	then	then	ADV
ejpam-3900	180	2	,	,	PUNCT
ejpam-3900	180	3	n∑	n∑	PROPN
ejpam-3900	180	4	k=0	k=0	PROPN
ejpam-3900	180	5	lm	lm	PROPN
ejpam-3900	180	6	,	,	PUNCT
ejpam-3900	180	7	r[n	r[n	NOUN
ejpam-3900	180	8	,	,	PUNCT
ejpam-3900	180	9	k]q	k]q	NOUN
ejpam-3900	181	1	[	[	X
ejpam-3900	181	2	t|m]k	t|m]k	NUM
ejpam-3900	181	3	,	,	PUNCT
ejpam-3900	181	4	q	q	NOUN
ejpam-3900	181	5	=	=	PUNCT
ejpam-3900	182	1	[	[	X
ejpam-3900	182	2	t+	t+	NOUN
ejpam-3900	182	3	2r|m]n	2r|m]n	NOUN
ejpam-3900	182	4	,	,	PUNCT
ejpam-3900	182	5	q.	q.	PROPN
ejpam-3900	182	6	r.	r.	PROPN
ejpam-3900	182	7	corcino	corcino	PROPN
ejpam-3900	182	8	,	,	PUNCT
ejpam-3900	182	9	j.	j.	PROPN
ejpam-3900	182	10	ontolan	ontolan	PROPN
ejpam-3900	182	11	,	,	PUNCT
ejpam-3900	182	12	m.	m.	NOUN
ejpam-3900	182	13	lobrigas	lobrigas	PROPN
ejpam-3900	182	14	/	/	SYM
ejpam-3900	182	15	eur	eur	PROPN
ejpam-3900	182	16	.	.	PUNCT
ejpam-3900	183	1	j.	j.	PROPN
ejpam-3900	183	2	pure	pure	PROPN
ejpam-3900	183	3	appl	appl	PROPN
ejpam-3900	183	4	.	.	PROPN
ejpam-3900	183	5	math	math	PROPN
ejpam-3900	183	6	,	,	PUNCT
ejpam-3900	183	7	14	14	NUM
ejpam-3900	183	8	(	(	PUNCT
ejpam-3900	183	9	1	1	NUM
ejpam-3900	183	10	)	)	PUNCT
ejpam-3900	183	11	(	(	PUNCT
ejpam-3900	183	12	2021	2021	NUM
ejpam-3900	183	13	)	)	PUNCT
ejpam-3900	183	14	,	,	PUNCT
ejpam-3900	183	15	65	65	NUM
ejpam-3900	183	16	-	-	SYM
ejpam-3900	183	17	81	81	NUM
ejpam-3900	183	18	73	73	NUM
ejpam-3900	183	19	next	next	ADV
ejpam-3900	183	20	,	,	PUNCT
ejpam-3900	183	21	we	we	PRON
ejpam-3900	183	22	show	show	VERB
ejpam-3900	183	23	that	that	SCONJ
ejpam-3900	183	24	n+1∑	n+1∑	PROPN
ejpam-3900	183	25	k=0	k=0	PROPN
ejpam-3900	183	26	lm	lm	PROPN
ejpam-3900	183	27	,	,	PUNCT
ejpam-3900	183	28	r[n+	r[n+	NOUN
ejpam-3900	183	29	1	1	NUM
ejpam-3900	183	30	,	,	PUNCT
ejpam-3900	183	31	k]q	k]q	VERB
ejpam-3900	184	1	[	[	X
ejpam-3900	184	2	t|m]k	t|m]k	NUM
ejpam-3900	184	3	,	,	PUNCT
ejpam-3900	184	4	q	q	NOUN
ejpam-3900	184	5	=	=	PUNCT
ejpam-3900	185	1	[	[	X
ejpam-3900	185	2	t+	t+	NOUN
ejpam-3900	185	3	2r|m]n+1,q	2r|m]n+1,q	NOUN
ejpam-3900	185	4	.	.	PUNCT
ejpam-3900	186	1	using	use	VERB
ejpam-3900	186	2	(	(	PUNCT
ejpam-3900	186	3	15	15	NUM
ejpam-3900	186	4	)	)	PUNCT
ejpam-3900	186	5	and	and	CCONJ
ejpam-3900	186	6	the	the	DET
ejpam-3900	186	7	fact	fact	NOUN
ejpam-3900	186	8	that	that	PRON
ejpam-3900	186	9	.	.	PUNCT
ejpam-3900	187	1	[	[	X
ejpam-3900	187	2	t|m]k+1,q	t|m]k+1,q	NOUN
ejpam-3900	187	3	=	=	SYM
ejpam-3900	188	1	[	[	X
ejpam-3900	188	2	t|m]k	t|m]k	NUM
ejpam-3900	188	3	,	,	PUNCT
ejpam-3900	188	4	q[t−	q[t−	PROPN
ejpam-3900	188	5	km]q	km]q	PROPN
ejpam-3900	188	6	,	,	PUNCT
ejpam-3900	188	7	we	we	PRON
ejpam-3900	188	8	get	get	VERB
ejpam-3900	188	9	n+1∑	n+1∑	PROPN
ejpam-3900	188	10	k=0	k=0	PROPN
ejpam-3900	188	11	lm	lm	PROPN
ejpam-3900	188	12	,	,	PUNCT
ejpam-3900	188	13	r[n+1	r[n+1	PROPN
ejpam-3900	188	14	,	,	PUNCT
ejpam-3900	188	15	k]q	k]q	VERB
ejpam-3900	189	1	[	[	X
ejpam-3900	189	2	t|m]k	t|m]k	NUM
ejpam-3900	189	3	,	,	PUNCT
ejpam-3900	189	4	q	q	X
ejpam-3900	189	5	=	=	SYM
ejpam-3900	189	6	n+1∑	n+1∑	PROPN
ejpam-3900	189	7	k=0	k=0	PROPN
ejpam-3900	189	8	{	{	PUNCT
ejpam-3900	189	9	q2r+m(k−1)+mnlm	q2r+m(k−1)+mnlm	X
ejpam-3900	189	10	,	,	PUNCT
ejpam-3900	189	11	r[n	r[n	NOUN
ejpam-3900	189	12	,	,	PUNCT
ejpam-3900	189	13	k−1]q+[2r+km+nm]qlm	k−1]q+[2r+km+nm]qlm	PROPN
ejpam-3900	189	14	,	,	PUNCT
ejpam-3900	189	15	r[n	r[n	NOUN
ejpam-3900	189	16	,	,	PUNCT
ejpam-3900	189	17	k]q}[t|m]k	k]q}[t|m]k	VERB
ejpam-3900	189	18	,	,	PUNCT
ejpam-3900	189	19	q	q	X
ejpam-3900	189	20	=	=	PUNCT
ejpam-3900	189	21	n+1∑	n+1∑	PROPN
ejpam-3900	189	22	k=0	k=0	PROPN
ejpam-3900	189	23	q2r+m(k−1)+mnlm	q2r+m(k−1)+mnlm	PROPN
ejpam-3900	189	24	,	,	PUNCT
ejpam-3900	189	25	r[n	r[n	VERB
ejpam-3900	189	26	,	,	PUNCT
ejpam-3900	189	27	k	k	PROPN
ejpam-3900	189	28	−	−	PROPN
ejpam-3900	190	1	1]q[t|m]k	1]q[t|m]k	NUM
ejpam-3900	190	2	,	,	PUNCT
ejpam-3900	190	3	q	q	X
ejpam-3900	191	1	+	+	CCONJ
ejpam-3900	191	2	n+1∑	n+1∑	ADJ
ejpam-3900	191	3	k=0	k=0	PROPN
ejpam-3900	192	1	[	[	X
ejpam-3900	192	2	2r	2r	X
ejpam-3900	192	3	+	+	NUM
ejpam-3900	192	4	km+	km+	PROPN
ejpam-3900	192	5	nm]qlm	nm]qlm	NOUN
ejpam-3900	192	6	,	,	PUNCT
ejpam-3900	192	7	r[n	r[n	NOUN
ejpam-3900	192	8	,	,	PUNCT
ejpam-3900	192	9	k]q[t|m]k	k]q[t|m]k	NOUN
ejpam-3900	192	10	,	,	PUNCT
ejpam-3900	192	11	q	q	PROPN
ejpam-3900	192	12	=	=	SYM
ejpam-3900	192	13	n∑	n∑	PROPN
ejpam-3900	192	14	k=0	k=0	PROPN
ejpam-3900	192	15	q2r+mk+mnlm	q2r+mk+mnlm	PROPN
ejpam-3900	192	16	,	,	PUNCT
ejpam-3900	192	17	r[n	r[n	NOUN
ejpam-3900	192	18	,	,	PUNCT
ejpam-3900	192	19	k]q[t|m]k+1,q	k]q[t|m]k+1,q	NOUN
ejpam-3900	192	20	+	+	CCONJ
ejpam-3900	193	1	n∑	n∑	NOUN
ejpam-3900	193	2	k=0	k=0	PROPN
ejpam-3900	194	1	[	[	X
ejpam-3900	194	2	2r	2r	X
ejpam-3900	194	3	+	+	NUM
ejpam-3900	194	4	km+	km+	PROPN
ejpam-3900	194	5	nm]qlm	nm]qlm	NOUN
ejpam-3900	194	6	,	,	PUNCT
ejpam-3900	194	7	r[n	r[n	NOUN
ejpam-3900	194	8	,	,	PUNCT
ejpam-3900	194	9	k]q[t|m]k	k]q[t|m]k	NOUN
ejpam-3900	194	10	,	,	PUNCT
ejpam-3900	194	11	q	q	PROPN
ejpam-3900	194	12	=	=	SYM
ejpam-3900	194	13	n∑	n∑	PROPN
ejpam-3900	194	14	k=0	k=0	PROPN
ejpam-3900	194	15	q2r+mk+mnlm	q2r+mk+mnlm	PROPN
ejpam-3900	194	16	,	,	PUNCT
ejpam-3900	194	17	r[n	r[n	NOUN
ejpam-3900	194	18	,	,	PUNCT
ejpam-3900	194	19	k]q[t|m]k	k]q[t|m]k	NOUN
ejpam-3900	194	20	,	,	PUNCT
ejpam-3900	194	21	q[t−	q[t−	PROPN
ejpam-3900	194	22	km]q	km]q	PROPN
ejpam-3900	194	23	+	+	CCONJ
ejpam-3900	194	24	n∑	n∑	NOUN
ejpam-3900	194	25	k=0	k=0	PROPN
ejpam-3900	195	1	[	[	X
ejpam-3900	195	2	2r	2r	X
ejpam-3900	195	3	+	+	NUM
ejpam-3900	195	4	km+	km+	PROPN
ejpam-3900	195	5	nm]qlm	nm]qlm	NOUN
ejpam-3900	195	6	,	,	PUNCT
ejpam-3900	195	7	r[n	r[n	NOUN
ejpam-3900	195	8	,	,	PUNCT
ejpam-3900	195	9	k]q[t|m]k	k]q[t|m]k	NOUN
ejpam-3900	195	10	,	,	PUNCT
ejpam-3900	195	11	q.	q.	PROPN
ejpam-3900	195	12	note	note	VERB
ejpam-3900	195	13	that	that	SCONJ
ejpam-3900	196	1	[	[	X
ejpam-3900	196	2	t	t	X
ejpam-3900	196	3	−	−	NOUN
ejpam-3900	196	4	k]q	k]q	NOUN
ejpam-3900	196	5	=	=	SYM
ejpam-3900	196	6	1	1	NUM
ejpam-3900	196	7	qk	qk	NOUN
ejpam-3900	196	8	(	(	PUNCT
ejpam-3900	196	9	[	[	X
ejpam-3900	196	10	t]q	t]q	NOUN
ejpam-3900	196	11	−	−	NOUN
ejpam-3900	197	1	[	[	X
ejpam-3900	197	2	k]q	k]q	NOUN
ejpam-3900	197	3	)	)	PUNCT
ejpam-3900	197	4	.	.	PUNCT
ejpam-3900	198	1	since	since	SCONJ
ejpam-3900	198	2	[	[	X
ejpam-3900	198	3	t	t	X
ejpam-3900	198	4	−	−	PROPN
ejpam-3900	198	5	km]q	km]q	PROPN
ejpam-3900	198	6	=	=	PUNCT
ejpam-3900	199	1	[	[	X
ejpam-3900	199	2	t	t	X
ejpam-3900	199	3	+	+	NUM
ejpam-3900	199	4	2r	2r	NUM
ejpam-3900	199	5	+	+	CCONJ
ejpam-3900	199	6	nm	nm	PROPN
ejpam-3900	199	7	−	−	PROPN
ejpam-3900	199	8	2r	2r	NUM
ejpam-3900	199	9	−	−	PROPN
ejpam-3900	199	10	nm	nm	PUNCT
ejpam-3900	199	11	−	−	PROPN
ejpam-3900	199	12	km]q	km]q	PROPN
ejpam-3900	200	1	=	=	SYM
ejpam-3900	201	1	[	[	X
ejpam-3900	201	2	(	(	PUNCT
ejpam-3900	201	3	t+	t+	NOUN
ejpam-3900	201	4	2r	2r	NUM
ejpam-3900	201	5	+	+	CCONJ
ejpam-3900	201	6	nm)−	nm)−	PROPN
ejpam-3900	201	7	(	(	PUNCT
ejpam-3900	201	8	2r	2r	NUM
ejpam-3900	201	9	+	+	CCONJ
ejpam-3900	201	10	km+	km+	PROPN
ejpam-3900	201	11	nm)]q	nm)]q	NOUN
ejpam-3900	201	12	,	,	PUNCT
ejpam-3900	201	13	then	then	ADV
ejpam-3900	201	14	[	[	X
ejpam-3900	201	15	t−	t−	PROPN
ejpam-3900	201	16	km]q	km]q	PROPN
ejpam-3900	201	17	=	=	SYM
ejpam-3900	201	18	1	1	NUM
ejpam-3900	201	19	q2r+mk+mn	q2r+mk+mn	X
ejpam-3900	201	20	(	(	PUNCT
ejpam-3900	201	21	[	[	X
ejpam-3900	201	22	t+	t+	X
ejpam-3900	201	23	2r	2r	NUM
ejpam-3900	201	24	+	+	CCONJ
ejpam-3900	201	25	nm]q	nm]q	PROPN
ejpam-3900	201	26	−	−	PROPN
ejpam-3900	202	1	[	[	X
ejpam-3900	202	2	2r	2r	X
ejpam-3900	202	3	+	+	NUM
ejpam-3900	202	4	km+	km+	PROPN
ejpam-3900	202	5	nm]q	nm]q	PROPN
ejpam-3900	202	6	)	)	PUNCT
ejpam-3900	202	7	.	.	PUNCT
ejpam-3900	203	1	thus	thus	ADV
ejpam-3900	203	2	,	,	PUNCT
ejpam-3900	203	3	n+1∑	n+1∑	PROPN
ejpam-3900	203	4	k=0	k=0	PROPN
ejpam-3900	203	5	lm	lm	PROPN
ejpam-3900	203	6	,	,	PUNCT
ejpam-3900	203	7	r[n+1	r[n+1	PROPN
ejpam-3900	203	8	,	,	PUNCT
ejpam-3900	203	9	k]q	k]q	VERB
ejpam-3900	204	1	[	[	X
ejpam-3900	204	2	t|m]k	t|m]k	NUM
ejpam-3900	204	3	,	,	PUNCT
ejpam-3900	204	4	q	q	NOUN
ejpam-3900	204	5	=	=	SYM
ejpam-3900	204	6	n∑	n∑	PROPN
ejpam-3900	204	7	k=0	k=0	PROPN
ejpam-3900	204	8	q2r+mk+mnlm	q2r+mk+mnlm	PROPN
ejpam-3900	204	9	,	,	PUNCT
ejpam-3900	204	10	r[n	r[n	NOUN
ejpam-3900	204	11	,	,	PUNCT
ejpam-3900	204	12	k]q[t|m]k	k]q[t|m]k	NOUN
ejpam-3900	204	13	,	,	PUNCT
ejpam-3900	204	14	q	q	X
ejpam-3900	204	15	{	{	PUNCT
ejpam-3900	204	16	q−(2r+mk+mn)([t+	q−(2r+mk+mn)([t+	NOUN
ejpam-3900	204	17	2r+nm]q−	2r+nm]q−	NUM
ejpam-3900	204	18	[	[	X
ejpam-3900	204	19	2r+km+nm]q)}+	2r+km+nm]q)}+	NUM
ejpam-3900	204	20	n∑	n∑	NOUN
ejpam-3900	204	21	k=0	k=0	PROPN
ejpam-3900	205	1	[	[	X
ejpam-3900	205	2	2r+km+nm]qlm	2r+km+nm]qlm	NUM
ejpam-3900	205	3	,	,	PUNCT
ejpam-3900	205	4	r[n	r[n	NOUN
ejpam-3900	205	5	,	,	PUNCT
ejpam-3900	205	6	k]q[t|m]k	k]q[t|m]k	NOUN
ejpam-3900	205	7	,	,	PUNCT
ejpam-3900	205	8	q	q	NOUN
ejpam-3900	205	9	=	=	SYM
ejpam-3900	205	10	n∑	n∑	PROPN
ejpam-3900	205	11	k=0	k=0	PROPN
ejpam-3900	205	12	lm	lm	PROPN
ejpam-3900	205	13	,	,	PUNCT
ejpam-3900	205	14	r[n	r[n	NOUN
ejpam-3900	205	15	,	,	PUNCT
ejpam-3900	205	16	k]q[t|m]k	k]q[t|m]k	NOUN
ejpam-3900	205	17	,	,	PUNCT
ejpam-3900	205	18	q([t+	q([t+	PROPN
ejpam-3900	205	19	2r	2r	NUM
ejpam-3900	205	20	+	+	CCONJ
ejpam-3900	205	21	nm]q	nm]q	PROPN
ejpam-3900	205	22	−	−	PROPN
ejpam-3900	206	1	[	[	X
ejpam-3900	206	2	2r	2r	X
ejpam-3900	206	3	+	+	NUM
ejpam-3900	206	4	km+	km+	PROPN
ejpam-3900	206	5	nm]q	nm]q	PROPN
ejpam-3900	206	6	)	)	PUNCT
ejpam-3900	207	1	+	+	CCONJ
ejpam-3900	208	1	n∑	n∑	NOUN
ejpam-3900	208	2	k=0	k=0	PROPN
ejpam-3900	209	1	[	[	X
ejpam-3900	209	2	2r	2r	X
ejpam-3900	209	3	+	+	NUM
ejpam-3900	209	4	km+	km+	PROPN
ejpam-3900	209	5	nm]qlm	nm]qlm	NOUN
ejpam-3900	209	6	,	,	PUNCT
ejpam-3900	209	7	r[n	r[n	NOUN
ejpam-3900	209	8	,	,	PUNCT
ejpam-3900	209	9	k]q[t|m]k	k]q[t|m]k	NOUN
ejpam-3900	209	10	,	,	PUNCT
ejpam-3900	209	11	q	q	NOUN
ejpam-3900	209	12	=	=	SYM
ejpam-3900	209	13	n∑	n∑	PROPN
ejpam-3900	209	14	k=0	k=0	PROPN
ejpam-3900	209	15	lm	lm	PROPN
ejpam-3900	209	16	,	,	PUNCT
ejpam-3900	209	17	r[n	r[n	NOUN
ejpam-3900	209	18	,	,	PUNCT
ejpam-3900	209	19	k]q[t|m]k	k]q[t|m]k	NOUN
ejpam-3900	209	20	,	,	PUNCT
ejpam-3900	209	21	q{[t+	q{[t+	PROPN
ejpam-3900	209	22	2r	2r	PROPN
ejpam-3900	209	23	+	+	CCONJ
ejpam-3900	209	24	nm]q	nm]q	PROPN
ejpam-3900	209	25	−	−	PROPN
ejpam-3900	210	1	[	[	X
ejpam-3900	210	2	2r	2r	X
ejpam-3900	210	3	+	+	NUM
ejpam-3900	210	4	km+	km+	PROPN
ejpam-3900	210	5	nm]q	nm]q	PROPN
ejpam-3900	210	6	+	+	PROPN
ejpam-3900	211	1	[	[	X
ejpam-3900	211	2	2r	2r	X
ejpam-3900	211	3	+	+	NUM
ejpam-3900	211	4	km+	km+	PROPN
ejpam-3900	211	5	nm]q	nm]q	PROPN
ejpam-3900	211	6	}	}	PUNCT
ejpam-3900	211	7	=	=	PUNCT
ejpam-3900	212	1	[	[	X
ejpam-3900	212	2	t+	t+	X
ejpam-3900	212	3	2r|m]nq	2r|m]nq	NUM
ejpam-3900	212	4	[	[	X
ejpam-3900	212	5	t+	t+	X
ejpam-3900	212	6	2r	2r	NUM
ejpam-3900	212	7	+	+	CCONJ
ejpam-3900	212	8	nm]q	nm]q	PROPN
ejpam-3900	212	9	=	=	PUNCT
ejpam-3900	213	1	[	[	X
ejpam-3900	213	2	t+	t+	NOUN
ejpam-3900	213	3	2r|m]n+1,q	2r|m]n+1,q	NOUN
ejpam-3900	213	4	.	.	PUNCT
ejpam-3900	214	1	r.	r.	PROPN
ejpam-3900	214	2	corcino	corcino	PROPN
ejpam-3900	214	3	,	,	PUNCT
ejpam-3900	214	4	j.	j.	PROPN
ejpam-3900	214	5	ontolan	ontolan	PROPN
ejpam-3900	214	6	,	,	PUNCT
ejpam-3900	214	7	m.	m.	NOUN
ejpam-3900	214	8	lobrigas	lobrigas	PROPN
ejpam-3900	214	9	/	/	SYM
ejpam-3900	214	10	eur	eur	PROPN
ejpam-3900	214	11	.	.	PUNCT
ejpam-3900	215	1	j.	j.	PROPN
ejpam-3900	215	2	pure	pure	PROPN
ejpam-3900	215	3	appl	appl	PROPN
ejpam-3900	215	4	.	.	PROPN
ejpam-3900	215	5	math	math	PROPN
ejpam-3900	215	6	,	,	PUNCT
ejpam-3900	215	7	14	14	NUM
ejpam-3900	215	8	(	(	PUNCT
ejpam-3900	215	9	1	1	NUM
ejpam-3900	215	10	)	)	PUNCT
ejpam-3900	215	11	(	(	PUNCT
ejpam-3900	215	12	2021	2021	NUM
ejpam-3900	215	13	)	)	PUNCT
ejpam-3900	215	14	,	,	PUNCT
ejpam-3900	215	15	65	65	NUM
ejpam-3900	215	16	-	-	SYM
ejpam-3900	215	17	81	81	NUM
ejpam-3900	215	18	74	74	NUM
ejpam-3900	215	19	this	this	PRON
ejpam-3900	215	20	proves	prove	VERB
ejpam-3900	215	21	the	the	DET
ejpam-3900	215	22	theorem	theorem	NOUN
ejpam-3900	215	23	.	.	PUNCT
ejpam-3900	216	1	next	next	ADV
ejpam-3900	216	2	,	,	PUNCT
ejpam-3900	216	3	we	we	PRON
ejpam-3900	216	4	establish	establish	VERB
ejpam-3900	216	5	the	the	DET
ejpam-3900	216	6	explicit	explicit	ADJ
ejpam-3900	216	7	formula	formula	NOUN
ejpam-3900	216	8	for	for	ADP
ejpam-3900	216	9	lm	lm	PROPN
ejpam-3900	216	10	,	,	PUNCT
ejpam-3900	216	11	r[n	r[n	NOUN
ejpam-3900	216	12	,	,	PUNCT
ejpam-3900	216	13	k]q	k]q	VERB
ejpam-3900	216	14	using	use	VERB
ejpam-3900	216	15	the	the	DET
ejpam-3900	216	16	horizontal	horizontal	ADJ
ejpam-3900	216	17	generating	generate	VERB
ejpam-3900	216	18	function	function	NOUN
ejpam-3900	216	19	of	of	ADP
ejpam-3900	216	20	lm	lm	PROPN
ejpam-3900	216	21	,	,	PUNCT
ejpam-3900	216	22	r[n	r[n	NOUN
ejpam-3900	216	23	,	,	PUNCT
ejpam-3900	216	24	k]q	k]q	PROPN
ejpam-3900	216	25	.	.	PUNCT
ejpam-3900	217	1	also	also	ADV
ejpam-3900	217	2	,	,	PUNCT
ejpam-3900	217	3	the	the	DET
ejpam-3900	217	4	exponential	exponential	ADJ
ejpam-3900	217	5	generating	generating	NOUN
ejpam-3900	217	6	function	function	NOUN
ejpam-3900	217	7	for	for	ADP
ejpam-3900	217	8	lm	lm	PROPN
ejpam-3900	217	9	,	,	PUNCT
ejpam-3900	217	10	r[n	r[n	NOUN
ejpam-3900	217	11	,	,	PUNCT
ejpam-3900	217	12	k]q	k]q	PROPN
ejpam-3900	217	13	is	be	AUX
ejpam-3900	217	14	obtained	obtain	VERB
ejpam-3900	217	15	using	use	VERB
ejpam-3900	217	16	the	the	DET
ejpam-3900	217	17	explicit	explicit	ADJ
ejpam-3900	217	18	formula	formula	NOUN
ejpam-3900	217	19	.	.	PUNCT
ejpam-3900	218	1	the	the	DET
ejpam-3900	218	2	explicit	explicit	ADJ
ejpam-3900	218	3	formula	formula	NOUN
ejpam-3900	218	4	for	for	ADP
ejpam-3900	218	5	the	the	DET
ejpam-3900	218	6	q	q	ADJ
ejpam-3900	218	7	-	-	PUNCT
ejpam-3900	218	8	difference	difference	NOUN
ejpam-3900	218	9	operator	operator	NOUN
ejpam-3900	218	10	is	be	AUX
ejpam-3900	218	11	as	as	SCONJ
ejpam-3900	218	12	follows	follow	VERB
ejpam-3900	218	13	4h	4h	PROPN
ejpam-3900	218	14	q	q	NOUN
ejpam-3900	218	15	,	,	PUNCT
ejpam-3900	218	16	kf(x	kf(x	NOUN
ejpam-3900	218	17	)	)	PUNCT
ejpam-3900	218	18	=	=	SYM
ejpam-3900	219	1	k∑	k∑	PROPN
ejpam-3900	219	2	j=0	j=0	PROPN
ejpam-3900	219	3	(	(	PUNCT
ejpam-3900	219	4	−1)k−jq	−1)k−jq	PROPN
ejpam-3900	219	5	(	(	PUNCT
ejpam-3900	219	6	k−j	k−j	X
ejpam-3900	219	7	2	2	NUM
ejpam-3900	219	8	)	)	PUNCT
ejpam-3900	220	1	[	[	X
ejpam-3900	220	2	kj	kj	X
ejpam-3900	220	3	]	]	PUNCT
ejpam-3900	220	4	f(x+	f(x+	NOUN
ejpam-3900	220	5	jh	jh	PROPN
ejpam-3900	220	6	)	)	PUNCT
ejpam-3900	220	7	.	.	PUNCT
ejpam-3900	221	1	(	(	PUNCT
ejpam-3900	221	2	17	17	NUM
ejpam-3900	221	3	)	)	PUNCT
ejpam-3900	221	4	the	the	DET
ejpam-3900	221	5	new	new	ADJ
ejpam-3900	221	6	q	q	NOUN
ejpam-3900	221	7	-	-	PUNCT
ejpam-3900	221	8	analogue	analogue	NOUN
ejpam-3900	221	9	of	of	ADP
ejpam-3900	221	10	newton	newton	PROPN
ejpam-3900	221	11	’s	’s	PART
ejpam-3900	221	12	interpolation	interpolation	NOUN
ejpam-3900	221	13	formula	formula	NOUN
ejpam-3900	221	14	in	in	ADP
ejpam-3900	221	15	[	[	X
ejpam-3900	221	16	9	9	NUM
ejpam-3900	221	17	]	]	PUNCT
ejpam-3900	221	18	is	be	AUX
ejpam-3900	221	19	given	give	VERB
ejpam-3900	221	20	by	by	ADP
ejpam-3900	221	21	fq(x	fq(x	NOUN
ejpam-3900	221	22	)	)	PUNCT
ejpam-3900	221	23	=	=	SYM
ejpam-3900	221	24	a0	a0	NOUN
ejpam-3900	221	25	+	+	CCONJ
ejpam-3900	221	26	a1[x−	a1[x−	NOUN
ejpam-3900	221	27	xo]q	xo]q	PROPN
ejpam-3900	221	28	+	+	X
ejpam-3900	221	29	.	.	PUNCT
ejpam-3900	221	30	.	.	PUNCT
ejpam-3900	222	1	.+	.+	X
ejpam-3900	222	2	am[x−	am[x−	VERB
ejpam-3900	222	3	xo]q[x−	xo]q[x−	PROPN
ejpam-3900	222	4	x1]q	x1]q	PROPN
ejpam-3900	222	5	.	.	PUNCT
ejpam-3900	222	6	.	.	PUNCT
ejpam-3900	222	7	.	.	PUNCT
ejpam-3900	223	1	[	[	X
ejpam-3900	223	2	x−	x−	PROPN
ejpam-3900	223	3	xm−1]q	xm−1]q	PROPN
ejpam-3900	223	4	,	,	PUNCT
ejpam-3900	223	5	which	which	PRON
ejpam-3900	223	6	is	be	AUX
ejpam-3900	223	7	equivalent	equivalent	ADJ
ejpam-3900	223	8	to	to	ADP
ejpam-3900	223	9	fq(x	fq(x	NOUN
ejpam-3900	223	10	)	)	PUNCT
ejpam-3900	223	11	=	=	SYM
ejpam-3900	223	12	fq(x0	fq(x0	NOUN
ejpam-3900	223	13	)	)	PUNCT
ejpam-3900	223	14	+	+	CCONJ
ejpam-3900	223	15	4qh	4qh	ADJ
ejpam-3900	223	16	,	,	PUNCT
ejpam-3900	223	17	hfq(x0)[x−	hfq(x0)[x−	NOUN
ejpam-3900	223	18	x0]q	x0]q	PROPN
ejpam-3900	224	1	[	[	X
ejpam-3900	224	2	1]qh	1]qh	NUM
ejpam-3900	224	3	!	!	PUNCT
ejpam-3900	225	1	[	[	X
ejpam-3900	225	2	h]q	h]q	X
ejpam-3900	225	3	+	+	NUM
ejpam-3900	225	4	4qh2,hfq(x0)[x−	4qh2,hfq(x0)[x−	NUM
ejpam-3900	225	5	x0]q[x−	x0]q[x−	PROPN
ejpam-3900	225	6	x1]q	x1]q	PUNCT
ejpam-3900	226	1	[	[	X
ejpam-3900	226	2	2]qh	2]qh	NUM
ejpam-3900	226	3	!	!	PUNCT
ejpam-3900	227	1	[	[	X
ejpam-3900	227	2	h]2q	h]2q	X
ejpam-3900	227	3	+	+	X
ejpam-3900	227	4	.	.	PUNCT
ejpam-3900	227	5	.	.	PUNCT
ejpam-3900	228	1	.+	.+	NOUN
ejpam-3900	228	2	4qhm	4qhm	NOUN
ejpam-3900	228	3	,	,	PUNCT
ejpam-3900	228	4	hfq(x0)[x−	hfq(x0)[x−	X
ejpam-3900	228	5	x0]q[x−	x0]q[x−	PROPN
ejpam-3900	228	6	x1]q	x1]q	X
ejpam-3900	228	7	.	.	PUNCT
ejpam-3900	228	8	.	.	PUNCT
ejpam-3900	228	9	.	.	PUNCT
ejpam-3900	229	1	[	[	X
ejpam-3900	229	2	x−	x−	PROPN
ejpam-3900	229	3	xm−1]q	xm−1]q	PUNCT
ejpam-3900	230	1	[	[	X
ejpam-3900	230	2	m]qh	m]qh	X
ejpam-3900	230	3	!	!	PUNCT
ejpam-3900	231	1	[	[	X
ejpam-3900	231	2	h]mq	h]mq	X
ejpam-3900	231	3	where	where	SCONJ
ejpam-3900	231	4	xk	xk	PROPN
ejpam-3900	232	1	=	=	PUNCT
ejpam-3900	232	2	x0	x0	PROPN
ejpam-3900	233	1	+	+	CCONJ
ejpam-3900	233	2	kh	kh	PROPN
ejpam-3900	233	3	,	,	PUNCT
ejpam-3900	233	4	k	k	PROPN
ejpam-3900	233	5	=	=	SYM
ejpam-3900	233	6	1	1	NUM
ejpam-3900	233	7	,	,	PUNCT
ejpam-3900	233	8	2	2	NUM
ejpam-3900	233	9	,	,	PUNCT
ejpam-3900	233	10	.	.	PUNCT
ejpam-3900	233	11	.	.	PUNCT
ejpam-3900	233	12	.	.	PUNCT
ejpam-3900	234	1	such	such	ADJ
ejpam-3900	234	2	that	that	SCONJ
ejpam-3900	234	3	if	if	SCONJ
ejpam-3900	234	4	x0	x0	PROPN
ejpam-3900	234	5	=	=	SYM
ejpam-3900	234	6	0	0	NUM
ejpam-3900	234	7	and	and	CCONJ
ejpam-3900	234	8	h	h	NOUN
ejpam-3900	234	9	=	=	SYM
ejpam-3900	234	10	m	m	PROPN
ejpam-3900	234	11	,	,	PUNCT
ejpam-3900	234	12	we	we	PRON
ejpam-3900	234	13	have	have	VERB
ejpam-3900	234	14	fq(x	fq(x	NOUN
ejpam-3900	234	15	)	)	PUNCT
ejpam-3900	235	1	=	=	SYM
ejpam-3900	235	2	fq(x0	fq(x0	NOUN
ejpam-3900	235	3	)	)	PUNCT
ejpam-3900	235	4	+	+	CCONJ
ejpam-3900	235	5	4qm	4qm	NOUN
ejpam-3900	235	6	,	,	PUNCT
ejpam-3900	235	7	mfq(0)[x]q	mfq(0)[x]q	PROPN
ejpam-3900	236	1	[	[	X
ejpam-3900	236	2	1]qm	1]qm	NUM
ejpam-3900	236	3	!	!	PUNCT
ejpam-3900	237	1	[	[	X
ejpam-3900	237	2	m]q	m]q	X
ejpam-3900	237	3	+	+	X
ejpam-3900	237	4	4qm2,mfq(0)[x]q[x−m]q	4qm2,mfq(0)[x]q[x−m]q	NUM
ejpam-3900	238	1	[	[	X
ejpam-3900	238	2	2]qm	2]qm	NUM
ejpam-3900	238	3	!	!	PUNCT
ejpam-3900	239	1	[	[	X
ejpam-3900	239	2	m]2q	m]2q	X
ejpam-3900	239	3	+	+	X
ejpam-3900	239	4	.	.	PUNCT
ejpam-3900	239	5	.	.	PUNCT
ejpam-3900	240	1	.+	.+	NOUN
ejpam-3900	240	2	4qmm	4qmm	NUM
ejpam-3900	240	3	,	,	PUNCT
ejpam-3900	240	4	mfq(0)[x]q[x−m]q	mfq(0)[x]q[x−m]q	PROPN
ejpam-3900	240	5	.	.	PUNCT
ejpam-3900	240	6	.	.	PUNCT
ejpam-3900	240	7	.	.	PUNCT
ejpam-3900	241	1	[	[	X
ejpam-3900	241	2	x−m(m−	x−m(m−	PROPN
ejpam-3900	241	3	1)]q	1)]q	NUM
ejpam-3900	242	1	[	[	X
ejpam-3900	242	2	m]qm	m]qm	NOUN
ejpam-3900	242	3	!	!	PUNCT
ejpam-3900	243	1	[	[	X
ejpam-3900	243	2	m]mq	m]mq	X
ejpam-3900	243	3	by	by	ADP
ejpam-3900	243	4	(	(	PUNCT
ejpam-3900	243	5	16	16	NUM
ejpam-3900	243	6	)	)	PUNCT
ejpam-3900	243	7	with	with	ADP
ejpam-3900	243	8	t	t	NOUN
ejpam-3900	243	9	=	=	SYM
ejpam-3900	243	10	x	x	NOUN
ejpam-3900	243	11	,	,	PUNCT
ejpam-3900	243	12	we	we	PRON
ejpam-3900	243	13	get	get	VERB
ejpam-3900	243	14	n∑	n∑	DET
ejpam-3900	243	15	k=0	k=0	PROPN
ejpam-3900	243	16	lm	lm	PROPN
ejpam-3900	243	17	,	,	PUNCT
ejpam-3900	243	18	r[n	r[n	NOUN
ejpam-3900	243	19	,	,	PUNCT
ejpam-3900	243	20	k]q[x|m]k	k]q[x|m]k	NOUN
ejpam-3900	243	21	,	,	PUNCT
ejpam-3900	243	22	q	q	NOUN
ejpam-3900	243	23	=	=	PUNCT
ejpam-3900	244	1	[	[	X
ejpam-3900	244	2	x+	x+	ADJ
ejpam-3900	244	3	2r|m]n	2r|m]n	NOUN
ejpam-3900	244	4	,	,	PUNCT
ejpam-3900	244	5	q	q	NOUN
ejpam-3900	244	6	which	which	PRON
ejpam-3900	244	7	can	can	AUX
ejpam-3900	244	8	be	be	AUX
ejpam-3900	244	9	rewritten	rewrite	VERB
ejpam-3900	244	10	as	as	ADP
ejpam-3900	244	11	n∑	n∑	PROPN
ejpam-3900	244	12	k=0	k=0	PROPN
ejpam-3900	244	13	lm	lm	PROPN
ejpam-3900	244	14	,	,	PUNCT
ejpam-3900	244	15	r[n	r[n	NOUN
ejpam-3900	244	16	,	,	PUNCT
ejpam-3900	244	17	k]q[x]q[x−m]q[x−	k]q[x]q[x−m]q[x−	PROPN
ejpam-3900	244	18	2m]q	2m]q	PROPN
ejpam-3900	244	19	.	.	PUNCT
ejpam-3900	244	20	.	.	PUNCT
ejpam-3900	244	21	.	.	PUNCT
ejpam-3900	245	1	[	[	X
ejpam-3900	245	2	x−	x−	PROPN
ejpam-3900	245	3	(	(	PUNCT
ejpam-3900	245	4	k	k	PROPN
ejpam-3900	245	5	−	−	PROPN
ejpam-3900	245	6	1)m]q	1)m]q	PROPN
ejpam-3900	246	1	=	=	SYM
ejpam-3900	247	1	[	[	X
ejpam-3900	247	2	x+	x+	ADJ
ejpam-3900	247	3	2r|m]n	2r|m]n	NOUN
ejpam-3900	247	4	,	,	PUNCT
ejpam-3900	247	5	q.	q.	PROPN
ejpam-3900	247	6	suppose	suppose	VERB
ejpam-3900	247	7	fq(x	fq(x	NOUN
ejpam-3900	247	8	)	)	PUNCT
ejpam-3900	247	9	=	=	SYM
ejpam-3900	248	1	[	[	X
ejpam-3900	248	2	x+	x+	ADJ
ejpam-3900	248	3	2r|m]n	2r|m]n	NOUN
ejpam-3900	248	4	,	,	PUNCT
ejpam-3900	248	5	q	q	NOUN
ejpam-3900	248	6	and	and	CCONJ
ejpam-3900	248	7	lm	lm	ADJ
ejpam-3900	248	8	,	,	PUNCT
ejpam-3900	248	9	r[n	r[n	NOUN
ejpam-3900	248	10	,	,	PUNCT
ejpam-3900	248	11	k]q	k]q	NOUN
ejpam-3900	248	12	=	=	SYM
ejpam-3900	248	13	4k	4k	PROPN
ejpam-3900	248	14	qm	qm	PROPN
ejpam-3900	248	15	,	,	PUNCT
ejpam-3900	248	16	mfq(0	mfq(0	NOUN
ejpam-3900	248	17	)	)	PUNCT
ejpam-3900	249	1	[	[	X
ejpam-3900	249	2	k]qm	k]qm	X
ejpam-3900	249	3	!	!	PUNCT
ejpam-3900	250	1	[	[	X
ejpam-3900	250	2	m]kq	m]kq	NOUN
ejpam-3900	250	3	=	=	SYM
ejpam-3900	250	4	1	1	NUM
ejpam-3900	251	1	[	[	X
ejpam-3900	251	2	k]qm	k]qm	X
ejpam-3900	251	3	!	!	PUNCT
ejpam-3900	252	1	[	[	X
ejpam-3900	252	2	m]kq	m]kq	X
ejpam-3900	252	3	·	·	PUNCT
ejpam-3900	252	4	4k	4k	NUM
ejpam-3900	252	5	qm	qm	PROPN
ejpam-3900	252	6	,	,	PUNCT
ejpam-3900	252	7	mfq(0	mfq(0	PROPN
ejpam-3900	252	8	)	)	PUNCT
ejpam-3900	252	9	r.	r.	PROPN
ejpam-3900	252	10	corcino	corcino	PROPN
ejpam-3900	252	11	,	,	PUNCT
ejpam-3900	252	12	j.	j.	PROPN
ejpam-3900	252	13	ontolan	ontolan	PROPN
ejpam-3900	252	14	,	,	PUNCT
ejpam-3900	252	15	m.	m.	NOUN
ejpam-3900	252	16	lobrigas	lobrigas	PROPN
ejpam-3900	252	17	/	/	SYM
ejpam-3900	252	18	eur	eur	PROPN
ejpam-3900	252	19	.	.	PUNCT
ejpam-3900	253	1	j.	j.	PROPN
ejpam-3900	253	2	pure	pure	PROPN
ejpam-3900	253	3	appl	appl	PROPN
ejpam-3900	253	4	.	.	PROPN
ejpam-3900	253	5	math	math	PROPN
ejpam-3900	253	6	,	,	PUNCT
ejpam-3900	253	7	14	14	NUM
ejpam-3900	253	8	(	(	PUNCT
ejpam-3900	253	9	1	1	NUM
ejpam-3900	253	10	)	)	PUNCT
ejpam-3900	253	11	(	(	PUNCT
ejpam-3900	253	12	2021	2021	NUM
ejpam-3900	253	13	)	)	PUNCT
ejpam-3900	253	14	,	,	PUNCT
ejpam-3900	253	15	65	65	NUM
ejpam-3900	253	16	-	-	SYM
ejpam-3900	253	17	81	81	NUM
ejpam-3900	253	18	75	75	NUM
ejpam-3900	253	19	note	note	NOUN
ejpam-3900	253	20	that	that	SCONJ
ejpam-3900	253	21	applying	apply	VERB
ejpam-3900	253	22	the	the	DET
ejpam-3900	253	23	above	above	PROPN
ejpam-3900	253	24	newton	newton	PROPN
ejpam-3900	253	25	’s	’s	PART
ejpam-3900	253	26	interpolation	interpolation	NOUN
ejpam-3900	253	27	formula	formula	NOUN
ejpam-3900	253	28	and	and	CCONJ
ejpam-3900	253	29	the	the	DET
ejpam-3900	253	30	identity	identity	NOUN
ejpam-3900	253	31	in	in	ADP
ejpam-3900	253	32	(	(	PUNCT
ejpam-3900	253	33	17	17	NUM
ejpam-3900	253	34	)	)	PUNCT
ejpam-3900	253	35	,	,	PUNCT
ejpam-3900	253	36	we	we	PRON
ejpam-3900	253	37	have	have	VERB
ejpam-3900	253	38	4f	4f	NUM
ejpam-3900	253	39	qm	qm	PROPN
ejpam-3900	253	40	,	,	PUNCT
ejpam-3900	253	41	mfq(x	mfq(x	PROPN
ejpam-3900	253	42	)	)	PUNCT
ejpam-3900	253	43	=	=	SYM
ejpam-3900	253	44	k∑	k∑	PROPN
ejpam-3900	253	45	j=0	j=0	PROPN
ejpam-3900	253	46	(	(	PUNCT
ejpam-3900	253	47	−1)k−jqm(k−j	−1)k−jqm(k−j	NUM
ejpam-3900	253	48	2	2	NUM
ejpam-3900	253	49	)	)	PUNCT
ejpam-3900	254	1	[	[	X
ejpam-3900	254	2	kj	kj	X
ejpam-3900	254	3	]	]	PUNCT
ejpam-3900	254	4	qmfq(x+	qmfq(x+	X
ejpam-3900	254	5	jm	jm	NOUN
ejpam-3900	254	6	)	)	PUNCT
ejpam-3900	254	7	=	=	SYM
ejpam-3900	254	8	k∑	k∑	PROPN
ejpam-3900	254	9	j=0	j=0	PROPN
ejpam-3900	254	10	(	(	PUNCT
ejpam-3900	254	11	−1)k−jqm(k−j	−1)k−jqm(k−j	NUM
ejpam-3900	254	12	2	2	NUM
ejpam-3900	254	13	)	)	PUNCT
ejpam-3900	255	1	[	[	X
ejpam-3900	255	2	kj	kj	X
ejpam-3900	255	3	]	]	PUNCT
ejpam-3900	255	4	qm	qm	PROPN
ejpam-3900	256	1	[	[	X
ejpam-3900	256	2	x+	x+	ADJ
ejpam-3900	256	3	jm+	jm+	NOUN
ejpam-3900	256	4	2r|m]n	2r|m]n	NUM
ejpam-3900	256	5	,	,	PUNCT
ejpam-3900	256	6	q.	q.	PROPN
ejpam-3900	256	7	evaluate	evaluate	VERB
ejpam-3900	256	8	at	at	ADP
ejpam-3900	256	9	x	x	X
ejpam-3900	256	10	=	=	SYM
ejpam-3900	256	11	0	0	NUM
ejpam-3900	256	12	,	,	PUNCT
ejpam-3900	256	13	4f	4f	NUM
ejpam-3900	256	14	qm	qm	PROPN
ejpam-3900	256	15	,	,	PUNCT
ejpam-3900	256	16	mfq(0	mfq(0	NOUN
ejpam-3900	256	17	)	)	PUNCT
ejpam-3900	257	1	=	=	SYM
ejpam-3900	257	2	k∑	k∑	PROPN
ejpam-3900	257	3	j=0	j=0	PROPN
ejpam-3900	257	4	(	(	PUNCT
ejpam-3900	257	5	−1)k−jqm(k−j	−1)k−jqm(k−j	NUM
ejpam-3900	257	6	2	2	NUM
ejpam-3900	257	7	)	)	PUNCT
ejpam-3900	258	1	[	[	X
ejpam-3900	258	2	kj	kj	X
ejpam-3900	258	3	]	]	X
ejpam-3900	258	4	qm	qm	PROPN
ejpam-3900	259	1	[	[	X
ejpam-3900	259	2	2r	2r	X
ejpam-3900	260	1	+	+	CCONJ
ejpam-3900	260	2	jm|m]n	jm|m]n	PROPN
ejpam-3900	260	3	,	,	PUNCT
ejpam-3900	260	4	q.	q.	PROPN
ejpam-3900	260	5	thus	thus	ADV
ejpam-3900	260	6	,	,	PUNCT
ejpam-3900	260	7	lm	lm	INTJ
ejpam-3900	260	8	,	,	PUNCT
ejpam-3900	260	9	r[n	r[n	NOUN
ejpam-3900	260	10	,	,	PUNCT
ejpam-3900	260	11	k]q	k]q	NOUN
ejpam-3900	260	12	=	=	SYM
ejpam-3900	260	13	1	1	NUM
ejpam-3900	261	1	[	[	X
ejpam-3900	261	2	k]qm	k]qm	X
ejpam-3900	261	3	!	!	PUNCT
ejpam-3900	262	1	[	[	X
ejpam-3900	262	2	m]kq	m]kq	PROPN
ejpam-3900	262	3	k∑	k∑	VERB
ejpam-3900	262	4	j=0	j=0	PROPN
ejpam-3900	262	5	(	(	PUNCT
ejpam-3900	262	6	−1)k−jqm(k−j	−1)k−jqm(k−j	NUM
ejpam-3900	262	7	2	2	NUM
ejpam-3900	262	8	)	)	PUNCT
ejpam-3900	263	1	[	[	X
ejpam-3900	263	2	kj	kj	X
ejpam-3900	263	3	]	]	X
ejpam-3900	263	4	qm	qm	PROPN
ejpam-3900	264	1	[	[	X
ejpam-3900	264	2	2r	2r	X
ejpam-3900	265	1	+	+	CCONJ
ejpam-3900	265	2	jm|m]n	jm|m]n	PROPN
ejpam-3900	265	3	,	,	PUNCT
ejpam-3900	265	4	q.	q.	PROPN
ejpam-3900	266	1	so	so	ADV
ejpam-3900	266	2	,	,	PUNCT
ejpam-3900	266	3	the	the	DET
ejpam-3900	266	4	explicit	explicit	ADJ
ejpam-3900	266	5	formula	formula	NOUN
ejpam-3900	266	6	for	for	ADP
ejpam-3900	266	7	lm	lm	PROPN
ejpam-3900	266	8	,	,	PUNCT
ejpam-3900	266	9	r[n	r[n	NOUN
ejpam-3900	266	10	,	,	PUNCT
ejpam-3900	266	11	k]q	k]q	NOUN
ejpam-3900	266	12	is	be	AUX
ejpam-3900	266	13	as	as	SCONJ
ejpam-3900	266	14	follows	follow	VERB
ejpam-3900	266	15	:	:	PUNCT
ejpam-3900	266	16	theorem	theorem	NOUN
ejpam-3900	266	17	3.2	3.2	NUM
ejpam-3900	266	18	.	.	PUNCT
ejpam-3900	267	1	the	the	DET
ejpam-3900	267	2	explicit	explicit	ADJ
ejpam-3900	267	3	formula	formula	NOUN
ejpam-3900	267	4	for	for	ADP
ejpam-3900	267	5	lm	lm	PROPN
ejpam-3900	267	6	,	,	PUNCT
ejpam-3900	267	7	r[n	r[n	NOUN
ejpam-3900	267	8	,	,	PUNCT
ejpam-3900	267	9	k]q	k]q	NOUN
ejpam-3900	267	10	is	be	AUX
ejpam-3900	267	11	given	give	VERB
ejpam-3900	267	12	by	by	ADP
ejpam-3900	267	13	lm	lm	PROPN
ejpam-3900	267	14	,	,	PUNCT
ejpam-3900	267	15	r[n	r[n	NOUN
ejpam-3900	267	16	,	,	PUNCT
ejpam-3900	267	17	k]q	k]q	NOUN
ejpam-3900	267	18	=	=	SYM
ejpam-3900	267	19	1	1	NUM
ejpam-3900	268	1	[	[	X
ejpam-3900	268	2	k]qm	k]qm	X
ejpam-3900	268	3	!	!	PUNCT
ejpam-3900	269	1	[	[	X
ejpam-3900	269	2	m]kq	m]kq	PROPN
ejpam-3900	269	3	k∑	k∑	VERB
ejpam-3900	269	4	j=0	j=0	PROPN
ejpam-3900	269	5	(	(	PUNCT
ejpam-3900	269	6	−1)k−jqm(k−j	−1)k−jqm(k−j	NUM
ejpam-3900	269	7	2	2	NUM
ejpam-3900	269	8	)	)	PUNCT
ejpam-3900	270	1	[	[	X
ejpam-3900	270	2	kj	kj	X
ejpam-3900	270	3	]	]	X
ejpam-3900	270	4	qm	qm	PROPN
ejpam-3900	271	1	[	[	X
ejpam-3900	271	2	2r	2r	X
ejpam-3900	272	1	+	+	CCONJ
ejpam-3900	272	2	jm|m]n	jm|m]n	PROPN
ejpam-3900	272	3	,	,	PUNCT
ejpam-3900	272	4	q	q	X
ejpam-3900	272	5	(	(	PUNCT
ejpam-3900	272	6	18	18	NUM
ejpam-3900	272	7	)	)	PUNCT
ejpam-3900	272	8	remark	remark	NOUN
ejpam-3900	272	9	3.3	3.3	NUM
ejpam-3900	272	10	.	.	PUNCT
ejpam-3900	273	1	when	when	SCONJ
ejpam-3900	273	2	q	q	X
ejpam-3900	273	3	→	→	SYM
ejpam-3900	273	4	1	1	NUM
ejpam-3900	273	5	,	,	PUNCT
ejpam-3900	273	6	the	the	DET
ejpam-3900	273	7	above	above	ADJ
ejpam-3900	273	8	theorem	theorem	NOUN
ejpam-3900	273	9	reduces	reduce	VERB
ejpam-3900	273	10	to	to	ADP
ejpam-3900	273	11	,	,	PUNCT
ejpam-3900	273	12	lm	lm	INTJ
ejpam-3900	273	13	,	,	PUNCT
ejpam-3900	273	14	r(n	r(n	PROPN
ejpam-3900	273	15	,	,	PUNCT
ejpam-3900	273	16	k	k	NOUN
ejpam-3900	273	17	)	)	PUNCT
ejpam-3900	273	18	=	=	SYM
ejpam-3900	273	19	1	1	NUM
ejpam-3900	273	20	k!mk	k!mk	X
ejpam-3900	273	21	k∑	k∑	PUNCT
ejpam-3900	273	22	j=0	j=0	PROPN
ejpam-3900	273	23	(	(	PUNCT
ejpam-3900	273	24	−1)k−j(kj	−1)k−j(kj	PROPN
ejpam-3900	273	25	)	)	PUNCT
ejpam-3900	273	26	(	(	PUNCT
ejpam-3900	273	27	2r	2r	NUM
ejpam-3900	273	28	+	+	SYM
ejpam-3900	273	29	jm|m)n	jm|m)n	PROPN
ejpam-3900	273	30	,	,	PUNCT
ejpam-3900	273	31	which	which	PRON
ejpam-3900	273	32	is	be	AUX
ejpam-3900	273	33	the	the	DET
ejpam-3900	273	34	explicit	explicit	ADJ
ejpam-3900	273	35	formula	formula	NOUN
ejpam-3900	273	36	of	of	ADP
ejpam-3900	273	37	lm	lm	PROPN
ejpam-3900	273	38	,	,	PUNCT
ejpam-3900	273	39	r(n	r(n	PROPN
ejpam-3900	273	40	,	,	PUNCT
ejpam-3900	273	41	k	k	NOUN
ejpam-3900	273	42	)	)	PUNCT
ejpam-3900	273	43	,	,	PUNCT
ejpam-3900	273	44	where	where	SCONJ
ejpam-3900	273	45	(	(	PUNCT
ejpam-3900	273	46	t|m)n	t|m)n	NUM
ejpam-3900	273	47	=	=	SYM
ejpam-3900	273	48	t(t+m	t(t+m	NOUN
ejpam-3900	273	49	)	)	PUNCT
ejpam-3900	273	50	.	.	PUNCT
ejpam-3900	273	51	.	.	PUNCT
ejpam-3900	273	52	.	.	PUNCT
ejpam-3900	274	1	(	(	PUNCT
ejpam-3900	274	2	t+	t+	NOUN
ejpam-3900	274	3	(	(	PUNCT
ejpam-3900	274	4	n−	n−	NOUN
ejpam-3900	274	5	1)m	1)m	NUM
ejpam-3900	274	6	)	)	PUNCT
ejpam-3900	274	7	.	.	PUNCT
ejpam-3900	275	1	remark	remark	VERB
ejpam-3900	275	2	3.4	3.4	NUM
ejpam-3900	275	3	.	.	PUNCT
ejpam-3900	276	1	the	the	DET
ejpam-3900	276	2	eq	eq	NOUN
ejpam-3900	276	3	.	.	PUNCT
ejpam-3900	277	1	(	(	PUNCT
ejpam-3900	277	2	18	18	NUM
ejpam-3900	277	3	)	)	PUNCT
ejpam-3900	277	4	can	can	AUX
ejpam-3900	277	5	also	also	ADV
ejpam-3900	277	6	be	be	AUX
ejpam-3900	277	7	written	write	VERB
ejpam-3900	277	8	as	as	ADP
ejpam-3900	277	9	lm	lm	PROPN
ejpam-3900	277	10	,	,	PUNCT
ejpam-3900	277	11	r[n	r[n	NOUN
ejpam-3900	277	12	,	,	PUNCT
ejpam-3900	277	13	k]q	k]q	NOUN
ejpam-3900	277	14	=	=	SYM
ejpam-3900	277	15	1	1	NUM
ejpam-3900	278	1	[	[	X
ejpam-3900	278	2	k]qm	k]qm	X
ejpam-3900	278	3	!	!	PUNCT
ejpam-3900	279	1	[	[	X
ejpam-3900	279	2	m]kq	m]kq	X
ejpam-3900	279	3	[	[	X
ejpam-3900	279	4	4k	4k	X
ejpam-3900	279	5	qm	qm	PROPN
ejpam-3900	279	6	,	,	PUNCT
ejpam-3900	279	7	m[x+	m[x+	NOUN
ejpam-3900	279	8	2r|m]n	2r|m]n	NOUN
ejpam-3900	279	9	,	,	PUNCT
ejpam-3900	279	10	q]x=0	q]x=0	ADV
ejpam-3900	279	11	theorem	theorem	VERB
ejpam-3900	279	12	3.5	3.5	NUM
ejpam-3900	279	13	.	.	PUNCT
ejpam-3900	280	1	for	for	ADP
ejpam-3900	280	2	nonnegative	nonnegative	ADJ
ejpam-3900	280	3	integers	integer	NOUN
ejpam-3900	280	4	n	n	PRON
ejpam-3900	280	5	and	and	CCONJ
ejpam-3900	280	6	k	k	NOUN
ejpam-3900	280	7	,	,	PUNCT
ejpam-3900	280	8	and	and	CCONJ
ejpam-3900	280	9	real	real	ADJ
ejpam-3900	280	10	number	number	NOUN
ejpam-3900	280	11	a	a	PRON
ejpam-3900	280	12	,	,	PUNCT
ejpam-3900	280	13	the	the	DET
ejpam-3900	280	14	q	q	ADJ
ejpam-3900	280	15	-	-	PUNCT
ejpam-3900	280	16	analogue	analogue	NOUN
ejpam-3900	280	17	lm	lm	PROPN
ejpam-3900	280	18	,	,	PUNCT
ejpam-3900	280	19	r[n	r[n	VERB
ejpam-3900	280	20	,	,	PUNCT
ejpam-3900	280	21	k]q	k]q	NOUN
ejpam-3900	280	22	has	have	VERB
ejpam-3900	280	23	an	an	DET
ejpam-3900	280	24	exponential	exponential	ADJ
ejpam-3900	280	25	generating	generate	VERB
ejpam-3900	280	26	function.∑	function.∑	NOUN
ejpam-3900	280	27	n≥o	n≥o	ADV
ejpam-3900	280	28	lm	lm	PROPN
ejpam-3900	280	29	,	,	PUNCT
ejpam-3900	280	30	r[n	r[n	NOUN
ejpam-3900	280	31	,	,	PUNCT
ejpam-3900	280	32	k]q	k]q	VERB
ejpam-3900	281	1	[	[	X
ejpam-3900	281	2	t]nq	t]nq	NOUN
ejpam-3900	281	3	[	[	X
ejpam-3900	281	4	n]q	n]q	X
ejpam-3900	281	5	!	!	PUNCT
ejpam-3900	282	1	=	=	SYM
ejpam-3900	282	2	1	1	NUM
ejpam-3900	283	1	[	[	X
ejpam-3900	283	2	k]qm	k]qm	X
ejpam-3900	283	3	!	!	PUNCT
ejpam-3900	284	1	[	[	X
ejpam-3900	284	2	m]kq	m]kq	X
ejpam-3900	284	3	[	[	X
ejpam-3900	284	4	4k	4k	X
ejpam-3900	284	5	qm	qm	PROPN
ejpam-3900	284	6	,	,	PUNCT
ejpam-3900	284	7	m(f	m(f	PROPN
ejpam-3900	284	8	[	[	X
ejpam-3900	284	9	x+	x+	PROPN
ejpam-3900	284	10	2r	2r	NUM
ejpam-3900	284	11	+	+	CCONJ
ejpam-3900	284	12	jm	jm	PROPN
ejpam-3900	284	13	,	,	PUNCT
ejpam-3900	284	14	m	m	PROPN
ejpam-3900	284	15	,	,	PUNCT
ejpam-3900	284	16	t])x=0	t])x=0	PROPN
ejpam-3900	284	17	,	,	PUNCT
ejpam-3900	284	18	(	(	PUNCT
ejpam-3900	284	19	19	19	NUM
ejpam-3900	284	20	)	)	PUNCT
ejpam-3900	285	1	where	where	SCONJ
ejpam-3900	285	2	f	f	PROPN
ejpam-3900	286	1	[	[	X
ejpam-3900	286	2	x	x	X
ejpam-3900	286	3	,	,	PUNCT
ejpam-3900	286	4	m	m	PROPN
ejpam-3900	286	5	,	,	PUNCT
ejpam-3900	286	6	t	t	X
ejpam-3900	286	7	]	]	X
ejpam-3900	286	8	=	=	PUNCT
ejpam-3900	286	9	∑	∑	PUNCT
ejpam-3900	286	10	n≥0	n≥0	PROPN
ejpam-3900	286	11	[	[	X
ejpam-3900	286	12	x|m]n	x|m]n	PROPN
ejpam-3900	286	13	,	,	PUNCT
ejpam-3900	286	14	q	q	X
ejpam-3900	287	1	[	[	X
ejpam-3900	287	2	t]nq	t]nq	X
ejpam-3900	287	3	[	[	X
ejpam-3900	287	4	n]q	n]q	X
ejpam-3900	287	5	!	!	PUNCT
ejpam-3900	287	6	.	.	PUNCT
ejpam-3900	288	1	r.	r.	PROPN
ejpam-3900	288	2	corcino	corcino	PROPN
ejpam-3900	288	3	,	,	PUNCT
ejpam-3900	288	4	j.	j.	PROPN
ejpam-3900	288	5	ontolan	ontolan	PROPN
ejpam-3900	288	6	,	,	PUNCT
ejpam-3900	288	7	m.	m.	NOUN
ejpam-3900	288	8	lobrigas	lobrigas	PROPN
ejpam-3900	288	9	/	/	SYM
ejpam-3900	288	10	eur	eur	PROPN
ejpam-3900	288	11	.	.	PUNCT
ejpam-3900	289	1	j.	j.	PROPN
ejpam-3900	289	2	pure	pure	PROPN
ejpam-3900	289	3	appl	appl	PROPN
ejpam-3900	289	4	.	.	PROPN
ejpam-3900	289	5	math	math	PROPN
ejpam-3900	289	6	,	,	PUNCT
ejpam-3900	289	7	14	14	NUM
ejpam-3900	289	8	(	(	PUNCT
ejpam-3900	289	9	1	1	NUM
ejpam-3900	289	10	)	)	PUNCT
ejpam-3900	289	11	(	(	PUNCT
ejpam-3900	289	12	2021	2021	NUM
ejpam-3900	289	13	)	)	PUNCT
ejpam-3900	289	14	,	,	PUNCT
ejpam-3900	289	15	65	65	NUM
ejpam-3900	289	16	-	-	SYM
ejpam-3900	289	17	81	81	NUM
ejpam-3900	289	18	76	76	NUM
ejpam-3900	289	19	proof	proof	NOUN
ejpam-3900	289	20	.	.	PUNCT
ejpam-3900	290	1	using	use	VERB
ejpam-3900	290	2	the	the	DET
ejpam-3900	290	3	explicit	explicit	ADJ
ejpam-3900	290	4	formula	formula	NOUN
ejpam-3900	290	5	in	in	ADP
ejpam-3900	290	6	(	(	PUNCT
ejpam-3900	290	7	18	18	NUM
ejpam-3900	290	8	)	)	PUNCT
ejpam-3900	290	9	,	,	PUNCT
ejpam-3900	290	10	we	we	PRON
ejpam-3900	290	11	obtained	obtain	VERB
ejpam-3900	290	12	∑	∑	PROPN
ejpam-3900	290	13	n≥0	n≥0	PROPN
ejpam-3900	290	14	lm	lm	PROPN
ejpam-3900	290	15	,	,	PUNCT
ejpam-3900	290	16	r[n	r[n	NOUN
ejpam-3900	290	17	,	,	PUNCT
ejpam-3900	290	18	k	k	X
ejpam-3900	290	19	]	]	X
ejpam-3900	291	1	[	[	X
ejpam-3900	291	2	t]nq	t]nq	X
ejpam-3900	291	3	[	[	X
ejpam-3900	291	4	n]q	n]q	X
ejpam-3900	291	5	!	!	PUNCT
ejpam-3900	291	6	=	=	PUNCT
ejpam-3900	292	1	∑	∑	PUNCT
ejpam-3900	292	2	n≥0	n≥0	ADJ
ejpam-3900	292	3	1	1	NUM
ejpam-3900	292	4	[	[	X
ejpam-3900	292	5	k]qm	k]qm	NOUN
ejpam-3900	292	6	!	!	PUNCT
ejpam-3900	293	1	[	[	X
ejpam-3900	293	2	m]kq	m]kq	PROPN
ejpam-3900	293	3	k∑	k∑	VERB
ejpam-3900	293	4	j=0	j=0	PROPN
ejpam-3900	293	5	(	(	PUNCT
ejpam-3900	293	6	−1)k−jqm(k−j	−1)k−jqm(k−j	NUM
ejpam-3900	293	7	2	2	NUM
ejpam-3900	293	8	)	)	PUNCT
ejpam-3900	294	1	[	[	X
ejpam-3900	294	2	kj	kj	X
ejpam-3900	294	3	]	]	X
ejpam-3900	294	4	qm	qm	PROPN
ejpam-3900	295	1	[	[	X
ejpam-3900	295	2	2r	2r	X
ejpam-3900	296	1	+	+	CCONJ
ejpam-3900	296	2	jm|m]n	jm|m]n	PROPN
ejpam-3900	296	3	,	,	PUNCT
ejpam-3900	296	4	q	q	X
ejpam-3900	297	1	[	[	X
ejpam-3900	297	2	t]nq	t]nq	X
ejpam-3900	297	3	[	[	X
ejpam-3900	297	4	n]q	n]q	X
ejpam-3900	297	5	!	!	PUNCT
ejpam-3900	298	1	=	=	PRON
ejpam-3900	298	2	k∑	k∑	PROPN
ejpam-3900	298	3	j=0	j=0	PROPN
ejpam-3900	298	4	1	1	NUM
ejpam-3900	299	1	[	[	X
ejpam-3900	299	2	k]qm	k]qm	X
ejpam-3900	299	3	!	!	PUNCT
ejpam-3900	300	1	[	[	X
ejpam-3900	300	2	m]kq	m]kq	PROPN
ejpam-3900	300	3	(	(	PUNCT
ejpam-3900	300	4	−1)k−jqm(k−j	−1)k−jqm(k−j	NUM
ejpam-3900	300	5	2	2	NUM
ejpam-3900	300	6	)	)	PUNCT
ejpam-3900	301	1	[	[	X
ejpam-3900	301	2	kj	kj	X
ejpam-3900	301	3	]	]	PUNCT
ejpam-3900	301	4	qm	qm	PROPN
ejpam-3900	301	5	∑	∑	PROPN
ejpam-3900	301	6	n≥0	n≥0	PROPN
ejpam-3900	301	7	[	[	X
ejpam-3900	301	8	2r	2r	NUM
ejpam-3900	301	9	+	+	CCONJ
ejpam-3900	301	10	jm|m]n	jm|m]n	PROPN
ejpam-3900	301	11	,	,	PUNCT
ejpam-3900	301	12	q	q	X
ejpam-3900	302	1	[	[	X
ejpam-3900	302	2	t]nq	t]nq	X
ejpam-3900	302	3	[	[	X
ejpam-3900	302	4	n]q	n]q	X
ejpam-3900	302	5	!	!	PUNCT
ejpam-3900	302	6	.	.	PUNCT
ejpam-3900	303	1	then	then	ADV
ejpam-3900	303	2	,	,	PUNCT
ejpam-3900	303	3	we	we	PRON
ejpam-3900	303	4	have	have	VERB
ejpam-3900	303	5	=	=	NOUN
ejpam-3900	303	6	1	1	NUM
ejpam-3900	304	1	[	[	X
ejpam-3900	304	2	k]qm	k]qm	X
ejpam-3900	304	3	!	!	PUNCT
ejpam-3900	305	1	[	[	X
ejpam-3900	305	2	m]kq	m]kq	PROPN
ejpam-3900	305	3	k∑	k∑	VERB
ejpam-3900	305	4	j=0	j=0	PROPN
ejpam-3900	305	5	(	(	PUNCT
ejpam-3900	305	6	−1)k−jqm(k−j	−1)k−jqm(k−j	NUM
ejpam-3900	305	7	2	2	NUM
ejpam-3900	305	8	)	)	PUNCT
ejpam-3900	306	1	[	[	X
ejpam-3900	306	2	kj	kj	X
ejpam-3900	306	3	]	]	PUNCT
ejpam-3900	306	4	qmf	qmf	VERB
ejpam-3900	306	5	[	[	X
ejpam-3900	306	6	2r	2r	NUM
ejpam-3900	306	7	+	+	CCONJ
ejpam-3900	306	8	jm	jm	PROPN
ejpam-3900	306	9	,	,	PUNCT
ejpam-3900	306	10	m	m	PROPN
ejpam-3900	306	11	,	,	PUNCT
ejpam-3900	306	12	t	t	X
ejpam-3900	306	13	]	]	X
ejpam-3900	306	14	=	=	SYM
ejpam-3900	306	15	1	1	NUM
ejpam-3900	307	1	[	[	X
ejpam-3900	307	2	k]qm	k]qm	X
ejpam-3900	307	3	!	!	PUNCT
ejpam-3900	308	1	[	[	X
ejpam-3900	308	2	m]kq	m]kq	X
ejpam-3900	308	3	[	[	X
ejpam-3900	308	4	4k	4k	X
ejpam-3900	308	5	qm	qm	PROPN
ejpam-3900	308	6	,	,	PUNCT
ejpam-3900	308	7	m(f	m(f	PROPN
ejpam-3900	308	8	[	[	X
ejpam-3900	308	9	x+	x+	PROPN
ejpam-3900	308	10	2r	2r	NUM
ejpam-3900	308	11	+	+	CCONJ
ejpam-3900	308	12	jm	jm	PROPN
ejpam-3900	308	13	,	,	PUNCT
ejpam-3900	308	14	m	m	PROPN
ejpam-3900	308	15	,	,	PUNCT
ejpam-3900	308	16	t])x=0	t])x=0	PROPN
ejpam-3900	308	17	.	.	PUNCT
ejpam-3900	308	18	remark	remark	PROPN
ejpam-3900	308	19	3.6	3.6	NUM
ejpam-3900	308	20	.	.	PUNCT
ejpam-3900	309	1	when	when	SCONJ
ejpam-3900	309	2	q	q	X
ejpam-3900	309	3	→	→	SYM
ejpam-3900	309	4	1	1	NUM
ejpam-3900	309	5	,	,	PUNCT
ejpam-3900	309	6	(	(	PUNCT
ejpam-3900	309	7	19	19	NUM
ejpam-3900	309	8	)	)	PUNCT
ejpam-3900	309	9	becomes	become	VERB
ejpam-3900	309	10	∑	∑	PROPN
ejpam-3900	309	11	n≥0	n≥0	PROPN
ejpam-3900	309	12	lm	lm	PROPN
ejpam-3900	309	13	,	,	PUNCT
ejpam-3900	309	14	r(n	r(n	PROPN
ejpam-3900	309	15	,	,	PUNCT
ejpam-3900	309	16	k	k	NOUN
ejpam-3900	309	17	)	)	PUNCT
ejpam-3900	309	18	tn	tn	PROPN
ejpam-3900	309	19	n	n	NOUN
ejpam-3900	309	20	!	!	PUNCT
ejpam-3900	310	1	=	=	SYM
ejpam-3900	310	2	1	1	NUM
ejpam-3900	310	3	k!mk	k!mk	X
ejpam-3900	310	4	k∑	k∑	PUNCT
ejpam-3900	310	5	j=0	j=0	PROPN
ejpam-3900	310	6	(	(	PUNCT
ejpam-3900	310	7	−1)k−j	−1)k−j	X
ejpam-3900	311	1	[	[	X
ejpam-3900	311	2	kj	kj	X
ejpam-3900	311	3	]	]	X
ejpam-3900	311	4	f	f	X
ejpam-3900	311	5	(	(	PUNCT
ejpam-3900	311	6	2r	2r	NUM
ejpam-3900	311	7	+	+	CCONJ
ejpam-3900	311	8	jm	jm	PROPN
ejpam-3900	311	9	,	,	PUNCT
ejpam-3900	311	10	m	m	PROPN
ejpam-3900	311	11	,	,	PUNCT
ejpam-3900	311	12	t	t	PROPN
ejpam-3900	311	13	)	)	PUNCT
ejpam-3900	311	14	where	where	SCONJ
ejpam-3900	311	15	f	f	PROPN
ejpam-3900	311	16	(	(	PUNCT
ejpam-3900	311	17	2r	2r	NUM
ejpam-3900	311	18	+	+	CCONJ
ejpam-3900	311	19	jm	jm	PROPN
ejpam-3900	311	20	,	,	PUNCT
ejpam-3900	311	21	m	m	PROPN
ejpam-3900	311	22	,	,	PUNCT
ejpam-3900	311	23	t	t	PROPN
ejpam-3900	311	24	)	)	PUNCT
ejpam-3900	311	25	=	=	PUNCT
ejpam-3900	312	1	∑	∑	PUNCT
ejpam-3900	312	2	n≥0	n≥0	PROPN
ejpam-3900	312	3	(	(	PUNCT
ejpam-3900	312	4	2r	2r	NUM
ejpam-3900	312	5	+	+	PROPN
ejpam-3900	312	6	jm|m)n	jm|m)n	PROPN
ejpam-3900	312	7	,	,	PUNCT
ejpam-3900	312	8	q	q	X
ejpam-3900	313	1	[	[	X
ejpam-3900	313	2	t]nq	t]nq	X
ejpam-3900	313	3	[	[	X
ejpam-3900	313	4	n]q	n]q	X
ejpam-3900	313	5	!	!	PUNCT
ejpam-3900	313	6	.	.	PUNCT
ejpam-3900	314	1	4	4	X
ejpam-3900	314	2	.	.	X
ejpam-3900	315	1	an	an	DET
ejpam-3900	315	2	explicit	explicit	ADJ
ejpam-3900	315	3	formula	formula	NOUN
ejpam-3900	315	4	for	for	ADP
ejpam-3900	315	5	(	(	PUNCT
ejpam-3900	315	6	q	q	ADJ
ejpam-3900	315	7	,	,	PUNCT
ejpam-3900	315	8	r)-dowling	r)-dowle	VERB
ejpam-3900	315	9	numbers	number	NOUN
ejpam-3900	315	10	one	one	NUM
ejpam-3900	315	11	of	of	ADP
ejpam-3900	315	12	the	the	DET
ejpam-3900	315	13	common	common	ADJ
ejpam-3900	315	14	properties	property	NOUN
ejpam-3900	315	15	of	of	ADP
ejpam-3900	315	16	lah	lah	NOUN
ejpam-3900	315	17	-	-	PUNCT
ejpam-3900	315	18	type	type	NOUN
ejpam-3900	315	19	numbers	number	NOUN
ejpam-3900	315	20	is	be	AUX
ejpam-3900	315	21	their	their	PRON
ejpam-3900	315	22	relation	relation	NOUN
ejpam-3900	315	23	with	with	ADP
ejpam-3900	315	24	both	both	DET
ejpam-3900	315	25	kinds	kind	NOUN
ejpam-3900	315	26	of	of	ADP
ejpam-3900	315	27	stirling	stirling	NOUN
ejpam-3900	315	28	-	-	PUNCT
ejpam-3900	315	29	type	type	NOUN
ejpam-3900	315	30	or	or	CCONJ
ejpam-3900	315	31	whitney	whitney	NOUN
ejpam-3900	315	32	-	-	PUNCT
ejpam-3900	315	33	type	type	NOUN
ejpam-3900	315	34	numbers	number	NOUN
ejpam-3900	315	35	.	.	PUNCT
ejpam-3900	316	1	analogous	analogous	ADJ
ejpam-3900	316	2	to	to	ADP
ejpam-3900	316	3	this	this	PRON
ejpam-3900	316	4	,	,	PUNCT
ejpam-3900	316	5	it	it	PRON
ejpam-3900	316	6	is	be	AUX
ejpam-3900	316	7	also	also	ADV
ejpam-3900	316	8	interesting	interesting	ADJ
ejpam-3900	316	9	to	to	PART
ejpam-3900	316	10	express	express	VERB
ejpam-3900	316	11	(	(	PUNCT
ejpam-3900	316	12	q	q	ADJ
ejpam-3900	316	13	,	,	PUNCT
ejpam-3900	316	14	r)-whitney	r)-whitney	ADJ
ejpam-3900	316	15	-	-	PUNCT
ejpam-3900	316	16	lah	lah	NOUN
ejpam-3900	316	17	numbers	number	NOUN
ejpam-3900	316	18	in	in	ADP
ejpam-3900	316	19	terms	term	NOUN
ejpam-3900	316	20	of	of	ADP
ejpam-3900	316	21	(	(	PUNCT
ejpam-3900	316	22	q	q	ADJ
ejpam-3900	316	23	,	,	PUNCT
ejpam-3900	316	24	r)-whitney	r)-whitney	NOUN
ejpam-3900	316	25	numbers	number	NOUN
ejpam-3900	316	26	.	.	PUNCT
ejpam-3900	317	1	to	to	PART
ejpam-3900	317	2	do	do	VERB
ejpam-3900	317	3	this	this	PRON
ejpam-3900	317	4	,	,	PUNCT
ejpam-3900	317	5	we	we	PRON
ejpam-3900	317	6	need	need	VERB
ejpam-3900	317	7	to	to	PART
ejpam-3900	317	8	define	define	VERB
ejpam-3900	317	9	the	the	DET
ejpam-3900	317	10	(	(	PUNCT
ejpam-3900	317	11	q	q	ADJ
ejpam-3900	317	12	,	,	PUNCT
ejpam-3900	317	13	r)-whitney	r)-whitney	NOUN
ejpam-3900	317	14	numbers	number	NOUN
ejpam-3900	317	15	of	of	ADP
ejpam-3900	317	16	the	the	DET
ejpam-3900	317	17	first	first	ADJ
ejpam-3900	317	18	kind	kind	NOUN
ejpam-3900	317	19	.	.	PUNCT
ejpam-3900	318	1	definition	definition	NOUN
ejpam-3900	318	2	4.1	4.1	NUM
ejpam-3900	318	3	.	.	PUNCT
ejpam-3900	319	1	the	the	DET
ejpam-3900	319	2	(	(	PUNCT
ejpam-3900	319	3	q	q	ADJ
ejpam-3900	319	4	,	,	PUNCT
ejpam-3900	319	5	r)-whitney	r)-whitney	NOUN
ejpam-3900	319	6	numbers	number	NOUN
ejpam-3900	319	7	of	of	ADP
ejpam-3900	319	8	the	the	DET
ejpam-3900	319	9	first	first	ADJ
ejpam-3900	319	10	kind	kind	NOUN
ejpam-3900	319	11	wm	wm	PROPN
ejpam-3900	319	12	,	,	PUNCT
ejpam-3900	319	13	r[n	r[n	NOUN
ejpam-3900	319	14	,	,	PUNCT
ejpam-3900	319	15	k]q	k]q	NOUN
ejpam-3900	319	16	are	be	AUX
ejpam-3900	319	17	defined	define	VERB
ejpam-3900	319	18	as	as	ADP
ejpam-3900	319	19	coefficients	coefficient	NOUN
ejpam-3900	319	20	of	of	ADP
ejpam-3900	319	21	the	the	DET
ejpam-3900	319	22	following	follow	VERB
ejpam-3900	319	23	generating	generate	VERB
ejpam-3900	319	24	function	function	NOUN
ejpam-3900	319	25	[	[	X
ejpam-3900	319	26	t−	t−	PROPN
ejpam-3900	319	27	r|m]n	r|m]n	NOUN
ejpam-3900	319	28	,	,	PUNCT
ejpam-3900	319	29	q	q	NOUN
ejpam-3900	320	1	=	=	SYM
ejpam-3900	320	2	n∑	n∑	PROPN
ejpam-3900	320	3	k=0	k=0	PROPN
ejpam-3900	320	4	wm	wm	PROPN
ejpam-3900	320	5	,	,	PUNCT
ejpam-3900	320	6	r[n	r[n	NOUN
ejpam-3900	320	7	,	,	PUNCT
ejpam-3900	320	8	k]q[t	k]q[t	X
ejpam-3900	320	9	]	]	X
ejpam-3900	320	10	k	k	X
ejpam-3900	320	11	q	q	X
ejpam-3900	320	12	.	.	PUNCT
ejpam-3900	321	1	(	(	PUNCT
ejpam-3900	321	2	20	20	X
ejpam-3900	321	3	)	)	PUNCT
ejpam-3900	321	4	note	note	NOUN
ejpam-3900	321	5	that	that	SCONJ
ejpam-3900	321	6	n+1∑	n+1∑	PROPN
ejpam-3900	321	7	k=0	k=0	PROPN
ejpam-3900	321	8	wm	wm	PROPN
ejpam-3900	321	9	,	,	PUNCT
ejpam-3900	321	10	r[n+	r[n+	NOUN
ejpam-3900	321	11	1	1	NUM
ejpam-3900	321	12	,	,	PUNCT
ejpam-3900	321	13	k]q[t	k]q[t	AUX
ejpam-3900	321	14	]	]	X
ejpam-3900	322	1	k	k	X
ejpam-3900	322	2	q	q	PUNCT
ejpam-3900	323	1	=	=	PUNCT
ejpam-3900	323	2	[	[	PUNCT
ejpam-3900	323	3	t−	t−	PROPN
ejpam-3900	323	4	r|m]n+1,q	r|m]n+1,q	NOUN
ejpam-3900	323	5	=	=	PUNCT
ejpam-3900	324	1	[	[	PUNCT
ejpam-3900	324	2	t−	t−	PROPN
ejpam-3900	324	3	r|m]n	r|m]n	NOUN
ejpam-3900	324	4	,	,	PUNCT
ejpam-3900	324	5	q[t−	q[t−	ADJ
ejpam-3900	324	6	r	r	NOUN
ejpam-3900	324	7	−	−	PROPN
ejpam-3900	324	8	nm]q	nm]q	PROPN
ejpam-3900	324	9	r.	r.	PROPN
ejpam-3900	324	10	corcino	corcino	PROPN
ejpam-3900	324	11	,	,	PUNCT
ejpam-3900	324	12	j.	j.	PROPN
ejpam-3900	324	13	ontolan	ontolan	PROPN
ejpam-3900	324	14	,	,	PUNCT
ejpam-3900	324	15	m.	m.	NOUN
ejpam-3900	324	16	lobrigas	lobrigas	PROPN
ejpam-3900	324	17	/	/	SYM
ejpam-3900	324	18	eur	eur	PROPN
ejpam-3900	324	19	.	.	PUNCT
ejpam-3900	325	1	j.	j.	PROPN
ejpam-3900	325	2	pure	pure	PROPN
ejpam-3900	325	3	appl	appl	PROPN
ejpam-3900	325	4	.	.	PROPN
ejpam-3900	325	5	math	math	PROPN
ejpam-3900	325	6	,	,	PUNCT
ejpam-3900	325	7	14	14	NUM
ejpam-3900	325	8	(	(	PUNCT
ejpam-3900	325	9	1	1	NUM
ejpam-3900	325	10	)	)	PUNCT
ejpam-3900	325	11	(	(	PUNCT
ejpam-3900	325	12	2021	2021	NUM
ejpam-3900	325	13	)	)	PUNCT
ejpam-3900	325	14	,	,	PUNCT
ejpam-3900	325	15	65	65	NUM
ejpam-3900	325	16	-	-	SYM
ejpam-3900	325	17	81	81	NUM
ejpam-3900	325	18	77	77	NUM
ejpam-3900	325	19	=	=	SYM
ejpam-3900	325	20	1	1	NUM
ejpam-3900	325	21	qr+nm	qr+nm	NUM
ejpam-3900	325	22	(	(	PUNCT
ejpam-3900	325	23	[	[	X
ejpam-3900	325	24	t]q	t]q	NOUN
ejpam-3900	325	25	−	−	NOUN
ejpam-3900	326	1	[	[	X
ejpam-3900	326	2	r	r	X
ejpam-3900	326	3	+	+	NUM
ejpam-3900	326	4	nm]q	nm]q	PROPN
ejpam-3900	326	5	)	)	PUNCT
ejpam-3900	326	6	n∑	n∑	PART
ejpam-3900	326	7	k=0	k=0	PROPN
ejpam-3900	326	8	wm	wm	PROPN
ejpam-3900	326	9	,	,	PUNCT
ejpam-3900	326	10	r[n	r[n	NOUN
ejpam-3900	326	11	,	,	PUNCT
ejpam-3900	326	12	k]q[t	k]q[t	X
ejpam-3900	326	13	]	]	X
ejpam-3900	326	14	k	k	NOUN
ejpam-3900	326	15	q	q	PUNCT
ejpam-3900	326	16	=	=	SYM
ejpam-3900	326	17	1	1	NUM
ejpam-3900	326	18	qr+nm	qr+nm	NUM
ejpam-3900	326	19	(	(	PUNCT
ejpam-3900	326	20	n∑	n∑	PROPN
ejpam-3900	326	21	k=0	k=0	PROPN
ejpam-3900	326	22	wm	wm	PROPN
ejpam-3900	326	23	,	,	PUNCT
ejpam-3900	326	24	r[n	r[n	NOUN
ejpam-3900	326	25	,	,	PUNCT
ejpam-3900	326	26	k]q[t	k]q[t	X
ejpam-3900	326	27	]	]	X
ejpam-3900	326	28	k+1	k+1	X
ejpam-3900	326	29	q	q	NOUN
ejpam-3900	327	1	−	−	PROPN
ejpam-3900	327	2	n∑	n∑	NOUN
ejpam-3900	327	3	k=0	k=0	PROPN
ejpam-3900	328	1	[	[	X
ejpam-3900	328	2	r	r	X
ejpam-3900	328	3	+	+	NUM
ejpam-3900	328	4	nm]qwm	nm]qwm	PRON
ejpam-3900	328	5	,	,	PUNCT
ejpam-3900	328	6	r[n	r[n	NOUN
ejpam-3900	328	7	,	,	PUNCT
ejpam-3900	328	8	k]q[t	k]q[t	X
ejpam-3900	328	9	]	]	X
ejpam-3900	328	10	k	k	X
ejpam-3900	328	11	q	q	PROPN
ejpam-3900	328	12	)	)	PUNCT
ejpam-3900	328	13	=	=	SYM
ejpam-3900	329	1	1	1	NUM
ejpam-3900	329	2	qr+nm	qr+nm	NUM
ejpam-3900	329	3	(	(	PUNCT
ejpam-3900	329	4	n+1∑	n+1∑	PROPN
ejpam-3900	329	5	k=0	k=0	PROPN
ejpam-3900	329	6	wm	wm	PROPN
ejpam-3900	329	7	,	,	PUNCT
ejpam-3900	329	8	r[n	r[n	PROPN
ejpam-3900	329	9	,	,	PUNCT
ejpam-3900	329	10	k	k	PROPN
ejpam-3900	329	11	−	−	PROPN
ejpam-3900	329	12	1]q[t	1]q[t	NUM
ejpam-3900	329	13	]	]	X
ejpam-3900	330	1	k	k	X
ejpam-3900	330	2	q	q	PUNCT
ejpam-3900	331	1	−	−	PROPN
ejpam-3900	331	2	n+1∑	n+1∑	ADJ
ejpam-3900	331	3	k=0	k=0	PROPN
ejpam-3900	332	1	[	[	X
ejpam-3900	332	2	r	r	X
ejpam-3900	332	3	+	+	NUM
ejpam-3900	332	4	nm]qwm	nm]qwm	PRON
ejpam-3900	332	5	,	,	PUNCT
ejpam-3900	332	6	r[n	r[n	NOUN
ejpam-3900	332	7	,	,	PUNCT
ejpam-3900	332	8	k]q[t	k]q[t	X
ejpam-3900	332	9	]	]	X
ejpam-3900	332	10	k	k	X
ejpam-3900	332	11	q	q	PROPN
ejpam-3900	332	12	)	)	PUNCT
ejpam-3900	333	1	=	=	SYM
ejpam-3900	333	2	n+1∑	n+1∑	ADJ
ejpam-3900	333	3	k=0	k=0	PROPN
ejpam-3900	333	4	1	1	PROPN
ejpam-3900	333	5	qr+nm	qr+nm	PROPN
ejpam-3900	333	6	(	(	PUNCT
ejpam-3900	333	7	wm	wm	PROPN
ejpam-3900	333	8	,	,	PUNCT
ejpam-3900	333	9	r[n	r[n	PROPN
ejpam-3900	333	10	,	,	PUNCT
ejpam-3900	333	11	k	k	PROPN
ejpam-3900	333	12	−	−	PROPN
ejpam-3900	333	13	1]q	1]q	NUM
ejpam-3900	333	14	−	−	PROPN
ejpam-3900	334	1	[	[	X
ejpam-3900	334	2	r	r	X
ejpam-3900	334	3	+	+	NUM
ejpam-3900	334	4	nm]qwm	nm]qwm	PRON
ejpam-3900	334	5	,	,	PUNCT
ejpam-3900	334	6	r[n	r[n	NOUN
ejpam-3900	334	7	,	,	PUNCT
ejpam-3900	334	8	k]q	k]q	NOUN
ejpam-3900	334	9	)	)	PUNCT
ejpam-3900	335	1	[	[	X
ejpam-3900	335	2	t]kq	t]kq	X
ejpam-3900	335	3	.	.	PUNCT
ejpam-3900	336	1	comparing	compare	VERB
ejpam-3900	336	2	the	the	DET
ejpam-3900	336	3	coefficients	coefficient	NOUN
ejpam-3900	336	4	of	of	ADP
ejpam-3900	336	5	[	[	X
ejpam-3900	336	6	t]kq	t]kq	PROPN
ejpam-3900	336	7	completes	complete	VERB
ejpam-3900	336	8	the	the	DET
ejpam-3900	336	9	proof	proof	NOUN
ejpam-3900	336	10	the	the	DET
ejpam-3900	336	11	following	follow	VERB
ejpam-3900	336	12	theorem	theorem	PROPN
ejpam-3900	336	13	.	.	PUNCT
ejpam-3900	336	14	theorem	theorem	VERB
ejpam-3900	336	15	4.2	4.2	NUM
ejpam-3900	336	16	.	.	PUNCT
ejpam-3900	337	1	the	the	DET
ejpam-3900	337	2	(	(	PUNCT
ejpam-3900	337	3	q	q	ADJ
ejpam-3900	337	4	,	,	PUNCT
ejpam-3900	337	5	r)-whitney	r)-whitney	NOUN
ejpam-3900	337	6	numbers	number	NOUN
ejpam-3900	337	7	of	of	ADP
ejpam-3900	337	8	the	the	DET
ejpam-3900	337	9	first	first	ADJ
ejpam-3900	337	10	kind	kind	NOUN
ejpam-3900	337	11	wm	wm	PROPN
ejpam-3900	337	12	,	,	PUNCT
ejpam-3900	337	13	r[n	r[n	VERB
ejpam-3900	337	14	,	,	PUNCT
ejpam-3900	337	15	k]q	k]q	AUX
ejpam-3900	337	16	satisfy	satisfy	VERB
ejpam-3900	337	17	the	the	DET
ejpam-3900	337	18	following	follow	VERB
ejpam-3900	337	19	triangular	triangular	NOUN
ejpam-3900	337	20	recurrence	recurrence	NOUN
ejpam-3900	337	21	relation	relation	NOUN
ejpam-3900	337	22	:	:	PUNCT
ejpam-3900	338	1	wm	wm	PROPN
ejpam-3900	338	2	,	,	PUNCT
ejpam-3900	338	3	r[n+	r[n+	NOUN
ejpam-3900	338	4	1	1	NUM
ejpam-3900	338	5	,	,	PUNCT
ejpam-3900	338	6	k]q[t	k]q[t	AUX
ejpam-3900	338	7	]	]	X
ejpam-3900	338	8	k	k	NOUN
ejpam-3900	338	9	q	q	PUNCT
ejpam-3900	338	10	=	=	SYM
ejpam-3900	338	11	1	1	NUM
ejpam-3900	338	12	qr+nm	qr+nm	NUM
ejpam-3900	338	13	(	(	PUNCT
ejpam-3900	338	14	wm	wm	PROPN
ejpam-3900	338	15	,	,	PUNCT
ejpam-3900	338	16	r[n	r[n	PROPN
ejpam-3900	338	17	,	,	PUNCT
ejpam-3900	338	18	k	k	PROPN
ejpam-3900	338	19	−	−	PROPN
ejpam-3900	339	1	1]q	1]q	NUM
ejpam-3900	339	2	−	−	PROPN
ejpam-3900	340	1	[	[	X
ejpam-3900	340	2	r	r	X
ejpam-3900	340	3	+	+	NUM
ejpam-3900	340	4	nm]qwm	nm]qwm	PRON
ejpam-3900	340	5	,	,	PUNCT
ejpam-3900	340	6	r[n	r[n	NOUN
ejpam-3900	340	7	,	,	PUNCT
ejpam-3900	340	8	k]q	k]q	PROPN
ejpam-3900	340	9	)	)	PUNCT
ejpam-3900	340	10	(	(	PUNCT
ejpam-3900	340	11	21	21	NUM
ejpam-3900	340	12	)	)	PUNCT
ejpam-3900	340	13	with	with	ADP
ejpam-3900	340	14	initial	initial	ADJ
ejpam-3900	340	15	condition	condition	NOUN
ejpam-3900	340	16	wm	wm	PROPN
ejpam-3900	340	17	,	,	PUNCT
ejpam-3900	340	18	r[0	r[0	PROPN
ejpam-3900	340	19	,	,	PUNCT
ejpam-3900	340	20	0]q	0]q	NOUN
ejpam-3900	341	1	=	=	SYM
ejpam-3900	341	2	1	1	NUM
ejpam-3900	341	3	,	,	PUNCT
ejpam-3900	341	4	wm	wm	PROPN
ejpam-3900	341	5	,	,	PUNCT
ejpam-3900	341	6	r[n	r[n	NOUN
ejpam-3900	341	7	,	,	PUNCT
ejpam-3900	341	8	0]q	0]q	NOUN
ejpam-3900	342	1	=	=	PUNCT
ejpam-3900	343	1	(	(	PUNCT
ejpam-3900	343	2	−1)nq−r−(n−1)m[r	−1)nq−r−(n−1)m[r	ADJ
ejpam-3900	343	3	+	+	CCONJ
ejpam-3900	343	4	(	(	PUNCT
ejpam-3900	343	5	n	n	NUM
ejpam-3900	343	6	−	−	PROPN
ejpam-3900	343	7	1)m]q	1)m]q	PROPN
ejpam-3900	343	8	and	and	CCONJ
ejpam-3900	343	9	wm	wm	PROPN
ejpam-3900	343	10	,	,	PUNCT
ejpam-3900	343	11	r[n	r[n	NOUN
ejpam-3900	343	12	,	,	PUNCT
ejpam-3900	343	13	k]q	k]q	NOUN
ejpam-3900	343	14	=	=	NOUN
ejpam-3900	343	15	0	0	PUNCT
ejpam-3900	344	1	if	if	SCONJ
ejpam-3900	344	2	n	n	PRON
ejpam-3900	344	3	<	<	X
ejpam-3900	344	4	k.	k.	PROPN
ejpam-3900	344	5	n	n	PROPN
ejpam-3900	344	6	/	/	SYM
ejpam-3900	344	7	k	k	NOUN
ejpam-3900	344	8	0	0	NUM
ejpam-3900	344	9	1	1	NUM
ejpam-3900	344	10	2	2	NUM
ejpam-3900	344	11	0	0	NUM
ejpam-3900	344	12	1	1	NUM
ejpam-3900	344	13	0	0	NUM
ejpam-3900	344	14	0	0	NUM
ejpam-3900	344	15	1	1	NUM
ejpam-3900	344	16	−q−r[r]q	−q−r[r]q	NOUN
ejpam-3900	344	17	q−r	q−r	PROPN
ejpam-3900	344	18	0	0	NUM
ejpam-3900	344	19	2	2	NUM
ejpam-3900	344	20	q−(r+m)[r	q−(r+m)[r	NOUN
ejpam-3900	344	21	+	+	NOUN
ejpam-3900	344	22	m]q	m]q	NOUN
ejpam-3900	344	23	−q−(2r+m)([r]q	−q−(2r+m)([r]q	X
ejpam-3900	345	1	+	+	PUNCT
ejpam-3900	346	1	[	[	X
ejpam-3900	346	2	r	r	X
ejpam-3900	346	3	+	+	NOUN
ejpam-3900	346	4	m]q	m]q	NOUN
ejpam-3900	346	5	)	)	PUNCT
ejpam-3900	346	6	q−(2r+m	q−(2r+m	PROPN
ejpam-3900	346	7	)	)	PUNCT
ejpam-3900	346	8	the	the	DET
ejpam-3900	346	9	next	next	ADJ
ejpam-3900	346	10	theorem	theorem	NOUN
ejpam-3900	346	11	contains	contain	VERB
ejpam-3900	346	12	the	the	DET
ejpam-3900	346	13	orthogonality	orthogonality	NOUN
ejpam-3900	346	14	relation	relation	NOUN
ejpam-3900	346	15	of	of	ADP
ejpam-3900	346	16	(	(	PUNCT
ejpam-3900	346	17	q	q	ADJ
ejpam-3900	346	18	,	,	PUNCT
ejpam-3900	346	19	r)-whitney	r)-whitney	NOUN
ejpam-3900	346	20	numbers	number	NOUN
ejpam-3900	346	21	of	of	ADP
ejpam-3900	346	22	the	the	DET
ejpam-3900	346	23	first	first	ADJ
ejpam-3900	346	24	and	and	CCONJ
ejpam-3900	346	25	second	second	ADJ
ejpam-3900	346	26	kinds	kind	NOUN
ejpam-3900	346	27	.	.	PUNCT
ejpam-3900	347	1	theorem	theorem	VERB
ejpam-3900	347	2	4.3	4.3	NUM
ejpam-3900	347	3	.	.	PUNCT
ejpam-3900	348	1	the	the	DET
ejpam-3900	348	2	following	follow	VERB
ejpam-3900	348	3	orthogonality	orthogonality	NOUN
ejpam-3900	348	4	relation	relation	NOUN
ejpam-3900	348	5	holds	hold	VERB
ejpam-3900	348	6	n∑	n∑	PROPN
ejpam-3900	348	7	k	k	PROPN
ejpam-3900	349	1	=	=	PROPN
ejpam-3900	349	2	j	j	PROPN
ejpam-3900	349	3	wm	wm	PROPN
ejpam-3900	349	4	,	,	PUNCT
ejpam-3900	349	5	r[n	r[n	PROPN
ejpam-3900	349	6	,	,	PUNCT
ejpam-3900	349	7	k]qwm	k]qwm	PROPN
ejpam-3900	349	8	,	,	PUNCT
ejpam-3900	349	9	r[k	r[k	PROPN
ejpam-3900	349	10	,	,	PUNCT
ejpam-3900	349	11	j]q	j]q	PROPN
ejpam-3900	349	12	=	=	PUNCT
ejpam-3900	349	13	n∑	n∑	PROPN
ejpam-3900	349	14	k	k	PROPN
ejpam-3900	350	1	=	=	PROPN
ejpam-3900	350	2	j	j	PROPN
ejpam-3900	350	3	wm	wm	PROPN
ejpam-3900	350	4	,	,	PUNCT
ejpam-3900	350	5	r[n	r[n	PROPN
ejpam-3900	350	6	,	,	PUNCT
ejpam-3900	350	7	k]qwm	k]qwm	PROPN
ejpam-3900	350	8	,	,	PUNCT
ejpam-3900	350	9	r[k	r[k	PROPN
ejpam-3900	350	10	,	,	PUNCT
ejpam-3900	350	11	j]q	j]q	NOUN
ejpam-3900	350	12	=	=	PUNCT
ejpam-3900	350	13	δnj	δnj	NOUN
ejpam-3900	350	14	=	=	SYM
ejpam-3900	350	15	{	{	PUNCT
ejpam-3900	350	16	0	0	NUM
ejpam-3900	350	17	,	,	PUNCT
ejpam-3900	350	18	if	if	SCONJ
ejpam-3900	350	19	j	j	PROPN
ejpam-3900	350	20	6=	6=	PROPN
ejpam-3900	350	21	n	n	PROPN
ejpam-3900	350	22	1	1	NUM
ejpam-3900	350	23	,	,	PUNCT
ejpam-3900	350	24	if	if	SCONJ
ejpam-3900	350	25	j	j	PROPN
ejpam-3900	350	26	=	=	SYM
ejpam-3900	350	27	n	n	PROPN
ejpam-3900	350	28	(	(	PUNCT
ejpam-3900	350	29	22	22	NUM
ejpam-3900	350	30	)	)	PUNCT
ejpam-3900	350	31	proof	proof	NOUN
ejpam-3900	350	32	.	.	PUNCT
ejpam-3900	351	1	applying	apply	VERB
ejpam-3900	351	2	equation	equation	NOUN
ejpam-3900	351	3	(	(	PUNCT
ejpam-3900	351	4	11	11	NUM
ejpam-3900	351	5	)	)	PUNCT
ejpam-3900	351	6	to	to	ADP
ejpam-3900	351	7	(	(	PUNCT
ejpam-3900	351	8	20	20	NUM
ejpam-3900	351	9	)	)	PUNCT
ejpam-3900	351	10	yields	yield	NOUN
ejpam-3900	351	11	[	[	PUNCT
ejpam-3900	351	12	t−	t−	PROPN
ejpam-3900	351	13	r|m]n	r|m]n	NOUN
ejpam-3900	351	14	,	,	PUNCT
ejpam-3900	351	15	q	q	NOUN
ejpam-3900	351	16	=	=	SYM
ejpam-3900	351	17	n∑	n∑	PROPN
ejpam-3900	351	18	k=0	k=0	PROPN
ejpam-3900	351	19	wm	wm	PROPN
ejpam-3900	351	20	,	,	PUNCT
ejpam-3900	351	21	r[n	r[n	NOUN
ejpam-3900	351	22	,	,	PUNCT
ejpam-3900	351	23	k]q[t	k]q[t	X
ejpam-3900	351	24	]	]	X
ejpam-3900	352	1	k	k	PROPN
ejpam-3900	352	2	q	q	PROPN
ejpam-3900	352	3	=	=	PUNCT
ejpam-3900	352	4	n∑	n∑	PROPN
ejpam-3900	352	5	k=0	k=0	PROPN
ejpam-3900	352	6	wm	wm	PROPN
ejpam-3900	352	7	,	,	PUNCT
ejpam-3900	352	8	r[n	r[n	PROPN
ejpam-3900	352	9	,	,	PUNCT
ejpam-3900	352	10	k]q	k]q	PROPN
ejpam-3900	352	11	k∑	k∑	VERB
ejpam-3900	352	12	j=0	j=0	PROPN
ejpam-3900	352	13	wm	wm	PROPN
ejpam-3900	352	14	,	,	PUNCT
ejpam-3900	352	15	r[k	r[k	PROPN
ejpam-3900	352	16	,	,	PUNCT
ejpam-3900	352	17	j]q[t−	j]q[t−	ADJ
ejpam-3900	352	18	r|m]j	r|m]j	PROPN
ejpam-3900	352	19	,	,	PUNCT
ejpam-3900	352	20	q	q	NOUN
ejpam-3900	352	21	=	=	SYM
ejpam-3900	352	22	n∑	n∑	NOUN
ejpam-3900	352	23	j=0	j=0	PROPN
ejpam-3900	352	24	n∑	n∑	PROPN
ejpam-3900	352	25	k	k	PROPN
ejpam-3900	353	1	=	=	PROPN
ejpam-3900	353	2	j	j	PROPN
ejpam-3900	353	3	wm	wm	PROPN
ejpam-3900	353	4	,	,	PUNCT
ejpam-3900	353	5	r[n	r[n	PROPN
ejpam-3900	353	6	,	,	PUNCT
ejpam-3900	353	7	k]qwm	k]qwm	PROPN
ejpam-3900	353	8	,	,	PUNCT
ejpam-3900	353	9	r[k	r[k	PROPN
ejpam-3900	353	10	,	,	PUNCT
ejpam-3900	353	11	j]q[t−	j]q[t−	ADJ
ejpam-3900	353	12	r|m]j	r|m]j	PROPN
ejpam-3900	353	13	,	,	PUNCT
ejpam-3900	353	14	q	q	NOUN
ejpam-3900	353	15	=	=	SYM
ejpam-3900	353	16	n∑	n∑	NOUN
ejpam-3900	353	17	j=0	j=0	PROPN
ejpam-3900	354	1			PROPN
ejpam-3900	354	2	n∑	n∑	PROPN
ejpam-3900	354	3	k	k	PROPN
ejpam-3900	354	4	=	=	PROPN
ejpam-3900	354	5	j	j	PROPN
ejpam-3900	354	6	wm	wm	PROPN
ejpam-3900	354	7	,	,	PUNCT
ejpam-3900	354	8	r[n	r[n	PROPN
ejpam-3900	354	9	,	,	PUNCT
ejpam-3900	354	10	k]qwm	k]qwm	PROPN
ejpam-3900	354	11	,	,	PUNCT
ejpam-3900	354	12	r[k	r[k	PROPN
ejpam-3900	354	13	,	,	PUNCT
ejpam-3900	354	14	j]q	j]q	ADJ
ejpam-3900	354	15			PROPN
ejpam-3900	355	1	[	[	X
ejpam-3900	355	2	t−	t−	PROPN
ejpam-3900	355	3	r|m]j	r|m]j	PROPN
ejpam-3900	355	4	,	,	PUNCT
ejpam-3900	355	5	q.	q.	PROPN
ejpam-3900	355	6	r.	r.	PROPN
ejpam-3900	355	7	corcino	corcino	PROPN
ejpam-3900	355	8	,	,	PUNCT
ejpam-3900	355	9	j.	j.	PROPN
ejpam-3900	355	10	ontolan	ontolan	PROPN
ejpam-3900	355	11	,	,	PUNCT
ejpam-3900	355	12	m.	m.	NOUN
ejpam-3900	355	13	lobrigas	lobrigas	PROPN
ejpam-3900	355	14	/	/	SYM
ejpam-3900	355	15	eur	eur	PROPN
ejpam-3900	355	16	.	.	PUNCT
ejpam-3900	356	1	j.	j.	PROPN
ejpam-3900	356	2	pure	pure	PROPN
ejpam-3900	356	3	appl	appl	PROPN
ejpam-3900	356	4	.	.	PROPN
ejpam-3900	356	5	math	math	PROPN
ejpam-3900	356	6	,	,	PUNCT
ejpam-3900	356	7	14	14	NUM
ejpam-3900	356	8	(	(	PUNCT
ejpam-3900	356	9	1	1	NUM
ejpam-3900	356	10	)	)	PUNCT
ejpam-3900	356	11	(	(	PUNCT
ejpam-3900	356	12	2021	2021	NUM
ejpam-3900	356	13	)	)	PUNCT
ejpam-3900	356	14	,	,	PUNCT
ejpam-3900	356	15	65	65	NUM
ejpam-3900	356	16	-	-	SYM
ejpam-3900	356	17	81	81	NUM
ejpam-3900	356	18	78	78	NUM
ejpam-3900	356	19	by	by	ADP
ejpam-3900	356	20	comparing	compare	VERB
ejpam-3900	356	21	coefficients	coefficient	NOUN
ejpam-3900	356	22	,	,	PUNCT
ejpam-3900	356	23	we	we	PRON
ejpam-3900	356	24	get	get	VERB
ejpam-3900	356	25	n∑	n∑	PROPN
ejpam-3900	357	1	k	k	PROPN
ejpam-3900	358	1	=	=	PROPN
ejpam-3900	358	2	j	j	PROPN
ejpam-3900	358	3	wm	wm	PROPN
ejpam-3900	358	4	,	,	PUNCT
ejpam-3900	358	5	r[n	r[n	PROPN
ejpam-3900	358	6	,	,	PUNCT
ejpam-3900	358	7	k]qwm	k]qwm	PROPN
ejpam-3900	358	8	,	,	PUNCT
ejpam-3900	358	9	r[k	r[k	PROPN
ejpam-3900	358	10	,	,	PUNCT
ejpam-3900	358	11	j]q	j]q	NOUN
ejpam-3900	358	12	=	=	PUNCT
ejpam-3900	358	13	{	{	PUNCT
ejpam-3900	358	14	0	0	NUM
ejpam-3900	358	15	,	,	PUNCT
ejpam-3900	358	16	if	if	SCONJ
ejpam-3900	358	17	j	j	PROPN
ejpam-3900	358	18	6=	6=	PROPN
ejpam-3900	358	19	n	n	PROPN
ejpam-3900	358	20	1	1	NUM
ejpam-3900	358	21	,	,	PUNCT
ejpam-3900	358	22	if	if	SCONJ
ejpam-3900	358	23	j	j	PROPN
ejpam-3900	358	24	=	=	SYM
ejpam-3900	358	25	n.	n.	PROPN
ejpam-3900	358	26	(	(	PUNCT
ejpam-3900	358	27	23	23	NUM
ejpam-3900	358	28	)	)	PUNCT
ejpam-3900	358	29	similarly	similarly	ADV
ejpam-3900	358	30	,	,	PUNCT
ejpam-3900	358	31	we	we	PRON
ejpam-3900	358	32	have	have	VERB
ejpam-3900	358	33	[	[	X
ejpam-3900	358	34	t]nq	t]nq	NOUN
ejpam-3900	358	35	=	=	SYM
ejpam-3900	358	36	n∑	n∑	PROPN
ejpam-3900	358	37	k=0	k=0	PROPN
ejpam-3900	358	38	wm	wm	PROPN
ejpam-3900	358	39	,	,	PUNCT
ejpam-3900	358	40	r[n	r[n	NOUN
ejpam-3900	358	41	,	,	PUNCT
ejpam-3900	358	42	k]q[t−	k]q[t−	NOUN
ejpam-3900	358	43	r|m]k	r|m]k	NUM
ejpam-3900	358	44	,	,	PUNCT
ejpam-3900	358	45	q	q	NOUN
ejpam-3900	358	46	=	=	SYM
ejpam-3900	358	47	n∑	n∑	PROPN
ejpam-3900	358	48	k=0	k=0	PROPN
ejpam-3900	358	49	wm	wm	PROPN
ejpam-3900	358	50	,	,	PUNCT
ejpam-3900	358	51	r[n	r[n	PROPN
ejpam-3900	358	52	,	,	PUNCT
ejpam-3900	358	53	k]q	k]q	PROPN
ejpam-3900	358	54	k∑	k∑	VERB
ejpam-3900	358	55	j=0	j=0	PROPN
ejpam-3900	358	56	wm	wm	PROPN
ejpam-3900	358	57	,	,	PUNCT
ejpam-3900	358	58	r[k	r[k	PROPN
ejpam-3900	358	59	,	,	PUNCT
ejpam-3900	358	60	j]qj[t	j]qj[t	NOUN
ejpam-3900	358	61	]	]	X
ejpam-3900	358	62	n	n	PRON
ejpam-3900	358	63	q	q	NOUN
ejpam-3900	358	64	=	=	SYM
ejpam-3900	358	65	n∑	n∑	PROPN
ejpam-3900	358	66	j=0	j=0	PROPN
ejpam-3900	358	67	n∑	n∑	PROPN
ejpam-3900	359	1	k	k	PROPN
ejpam-3900	360	1	=	=	PROPN
ejpam-3900	360	2	j	j	PROPN
ejpam-3900	360	3	wm	wm	PROPN
ejpam-3900	360	4	,	,	PUNCT
ejpam-3900	360	5	r[n	r[n	PROPN
ejpam-3900	360	6	,	,	PUNCT
ejpam-3900	360	7	k]qwm	k]qwm	PROPN
ejpam-3900	360	8	,	,	PUNCT
ejpam-3900	360	9	r[k	r[k	PROPN
ejpam-3900	360	10	,	,	PUNCT
ejpam-3900	360	11	j]q[t	j]q[t	ADV
ejpam-3900	360	12	]	]	X
ejpam-3900	360	13	j	j	PROPN
ejpam-3900	360	14	q	q	PROPN
ejpam-3900	360	15	=	=	SYM
ejpam-3900	360	16	n∑	n∑	NOUN
ejpam-3900	360	17	j=0	j=0	PROPN
ejpam-3900	361	1			PROPN
ejpam-3900	361	2	n∑	n∑	PROPN
ejpam-3900	361	3	k	k	PROPN
ejpam-3900	361	4	=	=	PROPN
ejpam-3900	361	5	j	j	PROPN
ejpam-3900	361	6	wm	wm	PROPN
ejpam-3900	361	7	,	,	PUNCT
ejpam-3900	361	8	r[n	r[n	PROPN
ejpam-3900	361	9	,	,	PUNCT
ejpam-3900	361	10	k]qwm	k]qwm	PROPN
ejpam-3900	361	11	,	,	PUNCT
ejpam-3900	361	12	r[k	r[k	PROPN
ejpam-3900	361	13	,	,	PUNCT
ejpam-3900	361	14	j]q	j]q	ADJ
ejpam-3900	361	15			PROPN
ejpam-3900	362	1	[	[	X
ejpam-3900	362	2	t]jq	t]jq	PROPN
ejpam-3900	362	3	.	.	PUNCT
ejpam-3900	362	4	hence	hence	ADV
ejpam-3900	362	5	,	,	PUNCT
ejpam-3900	362	6	n∑	n∑	PROPN
ejpam-3900	362	7	k	k	PROPN
ejpam-3900	363	1	=	=	PROPN
ejpam-3900	363	2	j	j	PROPN
ejpam-3900	363	3	wm	wm	PROPN
ejpam-3900	363	4	,	,	PUNCT
ejpam-3900	363	5	r[n	r[n	PROPN
ejpam-3900	363	6	,	,	PUNCT
ejpam-3900	363	7	k]qwm	k]qwm	PROPN
ejpam-3900	363	8	,	,	PUNCT
ejpam-3900	363	9	r[k	r[k	PROPN
ejpam-3900	363	10	,	,	PUNCT
ejpam-3900	363	11	j]q	j]q	NOUN
ejpam-3900	363	12	=	=	PUNCT
ejpam-3900	363	13	{	{	PUNCT
ejpam-3900	363	14	0	0	NUM
ejpam-3900	363	15	,	,	PUNCT
ejpam-3900	363	16	if	if	SCONJ
ejpam-3900	363	17	j	j	PROPN
ejpam-3900	363	18	6=	6=	PROPN
ejpam-3900	363	19	n	n	PROPN
ejpam-3900	363	20	1	1	NUM
ejpam-3900	363	21	,	,	PUNCT
ejpam-3900	363	22	if	if	SCONJ
ejpam-3900	363	23	j	j	PROPN
ejpam-3900	363	24	=	=	PROPN
ejpam-3900	363	25	n.	n.	PROPN
ejpam-3900	363	26	(	(	PUNCT
ejpam-3900	363	27	24	24	NUM
ejpam-3900	363	28	)	)	PUNCT
ejpam-3900	363	29	using	use	VERB
ejpam-3900	363	30	the	the	DET
ejpam-3900	363	31	orthogonality	orthogonality	NOUN
ejpam-3900	363	32	relations	relation	NOUN
ejpam-3900	363	33	in	in	ADP
ejpam-3900	363	34	(	(	PUNCT
ejpam-3900	363	35	23	23	NUM
ejpam-3900	363	36	)	)	PUNCT
ejpam-3900	363	37	and	and	CCONJ
ejpam-3900	363	38	(	(	PUNCT
ejpam-3900	363	39	24	24	NUM
ejpam-3900	363	40	)	)	PUNCT
ejpam-3900	363	41	,	,	PUNCT
ejpam-3900	363	42	we	we	PRON
ejpam-3900	363	43	can	can	AUX
ejpam-3900	363	44	easily	easily	ADV
ejpam-3900	363	45	prove	prove	VERB
ejpam-3900	363	46	the	the	DET
ejpam-3900	363	47	following	follow	VERB
ejpam-3900	363	48	inverse	inverse	NOUN
ejpam-3900	363	49	relation	relation	NOUN
ejpam-3900	363	50	.	.	PUNCT
ejpam-3900	364	1	theorem	theorem	VERB
ejpam-3900	364	2	4.4	4.4	NUM
ejpam-3900	364	3	.	.	PUNCT
ejpam-3900	365	1	the	the	DET
ejpam-3900	365	2	following	follow	VERB
ejpam-3900	365	3	inverse	inverse	NOUN
ejpam-3900	365	4	relations	relation	NOUN
ejpam-3900	365	5	hold	hold	VERB
ejpam-3900	365	6	:	:	PUNCT
ejpam-3900	365	7	fn	fn	PROPN
ejpam-3900	365	8	=	=	SYM
ejpam-3900	365	9	n∑	n∑	PROPN
ejpam-3900	365	10	k=0	k=0	PROPN
ejpam-3900	365	11	wm	wm	PROPN
ejpam-3900	365	12	,	,	PUNCT
ejpam-3900	365	13	r[n	r[n	PROPN
ejpam-3900	365	14	,	,	PUNCT
ejpam-3900	365	15	k]qgk	k]qgk	X
ejpam-3900	365	16	⇔	⇔	PROPN
ejpam-3900	365	17	gn	gn	PROPN
ejpam-3900	365	18	=	=	PROPN
ejpam-3900	365	19	n∑	n∑	PROPN
ejpam-3900	365	20	k=0	k=0	PROPN
ejpam-3900	365	21	wm	wm	PROPN
ejpam-3900	365	22	,	,	PUNCT
ejpam-3900	365	23	r[n	r[n	NOUN
ejpam-3900	365	24	,	,	PUNCT
ejpam-3900	365	25	k]qfk	k]qfk	NOUN
ejpam-3900	365	26	(	(	PUNCT
ejpam-3900	365	27	25	25	NUM
ejpam-3900	365	28	)	)	PUNCT
ejpam-3900	365	29	fk	fk	NOUN
ejpam-3900	365	30	=	=	PUNCT
ejpam-3900	365	31	∞∑	∞∑	PRON
ejpam-3900	365	32	n=0	n=0	NUM
ejpam-3900	365	33	wm	wm	PROPN
ejpam-3900	365	34	,	,	PUNCT
ejpam-3900	365	35	r[n	r[n	PROPN
ejpam-3900	365	36	,	,	PUNCT
ejpam-3900	365	37	k]qgn	k]qgn	X
ejpam-3900	365	38	⇔	⇔	PROPN
ejpam-3900	365	39	gk	gk	PROPN
ejpam-3900	366	1	=	=	PROPN
ejpam-3900	367	1	∞∑	∞∑	PROPN
ejpam-3900	367	2	n=0	n=0	NUM
ejpam-3900	367	3	wm	wm	PROPN
ejpam-3900	367	4	,	,	PUNCT
ejpam-3900	367	5	r[n	r[n	NOUN
ejpam-3900	367	6	,	,	PUNCT
ejpam-3900	367	7	k]qfk	k]qfk	NOUN
ejpam-3900	367	8	.	.	PUNCT
ejpam-3900	368	1	(	(	PUNCT
ejpam-3900	368	2	26	26	NUM
ejpam-3900	368	3	)	)	PUNCT
ejpam-3900	368	4	remark	remark	NOUN
ejpam-3900	368	5	4.5	4.5	NUM
ejpam-3900	368	6	.	.	PUNCT
ejpam-3900	369	1	using	use	VERB
ejpam-3900	369	2	the	the	DET
ejpam-3900	369	3	inverse	inverse	NOUN
ejpam-3900	369	4	relation	relation	NOUN
ejpam-3900	369	5	in	in	ADP
ejpam-3900	369	6	(	(	PUNCT
ejpam-3900	369	7	26	26	NUM
ejpam-3900	369	8	)	)	PUNCT
ejpam-3900	369	9	and	and	CCONJ
ejpam-3900	369	10	the	the	DET
ejpam-3900	369	11	exponential	exponential	ADJ
ejpam-3900	369	12	generating	generating	NOUN
ejpam-3900	369	13	function	function	NOUN
ejpam-3900	369	14	in	in	ADP
ejpam-3900	369	15	(	(	PUNCT
ejpam-3900	369	16	13	13	NUM
ejpam-3900	369	17	)	)	PUNCT
ejpam-3900	369	18	,	,	PUNCT
ejpam-3900	369	19	we	we	PRON
ejpam-3900	369	20	can	can	AUX
ejpam-3900	369	21	easily	easily	ADV
ejpam-3900	369	22	obtain	obtain	VERB
ejpam-3900	369	23	the	the	DET
ejpam-3900	369	24	following	following	ADJ
ejpam-3900	369	25	identity∑	identity∑	ADJ
ejpam-3900	369	26	n≥0	n≥0	PROPN
ejpam-3900	369	27	[	[	X
ejpam-3900	369	28	k]q!wm	k]q!wm	ADJ
ejpam-3900	369	29	,	,	PUNCT
ejpam-3900	369	30	r[n	r[n	NOUN
ejpam-3900	369	31	,	,	PUNCT
ejpam-3900	369	32	k]q[∆qm	k]q[∆qm	PROPN
ejpam-3900	369	33	,	,	PUNCT
ejpam-3900	369	34	mneq([x+	mneq([x+	PROPN
ejpam-3900	369	35	jm+	jm+	NOUN
ejpam-3900	369	36	r]q[t]q)]x=0	r]q[t]q)]x=0	NOUN
ejpam-3900	370	1	[	[	X
ejpam-3900	370	2	t]kq	t]kq	X
ejpam-3900	370	3	[	[	X
ejpam-3900	370	4	n]qm	n]qm	NOUN
ejpam-3900	370	5	!	!	PUNCT
ejpam-3900	371	1	[	[	X
ejpam-3900	371	2	m]nq	m]nq	X
ejpam-3900	371	3	=	=	SYM
ejpam-3900	371	4	1	1	NUM
ejpam-3900	371	5	.	.	PUNCT
ejpam-3900	371	6	(	(	PUNCT
ejpam-3900	371	7	27	27	NUM
ejpam-3900	371	8	)	)	PUNCT
ejpam-3900	371	9	also	also	ADV
ejpam-3900	371	10	,	,	PUNCT
ejpam-3900	371	11	using	use	VERB
ejpam-3900	371	12	the	the	DET
ejpam-3900	371	13	inverse	inverse	NOUN
ejpam-3900	371	14	relation	relation	NOUN
ejpam-3900	371	15	in	in	ADP
ejpam-3900	371	16	(	(	PUNCT
ejpam-3900	371	17	26	26	NUM
ejpam-3900	371	18	)	)	PUNCT
ejpam-3900	371	19	and	and	CCONJ
ejpam-3900	371	20	the	the	DET
ejpam-3900	371	21	rational	rational	ADJ
ejpam-3900	371	22	generating	generating	NOUN
ejpam-3900	371	23	function	function	NOUN
ejpam-3900	371	24	in	in	ADP
ejpam-3900	371	25	(	(	PUNCT
ejpam-3900	371	26	14	14	NUM
ejpam-3900	371	27	)	)	PUNCT
ejpam-3900	371	28	,	,	PUNCT
ejpam-3900	371	29	we	we	PRON
ejpam-3900	371	30	obtain	obtain	VERB
ejpam-3900	371	31	∑	∑	PROPN
ejpam-3900	371	32	n≥k	n≥k	PROPN
ejpam-3900	371	33	wm	wm	PROPN
ejpam-3900	371	34	,	,	PUNCT
ejpam-3900	371	35	r[n	r[n	PROPN
ejpam-3900	371	36	,	,	PUNCT
ejpam-3900	371	37	k]qq	k]qq	PROPN
ejpam-3900	371	38	m(n2)+nr[t]n−kq∏n	m(n2)+nr[t]n−kq∏n	PROPN
ejpam-3900	371	39	j=0(1−	j=0(1−	PROPN
ejpam-3900	372	1	[	[	X
ejpam-3900	372	2	mj	mj	X
ejpam-3900	372	3	+	+	NUM
ejpam-3900	372	4	r]q[t]q	r]q[t]q	NUM
ejpam-3900	372	5	)	)	PUNCT
ejpam-3900	372	6	=	=	SYM
ejpam-3900	372	7	1	1	X
ejpam-3900	372	8	.	.	PUNCT
ejpam-3900	372	9	(	(	PUNCT
ejpam-3900	372	10	28	28	NUM
ejpam-3900	372	11	)	)	PUNCT
ejpam-3900	372	12	thus	thus	ADV
ejpam-3900	372	13	,	,	PUNCT
ejpam-3900	372	14	combining	combine	VERB
ejpam-3900	372	15	(	(	PUNCT
ejpam-3900	372	16	27	27	NUM
ejpam-3900	372	17	)	)	PUNCT
ejpam-3900	372	18	and	and	CCONJ
ejpam-3900	372	19	(	(	PUNCT
ejpam-3900	372	20	28	28	NUM
ejpam-3900	372	21	)	)	PUNCT
ejpam-3900	372	22	yields	yield	VERB
ejpam-3900	372	23	∑	∑	PUNCT
ejpam-3900	372	24	n≥0	n≥0	PROPN
ejpam-3900	372	25	wm	wm	PROPN
ejpam-3900	372	26	,	,	PUNCT
ejpam-3900	372	27	r[n	r[n	NOUN
ejpam-3900	372	28	,	,	PUNCT
ejpam-3900	372	29	k]q	k]q	ADJ
ejpam-3900	372	30	{	{	PUNCT
ejpam-3900	373	1	[	[	X
ejpam-3900	373	2	k]q![∆qm	k]q![∆qm	ADJ
ejpam-3900	373	3	,	,	PUNCT
ejpam-3900	373	4	mneq([x+	mneq([x+	PROPN
ejpam-3900	373	5	jm+	jm+	NOUN
ejpam-3900	373	6	r]q[t]q)]x=0	r]q[t]q)]x=0	NOUN
ejpam-3900	374	1	[	[	X
ejpam-3900	374	2	n]qm	n]qm	NOUN
ejpam-3900	374	3	!	!	PUNCT
ejpam-3900	375	1	[	[	X
ejpam-3900	375	2	m]nq	m]nq	X
ejpam-3900	375	3	−	−	X
ejpam-3900	375	4	qm(n2)+nr[t]nq∏n	qm(n2)+nr[t]nq∏n	PROPN
ejpam-3900	375	5	j=0(1−	j=0(1−	PROPN
ejpam-3900	376	1	[	[	X
ejpam-3900	376	2	mj	mj	X
ejpam-3900	376	3	+	+	NUM
ejpam-3900	376	4	r]q[t]q	r]q[t]q	NUM
ejpam-3900	376	5	)	)	PUNCT
ejpam-3900	376	6	}	}	PUNCT
ejpam-3900	377	1	=	=	PUNCT
ejpam-3900	377	2	0	0	X
ejpam-3900	377	3	.	.	PUNCT
ejpam-3900	378	1	(	(	PUNCT
ejpam-3900	378	2	29	29	NUM
ejpam-3900	378	3	)	)	PUNCT
ejpam-3900	378	4	r.	r.	PROPN
ejpam-3900	378	5	corcino	corcino	PROPN
ejpam-3900	378	6	,	,	PUNCT
ejpam-3900	378	7	j.	j.	PROPN
ejpam-3900	378	8	ontolan	ontolan	PROPN
ejpam-3900	378	9	,	,	PUNCT
ejpam-3900	378	10	m.	m.	NOUN
ejpam-3900	378	11	lobrigas	lobrigas	PROPN
ejpam-3900	378	12	/	/	SYM
ejpam-3900	378	13	eur	eur	PROPN
ejpam-3900	378	14	.	.	PUNCT
ejpam-3900	379	1	j.	j.	PROPN
ejpam-3900	379	2	pure	pure	PROPN
ejpam-3900	379	3	appl	appl	PROPN
ejpam-3900	379	4	.	.	PROPN
ejpam-3900	379	5	math	math	PROPN
ejpam-3900	379	6	,	,	PUNCT
ejpam-3900	379	7	14	14	NUM
ejpam-3900	379	8	(	(	PUNCT
ejpam-3900	379	9	1	1	NUM
ejpam-3900	379	10	)	)	PUNCT
ejpam-3900	379	11	(	(	PUNCT
ejpam-3900	379	12	2021	2021	NUM
ejpam-3900	379	13	)	)	PUNCT
ejpam-3900	379	14	,	,	PUNCT
ejpam-3900	379	15	65	65	NUM
ejpam-3900	379	16	-	-	SYM
ejpam-3900	379	17	81	81	NUM
ejpam-3900	379	18	79	79	NUM
ejpam-3900	379	19	now	now	ADV
ejpam-3900	379	20	,	,	PUNCT
ejpam-3900	379	21	we	we	PRON
ejpam-3900	379	22	can	can	AUX
ejpam-3900	379	23	establish	establish	VERB
ejpam-3900	379	24	the	the	DET
ejpam-3900	379	25	relation	relation	NOUN
ejpam-3900	379	26	between	between	ADP
ejpam-3900	379	27	(	(	PUNCT
ejpam-3900	379	28	q	q	NOUN
ejpam-3900	379	29	,	,	PUNCT
ejpam-3900	379	30	r)-whitney	r)-whitney	ADJ
ejpam-3900	379	31	-	-	PUNCT
ejpam-3900	379	32	lah	lah	NOUN
ejpam-3900	379	33	numbers	number	NOUN
ejpam-3900	379	34	and	and	CCONJ
ejpam-3900	379	35	both	both	DET
ejpam-3900	379	36	kinds	kind	NOUN
ejpam-3900	379	37	of	of	ADP
ejpam-3900	379	38	(	(	PUNCT
ejpam-3900	379	39	q	q	ADJ
ejpam-3900	379	40	,	,	PUNCT
ejpam-3900	379	41	r)-whitney	r)-whitney	NOUN
ejpam-3900	379	42	numbers	number	NOUN
ejpam-3900	379	43	.	.	PUNCT
ejpam-3900	380	1	theorem	theorem	VERB
ejpam-3900	380	2	4.6	4.6	NUM
ejpam-3900	380	3	.	.	PUNCT
ejpam-3900	381	1	the	the	DET
ejpam-3900	381	2	(	(	PUNCT
ejpam-3900	381	3	q	q	ADJ
ejpam-3900	381	4	,	,	PUNCT
ejpam-3900	381	5	r)-whitney	r)-whitney	ADJ
ejpam-3900	381	6	-	-	PUNCT
ejpam-3900	381	7	lah	lah	PROPN
ejpam-3900	381	8	numbers	number	NOUN
ejpam-3900	381	9	satisfy	satisfy	VERB
ejpam-3900	381	10	the	the	DET
ejpam-3900	381	11	following	follow	VERB
ejpam-3900	381	12	relation	relation	NOUN
ejpam-3900	381	13	lm	lm	PROPN
ejpam-3900	381	14	,	,	PUNCT
ejpam-3900	381	15	r[n	r[n	NOUN
ejpam-3900	381	16	,	,	PUNCT
ejpam-3900	381	17	j]q	j]q	NOUN
ejpam-3900	381	18	=	=	PUNCT
ejpam-3900	381	19	n∑	n∑	PROPN
ejpam-3900	382	1	k	k	PROPN
ejpam-3900	382	2	=	=	PROPN
ejpam-3900	382	3	j	j	PROPN
ejpam-3900	382	4	wm,−r[n	wm,−r[n	PROPN
ejpam-3900	382	5	,	,	PUNCT
ejpam-3900	382	6	k]qwm	k]qwm	PROPN
ejpam-3900	382	7	,	,	PUNCT
ejpam-3900	382	8	r[k	r[k	PROPN
ejpam-3900	382	9	,	,	PUNCT
ejpam-3900	382	10	j]q	j]q	PROPN
ejpam-3900	382	11	.	.	PUNCT
ejpam-3900	383	1	(	(	PUNCT
ejpam-3900	383	2	30	30	X
ejpam-3900	383	3	)	)	PUNCT
ejpam-3900	383	4	proof	proof	NOUN
ejpam-3900	383	5	.	.	PUNCT
ejpam-3900	384	1	using	use	VERB
ejpam-3900	384	2	the	the	DET
ejpam-3900	384	3	horizontal	horizontal	ADJ
ejpam-3900	384	4	generating	generating	NOUN
ejpam-3900	384	5	functions	function	NOUN
ejpam-3900	384	6	for	for	ADP
ejpam-3900	384	7	(	(	PUNCT
ejpam-3900	384	8	q	q	ADJ
ejpam-3900	384	9	,	,	PUNCT
ejpam-3900	384	10	r)-whitney	r)-whitney	NOUN
ejpam-3900	384	11	numbers	number	NOUN
ejpam-3900	384	12	and	and	CCONJ
ejpam-3900	384	13	(	(	PUNCT
ejpam-3900	384	14	q	q	INTJ
ejpam-3900	384	15	,	,	PUNCT
ejpam-3900	384	16	r)whitney	r)whitney	NOUN
ejpam-3900	384	17	numbers	number	NOUN
ejpam-3900	384	18	,	,	PUNCT
ejpam-3900	384	19	we	we	PRON
ejpam-3900	384	20	have	have	VERB
ejpam-3900	384	21	n∑	n∑	ADJ
ejpam-3900	384	22	k=0	k=0	PROPN
ejpam-3900	384	23	lm	lm	PROPN
ejpam-3900	384	24	,	,	PUNCT
ejpam-3900	384	25	r[n	r[n	NOUN
ejpam-3900	384	26	,	,	PUNCT
ejpam-3900	384	27	k]q[t−	k]q[t−	NOUN
ejpam-3900	384	28	r|m]k	r|m]k	NUM
ejpam-3900	384	29	,	,	PUNCT
ejpam-3900	384	30	q	q	NOUN
ejpam-3900	385	1	=	=	PUNCT
ejpam-3900	386	1	[	[	X
ejpam-3900	386	2	t+	t+	NOUN
ejpam-3900	386	3	r|m]n	r|m]n	NOUN
ejpam-3900	386	4	,	,	PUNCT
ejpam-3900	386	5	q	q	NOUN
ejpam-3900	386	6	=	=	SYM
ejpam-3900	386	7	n∑	n∑	PROPN
ejpam-3900	386	8	k=0	k=0	PROPN
ejpam-3900	386	9	wm,−r[n	wm,−r[n	PROPN
ejpam-3900	386	10	,	,	PUNCT
ejpam-3900	386	11	k]q[t	k]q[t	X
ejpam-3900	386	12	]	]	X
ejpam-3900	386	13	k	k	PROPN
ejpam-3900	386	14	q	q	PROPN
ejpam-3900	386	15	=	=	SYM
ejpam-3900	386	16	n∑	n∑	PROPN
ejpam-3900	386	17	k=0	k=0	PROPN
ejpam-3900	386	18	wm,−r[n	wm,−r[n	PROPN
ejpam-3900	386	19	,	,	PUNCT
ejpam-3900	386	20	k]q	k]q	VERB
ejpam-3900	386	21	k∑	k∑	VERB
ejpam-3900	386	22	j=0	j=0	PROPN
ejpam-3900	386	23	wm	wm	PROPN
ejpam-3900	386	24	,	,	PUNCT
ejpam-3900	386	25	r[k	r[k	PROPN
ejpam-3900	386	26	,	,	PUNCT
ejpam-3900	386	27	j]q[t−	j]q[t−	ADJ
ejpam-3900	386	28	r|m]j	r|m]j	PROPN
ejpam-3900	386	29	,	,	PUNCT
ejpam-3900	386	30	q	q	NOUN
ejpam-3900	386	31	=	=	SYM
ejpam-3900	386	32	n∑	n∑	NOUN
ejpam-3900	386	33	j=0	j=0	PROPN
ejpam-3900	386	34	n∑	n∑	PROPN
ejpam-3900	386	35	k	k	PROPN
ejpam-3900	387	1	=	=	PROPN
ejpam-3900	387	2	j	j	PROPN
ejpam-3900	387	3	wm,−r[n	wm,−r[n	PROPN
ejpam-3900	387	4	,	,	PUNCT
ejpam-3900	387	5	k]qwm	k]qwm	PROPN
ejpam-3900	387	6	,	,	PUNCT
ejpam-3900	387	7	r[k	r[k	PROPN
ejpam-3900	387	8	,	,	PUNCT
ejpam-3900	387	9	j]q[t−	j]q[t−	ADJ
ejpam-3900	387	10	r|m]j	r|m]j	PROPN
ejpam-3900	387	11	,	,	PUNCT
ejpam-3900	387	12	q	q	PROPN
ejpam-3900	387	13	n∑	n∑	NOUN
ejpam-3900	387	14	j=0	j=0	PROPN
ejpam-3900	387	15	lm	lm	PROPN
ejpam-3900	387	16	,	,	PUNCT
ejpam-3900	387	17	r[n	r[n	NOUN
ejpam-3900	387	18	,	,	PUNCT
ejpam-3900	387	19	j]q[t|m]j	j]q[t|m]j	PROPN
ejpam-3900	387	20	,	,	PUNCT
ejpam-3900	387	21	q	q	PROPN
ejpam-3900	387	22	=	=	SYM
ejpam-3900	387	23	n∑	n∑	NOUN
ejpam-3900	387	24	j=0	j=0	PROPN
ejpam-3900	388	1			PROPN
ejpam-3900	388	2	n∑	n∑	PROPN
ejpam-3900	388	3	k	k	PROPN
ejpam-3900	388	4	=	=	PROPN
ejpam-3900	388	5	j	j	PROPN
ejpam-3900	388	6	wm,−r[n	wm,−r[n	PROPN
ejpam-3900	388	7	,	,	PUNCT
ejpam-3900	388	8	k]qwm	k]qwm	PROPN
ejpam-3900	388	9	,	,	PUNCT
ejpam-3900	388	10	r[k	r[k	PROPN
ejpam-3900	388	11	,	,	PUNCT
ejpam-3900	388	12	j]q	j]q	ADJ
ejpam-3900	388	13			PROPN
ejpam-3900	389	1	[	[	X
ejpam-3900	389	2	t−	t−	PROPN
ejpam-3900	389	3	r|m]j	r|m]j	PROPN
ejpam-3900	389	4	,	,	PUNCT
ejpam-3900	389	5	q.	q.	NOUN
ejpam-3900	389	6	comparing	compare	VERB
ejpam-3900	389	7	the	the	DET
ejpam-3900	389	8	coefficients	coefficient	NOUN
ejpam-3900	389	9	of	of	ADP
ejpam-3900	389	10	[	[	X
ejpam-3900	389	11	t|m]j	t|m]j	PROPN
ejpam-3900	389	12	,	,	PUNCT
ejpam-3900	389	13	q	q	PUNCT
ejpam-3900	389	14	completes	complete	VERB
ejpam-3900	389	15	the	the	DET
ejpam-3900	389	16	proof	proof	NOUN
ejpam-3900	389	17	.	.	PUNCT
ejpam-3900	390	1	the	the	DET
ejpam-3900	390	2	following	follow	VERB
ejpam-3900	390	3	theorem	theorem	NOUN
ejpam-3900	390	4	contains	contain	VERB
ejpam-3900	390	5	the	the	DET
ejpam-3900	390	6	main	main	ADJ
ejpam-3900	390	7	result	result	NOUN
ejpam-3900	390	8	of	of	ADP
ejpam-3900	390	9	this	this	DET
ejpam-3900	390	10	paper	paper	NOUN
ejpam-3900	390	11	.	.	PUNCT
ejpam-3900	391	1	theorem	theorem	VERB
ejpam-3900	391	2	4.7	4.7	NUM
ejpam-3900	391	3	.	.	PUNCT
ejpam-3900	392	1	the	the	DET
ejpam-3900	392	2	explicit	explicit	ADJ
ejpam-3900	392	3	formula	formula	NOUN
ejpam-3900	392	4	for	for	ADP
ejpam-3900	392	5	the	the	DET
ejpam-3900	392	6	first	first	ADJ
ejpam-3900	392	7	form	form	NOUN
ejpam-3900	392	8	(	(	PUNCT
ejpam-3900	392	9	q	q	ADJ
ejpam-3900	392	10	,	,	PUNCT
ejpam-3900	392	11	r)-dowling	r)-dowle	VERB
ejpam-3900	392	12	numbers	number	NOUN
ejpam-3900	392	13	dm	dm	VERB
ejpam-3900	392	14	,	,	PUNCT
ejpam-3900	392	15	r[n]q	r[n]q	NOUN
ejpam-3900	392	16	is	be	AUX
ejpam-3900	392	17	given	give	VERB
ejpam-3900	392	18	by	by	ADP
ejpam-3900	392	19	dm	dm	PROPN
ejpam-3900	392	20	,	,	PUNCT
ejpam-3900	392	21	r[n]q	r[n]q	NOUN
ejpam-3900	392	22	=	=	SYM
ejpam-3900	392	23	n∑	n∑	PRON
ejpam-3900	392	24	k=0	k=0	PROPN
ejpam-3900	392	25	wm,−r[n	wm,−r[n	PROPN
ejpam-3900	392	26	,	,	PUNCT
ejpam-3900	392	27	k]q	k]q	VERB
ejpam-3900	392	28			PROPN
ejpam-3900	392	29	k∑	k∑	PROPN
ejpam-3900	392	30	j=0	j=0	PROPN
ejpam-3900	392	31	lm	lm	PROPN
ejpam-3900	392	32	,	,	PUNCT
ejpam-3900	392	33	r[k	r[k	PROPN
ejpam-3900	392	34	,	,	PUNCT
ejpam-3900	392	35	j]q	j]q	PROPN
ejpam-3900	392	36			PROPN
ejpam-3900	392	37	,	,	PUNCT
ejpam-3900	392	38	proof	proof	NOUN
ejpam-3900	392	39	.	.	PUNCT
ejpam-3900	393	1	using	use	VERB
ejpam-3900	393	2	the	the	DET
ejpam-3900	393	3	inverse	inverse	NOUN
ejpam-3900	393	4	relation	relation	NOUN
ejpam-3900	393	5	(	(	PUNCT
ejpam-3900	393	6	25	25	NUM
ejpam-3900	393	7	)	)	PUNCT
ejpam-3900	393	8	with	with	ADP
ejpam-3900	393	9	fn	fn	NOUN
ejpam-3900	393	10	=	=	SYM
ejpam-3900	393	11	lm	lm	PROPN
ejpam-3900	393	12	,	,	PUNCT
ejpam-3900	393	13	r[n	r[n	NOUN
ejpam-3900	393	14	,	,	PUNCT
ejpam-3900	393	15	j]q	j]q	PROPN
ejpam-3900	393	16	,	,	PUNCT
ejpam-3900	393	17	gk	gk	PROPN
ejpam-3900	393	18	=	=	PUNCT
ejpam-3900	393	19	wm	wm	PROPN
ejpam-3900	393	20	,	,	PUNCT
ejpam-3900	393	21	r[k	r[k	PROPN
ejpam-3900	393	22	,	,	PUNCT
ejpam-3900	393	23	j]q	j]q	PROPN
ejpam-3900	393	24	,	,	PUNCT
ejpam-3900	393	25	relation	relation	NOUN
ejpam-3900	393	26	(	(	PUNCT
ejpam-3900	393	27	30	30	NUM
ejpam-3900	393	28	)	)	PUNCT
ejpam-3900	393	29	can	can	AUX
ejpam-3900	393	30	be	be	AUX
ejpam-3900	393	31	transformed	transform	VERB
ejpam-3900	393	32	as	as	ADP
ejpam-3900	393	33	wm	wm	PROPN
ejpam-3900	393	34	,	,	PUNCT
ejpam-3900	393	35	r[n	r[n	NOUN
ejpam-3900	393	36	,	,	PUNCT
ejpam-3900	393	37	j]q	j]q	NOUN
ejpam-3900	393	38	=	=	PUNCT
ejpam-3900	394	1	n∑	n∑	PROPN
ejpam-3900	394	2	k	k	PROPN
ejpam-3900	395	1	=	=	PROPN
ejpam-3900	395	2	j	j	PROPN
ejpam-3900	395	3	wm,−r[n	wm,−r[n	PROPN
ejpam-3900	395	4	,	,	PUNCT
ejpam-3900	395	5	k]qlm	k]qlm	NOUN
ejpam-3900	395	6	,	,	PUNCT
ejpam-3900	395	7	r[k	r[k	PROPN
ejpam-3900	395	8	,	,	PUNCT
ejpam-3900	395	9	j]q	j]q	PROPN
ejpam-3900	395	10	.	.	PUNCT
ejpam-3900	396	1	(	(	PUNCT
ejpam-3900	396	2	31	31	NUM
ejpam-3900	396	3	)	)	PUNCT
ejpam-3900	396	4	then	then	ADV
ejpam-3900	396	5	summing	sum	VERB
ejpam-3900	396	6	up	up	ADP
ejpam-3900	396	7	both	both	DET
ejpam-3900	396	8	sides	side	NOUN
ejpam-3900	396	9	over	over	ADP
ejpam-3900	396	10	j	j	PROPN
ejpam-3900	396	11	yields	yield	VERB
ejpam-3900	396	12	dm	dm	PROPN
ejpam-3900	396	13	,	,	PUNCT
ejpam-3900	396	14	r[n]q	r[n]q	NOUN
ejpam-3900	396	15	=	=	SYM
ejpam-3900	396	16	n∑	n∑	X
ejpam-3900	396	17	j=0	j=0	PROPN
ejpam-3900	396	18	wm	wm	PROPN
ejpam-3900	396	19	,	,	PUNCT
ejpam-3900	396	20	r[n	r[n	NOUN
ejpam-3900	396	21	,	,	PUNCT
ejpam-3900	396	22	j]q	j]q	NOUN
ejpam-3900	396	23	=	=	SYM
ejpam-3900	396	24	n∑	n∑	PROPN
ejpam-3900	396	25	j=0	j=0	PROPN
ejpam-3900	396	26	n∑	n∑	PROPN
ejpam-3900	397	1	k	k	PROPN
ejpam-3900	397	2	=	=	PROPN
ejpam-3900	397	3	j	j	PROPN
ejpam-3900	397	4	wm,−r[n	wm,−r[n	PROPN
ejpam-3900	397	5	,	,	PUNCT
ejpam-3900	397	6	k]qlm	k]qlm	NOUN
ejpam-3900	397	7	,	,	PUNCT
ejpam-3900	397	8	r[k	r[k	PROPN
ejpam-3900	397	9	,	,	PUNCT
ejpam-3900	397	10	j]q	j]q	ADJ
ejpam-3900	397	11	references	reference	VERB
ejpam-3900	397	12	80	80	NUM
ejpam-3900	397	13	=	=	SYM
ejpam-3900	397	14	n∑	n∑	PROPN
ejpam-3900	397	15	k=0	k=0	PROPN
ejpam-3900	397	16	wm,−r[n	wm,−r[n	PROPN
ejpam-3900	397	17	,	,	PUNCT
ejpam-3900	397	18	k]q	k]q	VERB
ejpam-3900	397	19			PROPN
ejpam-3900	397	20	k∑	k∑	PROPN
ejpam-3900	397	21	j=0	j=0	PROPN
ejpam-3900	397	22	lm	lm	PROPN
ejpam-3900	397	23	,	,	PUNCT
ejpam-3900	397	24	r[k	r[k	PROPN
ejpam-3900	397	25	,	,	PUNCT
ejpam-3900	397	26	j]q	j]q	PROPN
ejpam-3900	397	27			PROPN
ejpam-3900	397	28	,	,	PUNCT
ejpam-3900	397	29	which	which	PRON
ejpam-3900	397	30	is	be	AUX
ejpam-3900	397	31	exactly	exactly	ADV
ejpam-3900	397	32	the	the	DET
ejpam-3900	397	33	desired	desire	VERB
ejpam-3900	397	34	explicit	explicit	ADJ
ejpam-3900	397	35	formula	formula	NOUN
ejpam-3900	397	36	for	for	ADP
ejpam-3900	397	37	(	(	PUNCT
ejpam-3900	397	38	q	q	ADJ
ejpam-3900	397	39	,	,	PUNCT
ejpam-3900	397	40	r)-dowling	r)-dowling	ADJ
ejpam-3900	397	41	numbers	number	NOUN
ejpam-3900	397	42	.	.	PUNCT
ejpam-3900	398	1	the	the	DET
ejpam-3900	398	2	above	above	ADJ
ejpam-3900	398	3	explicit	explicit	ADJ
ejpam-3900	398	4	formula	formula	NOUN
ejpam-3900	398	5	may	may	AUX
ejpam-3900	398	6	also	also	ADV
ejpam-3900	398	7	be	be	AUX
ejpam-3900	398	8	called	call	VERB
ejpam-3900	398	9	a	a	DET
ejpam-3900	398	10	qi	qi	NOUN
ejpam-3900	398	11	-	-	PUNCT
ejpam-3900	398	12	type	type	NOUN
ejpam-3900	398	13	formula	formula	NOUN
ejpam-3900	398	14	for	for	ADP
ejpam-3900	398	15	(	(	PUNCT
ejpam-3900	398	16	q	q	ADJ
ejpam-3900	398	17	,	,	PUNCT
ejpam-3900	398	18	r)-dowling	r)-dowling	ADJ
ejpam-3900	398	19	numbers	number	NOUN
ejpam-3900	398	20	,	,	PUNCT
ejpam-3900	398	21	which	which	PRON
ejpam-3900	398	22	is	be	AUX
ejpam-3900	398	23	analogous	analogous	ADJ
ejpam-3900	398	24	to	to	ADP
ejpam-3900	398	25	explicit	explicit	ADJ
ejpam-3900	398	26	formula	formula	NOUN
ejpam-3900	398	27	obtained	obtain	VERB
ejpam-3900	398	28	f.	f.	PROPN
ejpam-3900	398	29	qi	qi	PROPN
ejpam-3900	398	30	[	[	X
ejpam-3900	398	31	11	11	NUM
ejpam-3900	398	32	]	]	PUNCT
ejpam-3900	398	33	.	.	PUNCT
ejpam-3900	399	1	5	5	X
ejpam-3900	399	2	.	.	X
ejpam-3900	399	3	conclusion	conclusion	NOUN
ejpam-3900	399	4	the	the	DET
ejpam-3900	399	5	explicit	explicit	ADJ
ejpam-3900	399	6	formula	formula	NOUN
ejpam-3900	399	7	for	for	ADP
ejpam-3900	399	8	the	the	DET
ejpam-3900	399	9	first	first	ADJ
ejpam-3900	399	10	form	form	NOUN
ejpam-3900	399	11	(	(	PUNCT
ejpam-3900	399	12	q	q	ADJ
ejpam-3900	399	13	,	,	PUNCT
ejpam-3900	399	14	r)-dowling	r)-dowle	VERB
ejpam-3900	399	15	numbers	number	NOUN
ejpam-3900	399	16	has	have	AUX
ejpam-3900	399	17	already	already	ADV
ejpam-3900	399	18	been	be	AUX
ejpam-3900	399	19	derived	derive	VERB
ejpam-3900	399	20	by	by	ADP
ejpam-3900	399	21	establishing	establish	VERB
ejpam-3900	399	22	an	an	DET
ejpam-3900	399	23	appropriate	appropriate	ADJ
ejpam-3900	399	24	(	(	PUNCT
ejpam-3900	399	25	q	q	NOUN
ejpam-3900	399	26	,	,	PUNCT
ejpam-3900	399	27	r)-whitney	r)-whitney	ADJ
ejpam-3900	399	28	-	-	PUNCT
ejpam-3900	399	29	lah	lah	NOUN
ejpam-3900	399	30	numbers	number	NOUN
ejpam-3900	399	31	and	and	CCONJ
ejpam-3900	399	32	(	(	PUNCT
ejpam-3900	399	33	q	q	ADJ
ejpam-3900	399	34	,	,	PUNCT
ejpam-3900	399	35	r)-whitney	r)-whitney	NOUN
ejpam-3900	399	36	numbers	number	NOUN
ejpam-3900	399	37	of	of	ADP
ejpam-3900	399	38	the	the	DET
ejpam-3900	399	39	first	first	ADJ
ejpam-3900	399	40	kind	kind	NOUN
ejpam-3900	399	41	.	.	PUNCT
ejpam-3900	400	1	to	to	PART
ejpam-3900	400	2	establish	establish	VERB
ejpam-3900	400	3	explicit	explicit	ADJ
ejpam-3900	400	4	formulas	formula	NOUN
ejpam-3900	400	5	for	for	ADP
ejpam-3900	400	6	the	the	DET
ejpam-3900	400	7	two	two	NUM
ejpam-3900	400	8	other	other	ADJ
ejpam-3900	400	9	forms	form	NOUN
ejpam-3900	400	10	of	of	ADP
ejpam-3900	400	11	(	(	PUNCT
ejpam-3900	400	12	q	q	ADJ
ejpam-3900	400	13	,	,	PUNCT
ejpam-3900	400	14	r)-dowling	r)-dowling	ADJ
ejpam-3900	400	15	numbers	number	NOUN
ejpam-3900	400	16	,	,	PUNCT
ejpam-3900	400	17	it	it	PRON
ejpam-3900	400	18	entails	entail	VERB
ejpam-3900	400	19	defining	define	VERB
ejpam-3900	400	20	appropriate	appropriate	ADJ
ejpam-3900	400	21	versions	version	NOUN
ejpam-3900	400	22	of	of	ADP
ejpam-3900	400	23	(	(	PUNCT
ejpam-3900	400	24	q	q	ADJ
ejpam-3900	400	25	,	,	PUNCT
ejpam-3900	400	26	r)-whitney	r)-whitney	ADJ
ejpam-3900	400	27	-	-	PUNCT
ejpam-3900	400	28	lah	lah	NOUN
ejpam-3900	400	29	numbers	number	NOUN
ejpam-3900	400	30	and	and	CCONJ
ejpam-3900	400	31	(	(	PUNCT
ejpam-3900	400	32	q	q	INTJ
ejpam-3900	400	33	,	,	PUNCT
ejpam-3900	400	34	r)whitney	r)whitney	NOUN
ejpam-3900	400	35	numbers	number	NOUN
ejpam-3900	400	36	of	of	ADP
ejpam-3900	400	37	the	the	DET
ejpam-3900	400	38	first	first	ADJ
ejpam-3900	400	39	kind	kind	NOUN
ejpam-3900	400	40	.	.	PUNCT
ejpam-3900	401	1	it	it	PRON
ejpam-3900	401	2	is	be	AUX
ejpam-3900	401	3	left	leave	VERB
ejpam-3900	401	4	to	to	ADP
ejpam-3900	401	5	the	the	DET
ejpam-3900	401	6	readers	reader	NOUN
ejpam-3900	401	7	to	to	PART
ejpam-3900	401	8	derive	derive	VERB
ejpam-3900	401	9	these	these	DET
ejpam-3900	401	10	explicit	explicit	ADJ
ejpam-3900	401	11	formulas	formula	NOUN
ejpam-3900	401	12	.	.	PUNCT
ejpam-3900	402	1	this	this	DET
ejpam-3900	402	2	paper	paper	NOUN
ejpam-3900	402	3	is	be	AUX
ejpam-3900	402	4	also	also	ADV
ejpam-3900	402	5	related	relate	VERB
ejpam-3900	402	6	to	to	ADP
ejpam-3900	402	7	[	[	X
ejpam-3900	402	8	7	7	NUM
ejpam-3900	402	9	,	,	PUNCT
ejpam-3900	402	10	12	12	NUM
ejpam-3900	402	11	,	,	PUNCT
ejpam-3900	402	12	13	13	NUM
ejpam-3900	402	13	]	]	PUNCT
ejpam-3900	402	14	.	.	PUNCT
ejpam-3900	403	1	with	with	ADP
ejpam-3900	403	2	these	these	PRON
ejpam-3900	403	3	,	,	PUNCT
ejpam-3900	403	4	more	more	ADJ
ejpam-3900	403	5	properties	property	NOUN
ejpam-3900	403	6	and	and	CCONJ
ejpam-3900	403	7	relations	relation	NOUN
ejpam-3900	403	8	can	can	AUX
ejpam-3900	403	9	further	far	ADV
ejpam-3900	403	10	be	be	AUX
ejpam-3900	403	11	established	establish	VERB
ejpam-3900	403	12	.	.	PUNCT
ejpam-3900	404	1	acknowledgements	acknowledgement	NOUN
ejpam-3900	404	2	this	this	DET
ejpam-3900	404	3	research	research	NOUN
ejpam-3900	404	4	has	have	AUX
ejpam-3900	404	5	been	be	AUX
ejpam-3900	404	6	funded	fund	VERB
ejpam-3900	404	7	by	by	ADP
ejpam-3900	404	8	cebu	cebu	PROPN
ejpam-3900	404	9	normal	normal	ADJ
ejpam-3900	404	10	university	university	PROPN
ejpam-3900	404	11	(	(	PUNCT
ejpam-3900	404	12	cnu	cnu	PROPN
ejpam-3900	404	13	)	)	PUNCT
ejpam-3900	404	14	and	and	CCONJ
ejpam-3900	404	15	the	the	DET
ejpam-3900	404	16	commission	commission	NOUN
ejpam-3900	404	17	on	on	ADP
ejpam-3900	404	18	higher	high	ADJ
ejpam-3900	404	19	education	education	NOUN
ejpam-3900	404	20	grants	grant	NOUN
ejpam-3900	404	21	-	-	PUNCT
ejpam-3900	404	22	in	in	ADP
ejpam-3900	404	23	-	-	PUNCT
ejpam-3900	404	24	aid	aid	NOUN
ejpam-3900	404	25	for	for	ADP
ejpam-3900	404	26	research	research	NOUN
ejpam-3900	404	27	(	(	PUNCT
ejpam-3900	404	28	ched	che	VERB
ejpam-3900	404	29	-	-	PUNCT
ejpam-3900	404	30	gia	gia	NOUN
ejpam-3900	404	31	)	)	PUNCT
ejpam-3900	404	32	.	.	PUNCT
ejpam-3900	405	1	references	reference	NOUN
ejpam-3900	405	2	[	[	X
ejpam-3900	405	3	1	1	NUM
ejpam-3900	405	4	]	]	X
ejpam-3900	405	5	g.s	g.s	PROPN
ejpam-3900	405	6	.	.	PROPN
ejpam-3900	405	7	cheon	cheon	PROPN
ejpam-3900	405	8	and	and	CCONJ
ejpam-3900	405	9	j.	j.	PROPN
ejpam-3900	405	10	h.	h.	PROPN
ejpam-3900	405	11	jung	jung	PROPN
ejpam-3900	405	12	.	.	PUNCT
ejpam-3900	406	1	r	r	X
ejpam-3900	406	2	-	-	PUNCT
ejpam-3900	406	3	whitney	whitney	NOUN
ejpam-3900	406	4	number	number	NOUN
ejpam-3900	406	5	of	of	ADP
ejpam-3900	406	6	dowling	dowle	VERB
ejpam-3900	406	7	lattices	lattice	NOUN
ejpam-3900	406	8	.	.	PUNCT
ejpam-3900	407	1	discrete	discrete	ADJ
ejpam-3900	407	2	math	math	NOUN
ejpam-3900	407	3	.	.	PUNCT
ejpam-3900	407	4	,	,	PUNCT
ejpam-3900	407	5	312:2337–2348	312:2337–2348	NUM
ejpam-3900	407	6	,	,	PUNCT
ejpam-3900	407	7	2012	2012	NUM
ejpam-3900	407	8	.	.	PUNCT
ejpam-3900	408	1	[	[	X
ejpam-3900	408	2	2	2	NUM
ejpam-3900	408	3	]	]	X
ejpam-3900	408	4	ja	ja	PROPN
ejpam-3900	408	5	.	.	PUNCT
ejpam-3900	408	6	cillar	cillar	PROPN
ejpam-3900	408	7	and	and	CCONJ
ejpam-3900	408	8	r.	r.	PROPN
ejpam-3900	408	9	corcino	corcino	PROPN
ejpam-3900	408	10	.	.	PUNCT
ejpam-3900	409	1	a	a	DET
ejpam-3900	409	2	q	q	NOUN
ejpam-3900	409	3	-	-	PUNCT
ejpam-3900	409	4	analogue	analogue	NOUN
ejpam-3900	409	5	of	of	ADP
ejpam-3900	409	6	qi	qi	NOUN
ejpam-3900	409	7	formula	formula	NOUN
ejpam-3900	409	8	for	for	ADP
ejpam-3900	409	9	r	r	NOUN
ejpam-3900	409	10	-	-	PUNCT
ejpam-3900	409	11	dowling	dowle	VERB
ejpam-3900	409	12	numbers	number	NOUN
ejpam-3900	409	13	.	.	PUNCT
ejpam-3900	410	1	commun	commun	PROPN
ejpam-3900	410	2	.	.	PUNCT
ejpam-3900	411	1	korean	korean	ADJ
ejpam-3900	411	2	math	math	PROPN
ejpam-3900	411	3	.	.	PUNCT
ejpam-3900	412	1	soc	soc	PROPN
ejpam-3900	412	2	.	.	PUNCT
ejpam-3900	412	3	,	,	PUNCT
ejpam-3900	412	4	35(1):21–31	35(1):21–31	NUM
ejpam-3900	412	5	,	,	PUNCT
ejpam-3900	412	6	2020	2020	NUM
ejpam-3900	412	7	.	.	PUNCT
ejpam-3900	413	1	[	[	X
ejpam-3900	413	2	3	3	X
ejpam-3900	413	3	]	]	X
ejpam-3900	413	4	r.	r.	PROPN
ejpam-3900	413	5	corcino	corcino	PROPN
ejpam-3900	413	6	,	,	PUNCT
ejpam-3900	413	7	mj	mj	PROPN
ejpam-3900	413	8	.	.	PUNCT
ejpam-3900	413	9	latayada	latayada	PROPN
ejpam-3900	413	10	,	,	PUNCT
ejpam-3900	413	11	and	and	CCONJ
ejpam-3900	413	12	mar	mar	PROPN
ejpam-3900	413	13	.	.	PROPN
ejpam-3900	413	14	vega	vega	PROPN
ejpam-3900	413	15	.	.	PUNCT
ejpam-3900	414	1	hankel	hankel	PROPN
ejpam-3900	414	2	transform	transform	NOUN
ejpam-3900	414	3	of	of	ADP
ejpam-3900	414	4	(	(	PUNCT
ejpam-3900	414	5	q	q	ADJ
ejpam-3900	414	6	,	,	PUNCT
ejpam-3900	414	7	r)-dowling	r)-dowle	VERB
ejpam-3900	414	8	numbers	number	NOUN
ejpam-3900	414	9	.	.	PUNCT
ejpam-3900	415	1	eur	eur	PROPN
ejpam-3900	415	2	.	.	PUNCT
ejpam-3900	416	1	j.	j.	PROPN
ejpam-3900	416	2	pure	pure	PROPN
ejpam-3900	416	3	appl	appl	PROPN
ejpam-3900	416	4	.	.	PROPN
ejpam-3900	416	5	math	math	PROPN
ejpam-3900	416	6	,	,	PUNCT
ejpam-3900	416	7	12(2):279–293	12(2):279–293	PROPN
ejpam-3900	416	8	,	,	PUNCT
ejpam-3900	416	9	2019	2019	NUM
ejpam-3900	416	10	.	.	PUNCT
ejpam-3900	417	1	[	[	X
ejpam-3900	417	2	4	4	X
ejpam-3900	417	3	]	]	X
ejpam-3900	417	4	r.b	r.b	PROPN
ejpam-3900	417	5	.	.	PROPN
ejpam-3900	417	6	corcino	corcino	PROPN
ejpam-3900	417	7	and	and	CCONJ
ejpam-3900	417	8	c.b	c.b	PROPN
ejpam-3900	417	9	.	.	PROPN
ejpam-3900	417	10	corcino	corcino	PROPN
ejpam-3900	417	11	.	.	PUNCT
ejpam-3900	418	1	the	the	DET
ejpam-3900	418	2	hankel	hankel	NOUN
ejpam-3900	418	3	transform	transform	NOUN
ejpam-3900	418	4	of	of	ADP
ejpam-3900	418	5	generalized	generalized	ADJ
ejpam-3900	418	6	bell	bell	NOUN
ejpam-3900	418	7	numbers	number	NOUN
ejpam-3900	418	8	and	and	CCONJ
ejpam-3900	418	9	its	its	PRON
ejpam-3900	418	10	q	q	NOUN
ejpam-3900	418	11	-	-	PUNCT
ejpam-3900	418	12	analogue	analogue	NOUN
ejpam-3900	418	13	.	.	PUNCT
ejpam-3900	419	1	util	util	PROPN
ejpam-3900	419	2	.	.	PUNCT
ejpam-3900	420	1	math	math	NOUN
ejpam-3900	420	2	.	.	PUNCT
ejpam-3900	420	3	,	,	PUNCT
ejpam-3900	421	1	89:297–309	89:297–309	NUM
ejpam-3900	421	2	,	,	PUNCT
ejpam-3900	421	3	2012	2012	NUM
ejpam-3900	421	4	.	.	PUNCT
ejpam-3900	422	1	[	[	X
ejpam-3900	422	2	5	5	X
ejpam-3900	422	3	]	]	X
ejpam-3900	422	4	r.b	r.b	PROPN
ejpam-3900	422	5	.	.	PROPN
ejpam-3900	422	6	corcino	corcino	PROPN
ejpam-3900	422	7	and	and	CCONJ
ejpam-3900	422	8	c.b	c.b	PROPN
ejpam-3900	422	9	.	.	PROPN
ejpam-3900	422	10	montero	montero	PROPN
ejpam-3900	422	11	.	.	PUNCT
ejpam-3900	423	1	a	a	DET
ejpam-3900	423	2	q	q	NOUN
ejpam-3900	423	3	-	-	PUNCT
ejpam-3900	423	4	analogue	analogue	NOUN
ejpam-3900	423	5	of	of	ADP
ejpam-3900	423	6	rucinski	rucinski	ADJ
ejpam-3900	423	7	-	-	PUNCT
ejpam-3900	423	8	voigt	voigt	NOUN
ejpam-3900	423	9	numbers	number	NOUN
ejpam-3900	423	10	.	.	PUNCT
ejpam-3900	424	1	isrn	isrn	NOUN
ejpam-3900	424	2	discrete	discrete	VERB
ejpam-3900	424	3	math	math	NOUN
ejpam-3900	424	4	.	.	PUNCT
ejpam-3900	425	1	,	,	PUNCT
ejpam-3900	425	2	2012:18	2012:18	NUM
ejpam-3900	425	3	pages	page	NOUN
ejpam-3900	425	4	,	,	PUNCT
ejpam-3900	425	5	2012	2012	NUM
ejpam-3900	425	6	.	.	PUNCT
ejpam-3900	426	1	[	[	X
ejpam-3900	426	2	6	6	NUM
ejpam-3900	426	3	]	]	X
ejpam-3900	426	4	r.b	r.b	PROPN
ejpam-3900	426	5	.	.	PROPN
ejpam-3900	426	6	corcino	corcino	PROPN
ejpam-3900	426	7	,	,	PUNCT
ejpam-3900	426	8	j.m	j.m	PROPN
ejpam-3900	426	9	.	.	PROPN
ejpam-3900	426	10	ontolan	ontolan	PROPN
ejpam-3900	426	11	,	,	PUNCT
ejpam-3900	426	12	j.	j.	PROPN
ejpam-3900	426	13	cañete	cañete	PROPN
ejpam-3900	426	14	,	,	PUNCT
ejpam-3900	426	15	and	and	CCONJ
ejpam-3900	426	16	m.r	m.r	PROPN
ejpam-3900	426	17	.	.	PROPN
ejpam-3900	426	18	latayad	latayad	PROPN
ejpam-3900	426	19	.	.	PUNCT
ejpam-3900	427	1	a	a	DET
ejpam-3900	427	2	q	q	NOUN
ejpam-3900	427	3	-	-	PUNCT
ejpam-3900	427	4	analogue	analogue	NOUN
ejpam-3900	427	5	of	of	ADP
ejpam-3900	427	6	r	r	NOUN
ejpam-3900	427	7	-	-	PUNCT
ejpam-3900	427	8	whitney	whitney	NOUN
ejpam-3900	427	9	numbers	number	NOUN
ejpam-3900	427	10	of	of	ADP
ejpam-3900	427	11	the	the	DET
ejpam-3900	427	12	second	second	ADJ
ejpam-3900	427	13	kind	kind	NOUN
ejpam-3900	427	14	and	and	CCONJ
ejpam-3900	427	15	its	its	PRON
ejpam-3900	427	16	hankel	hankel	NOUN
ejpam-3900	427	17	transform	transform	NOUN
ejpam-3900	427	18	.	.	PUNCT
ejpam-3900	428	1	j.	j.	PROPN
ejpam-3900	428	2	math	math	PROPN
ejpam-3900	428	3	.	.	PUNCT
ejpam-3900	429	1	computer	computer	NOUN
ejpam-3900	429	2	sci	sci	PROPN
ejpam-3900	429	3	.	.	PROPN
ejpam-3900	429	4	,	,	PUNCT
ejpam-3900	429	5	21:258	21:258	NUM
ejpam-3900	429	6	–	–	PUNCT
ejpam-3900	429	7	272	272	NUM
ejpam-3900	429	8	,	,	PUNCT
ejpam-3900	429	9	2020	2020	NUM
ejpam-3900	429	10	.	.	PUNCT
ejpam-3900	430	1	references	reference	NOUN
ejpam-3900	430	2	81	81	NUM
ejpam-3900	431	1	[	[	X
ejpam-3900	431	2	7	7	NUM
ejpam-3900	431	3	]	]	X
ejpam-3900	431	4	u.	u.	PROPN
ejpam-3900	431	5	duran	duran	PROPN
ejpam-3900	431	6	,	,	PUNCT
ejpam-3900	431	7	m.	m.	NOUN
ejpam-3900	431	8	acikgoz	acikgoz	ADJ
ejpam-3900	431	9	,	,	PUNCT
ejpam-3900	431	10	and	and	CCONJ
ejpam-3900	431	11	s.	s.	PROPN
ejpam-3900	431	12	araci	araci	PROPN
ejpam-3900	431	13	.	.	PUNCT
ejpam-3900	432	1	on	on	ADP
ejpam-3900	432	2	(	(	PUNCT
ejpam-3900	432	3	q	q	NOUN
ejpam-3900	432	4	,	,	PUNCT
ejpam-3900	432	5	r	r	NOUN
ejpam-3900	432	6	,	,	PUNCT
ejpam-3900	432	7	w)-stirling	w)-stirle	VERB
ejpam-3900	432	8	numbers	number	NOUN
ejpam-3900	432	9	of	of	ADP
ejpam-3900	432	10	the	the	DET
ejpam-3900	432	11	second	second	ADJ
ejpam-3900	432	12	kind	kind	NOUN
ejpam-3900	432	13	.	.	PUNCT
ejpam-3900	433	1	j.	j.	PROPN
ejpam-3900	433	2	inequal	inequal	PROPN
ejpam-3900	433	3	.	.	PUNCT
ejpam-3900	434	1	spec	spec	PROPN
ejpam-3900	434	2	.	.	PUNCT
ejpam-3900	435	1	funct	funct	PROPN
ejpam-3900	435	2	.	.	PUNCT
ejpam-3900	435	3	,	,	PUNCT
ejpam-3900	436	1	9(1):9–16	9(1):9–16	NUM
ejpam-3900	436	2	,	,	PUNCT
ejpam-3900	436	3	2018	2018	NUM
ejpam-3900	436	4	.	.	PUNCT
ejpam-3900	437	1	[	[	X
ejpam-3900	437	2	8	8	NUM
ejpam-3900	437	3	]	]	X
ejpam-3900	437	4	lindsay	lindsay	PROPN
ejpam-3900	437	5	j.	j.	PROPN
ejpam-3900	437	6	et	et	PROPN
ejpam-3900	437	7	.	.	PUNCT
ejpam-3900	438	1	al	al	PROPN
ejpam-3900	438	2	.	.	PUNCT
ejpam-3900	439	1	a	a	DET
ejpam-3900	439	2	new	new	ADJ
ejpam-3900	439	3	combinatorial	combinatorial	ADJ
ejpam-3900	439	4	interpretation	interpretation	NOUN
ejpam-3900	439	5	of	of	ADP
ejpam-3900	439	6	a	a	DET
ejpam-3900	439	7	q	q	NOUN
ejpam-3900	439	8	-	-	PUNCT
ejpam-3900	439	9	analogue	analogue	NOUN
ejpam-3900	439	10	of	of	ADP
ejpam-3900	439	11	the	the	DET
ejpam-3900	439	12	lah	lah	PROPN
ejpam-3900	439	13	numbers	number	NOUN
ejpam-3900	439	14	.	.	PUNCT
ejpam-3900	440	1	j.	j.	PROPN
ejpam-3900	440	2	combi	combi	PROPN
ejpam-3900	440	3	.	.	PROPN
ejpam-3900	440	4	,	,	PUNCT
ejpam-3900	440	5	2(2):245–264	2(2):245–264	NUM
ejpam-3900	440	6	,	,	PUNCT
ejpam-3900	440	7	2011	2011	NUM
ejpam-3900	440	8	.	.	PUNCT
ejpam-3900	441	1	[	[	X
ejpam-3900	441	2	9	9	NUM
ejpam-3900	441	3	]	]	PUNCT
ejpam-3900	441	4	m.	m.	NOUN
ejpam-3900	441	5	kim	kim	PROPN
ejpam-3900	441	6	and	and	CCONJ
ejpam-3900	441	7	j.	j.	PROPN
ejpam-3900	441	8	son	son	PROPN
ejpam-3900	441	9	.	.	PUNCT
ejpam-3900	442	1	a	a	DET
ejpam-3900	442	2	note	note	NOUN
ejpam-3900	442	3	on	on	ADP
ejpam-3900	442	4	q	q	ADJ
ejpam-3900	442	5	-	-	PUNCT
ejpam-3900	442	6	difference	difference	NOUN
ejpam-3900	442	7	operators	operator	NOUN
ejpam-3900	442	8	.	.	PUNCT
ejpam-3900	443	1	commun	commun	PROPN
ejpam-3900	443	2	.	.	PUNCT
ejpam-3900	444	1	korean	korean	ADJ
ejpam-3900	444	2	math	math	PROPN
ejpam-3900	444	3	.	.	PUNCT
ejpam-3900	445	1	soc	soc	PROPN
ejpam-3900	445	2	.	.	PROPN
ejpam-3900	445	3	,	,	PUNCT
ejpam-3900	445	4	17(3):423–430	17(3):423–430	PROPN
ejpam-3900	445	5	,	,	PUNCT
ejpam-3900	445	6	2002	2002	NUM
ejpam-3900	445	7	.	.	PUNCT
ejpam-3900	446	1	[	[	X
ejpam-3900	446	2	10	10	NUM
ejpam-3900	446	3	]	]	X
ejpam-3900	446	4	i.	i.	NOUN
ejpam-3900	446	5	mező.	mező.	X
ejpam-3900	446	6	a	a	DET
ejpam-3900	446	7	new	new	ADJ
ejpam-3900	446	8	formula	formula	NOUN
ejpam-3900	446	9	for	for	ADP
ejpam-3900	446	10	the	the	DET
ejpam-3900	446	11	bernoulli	bernoulli	NOUN
ejpam-3900	446	12	polynomials	polynomial	NOUN
ejpam-3900	446	13	.	.	PUNCT
ejpam-3900	447	1	result	result	VERB
ejpam-3900	447	2	.	.	PUNCT
ejpam-3900	448	1	math	math	NOUN
ejpam-3900	448	2	,	,	PUNCT
ejpam-3900	448	3	58:330–333	58:330–333	PROPN
ejpam-3900	448	4	,	,	PUNCT
ejpam-3900	448	5	2010	2010	NUM
ejpam-3900	448	6	.	.	PUNCT
ejpam-3900	449	1	[	[	X
ejpam-3900	449	2	11	11	NUM
ejpam-3900	449	3	]	]	X
ejpam-3900	449	4	f.	f.	PROPN
ejpam-3900	449	5	qi	qi	PROPN
ejpam-3900	449	6	.	.	PUNCT
ejpam-3900	450	1	an	an	DET
ejpam-3900	450	2	explicit	explicit	ADJ
ejpam-3900	450	3	formula	formula	NOUN
ejpam-3900	450	4	for	for	ADP
ejpam-3900	450	5	the	the	DET
ejpam-3900	450	6	bell	bell	NOUN
ejpam-3900	450	7	numbers	number	NOUN
ejpam-3900	450	8	in	in	ADP
ejpam-3900	450	9	terms	term	NOUN
ejpam-3900	450	10	of	of	ADP
ejpam-3900	450	11	lah	lah	NOUN
ejpam-3900	450	12	and	and	CCONJ
ejpam-3900	450	13	stirling	stirling	NOUN
ejpam-3900	450	14	numbers	number	NOUN
ejpam-3900	450	15	.	.	PUNCT
ejpam-3900	451	1	mediterr	mediterr	PROPN
ejpam-3900	451	2	.	.	PUNCT
ejpam-3900	452	1	j.	j.	PROPN
ejpam-3900	452	2	math	math	PROPN
ejpam-3900	452	3	.	.	PUNCT
ejpam-3900	452	4	,	,	PUNCT
ejpam-3900	452	5	13(5):2795–2800	13(5):2795–2800	NUM
ejpam-3900	452	6	,	,	PUNCT
ejpam-3900	452	7	2016	2016	NUM
ejpam-3900	452	8	.	.	PUNCT
ejpam-3900	453	1	[	[	X
ejpam-3900	453	2	12	12	NUM
ejpam-3900	453	3	]	]	X
ejpam-3900	453	4	srivastava	srivastava	PROPN
ejpam-3900	453	5	,	,	PUNCT
ejpam-3900	453	6	hm	hm	INTJ
ejpam-3900	453	7	.	.	PROPN
ejpam-3900	453	8	,	,	PUNCT
ejpam-3900	453	9	m.	m.	NOUN
ejpam-3900	453	10	riyasat	riyasat	PROPN
ejpam-3900	453	11	,	,	PUNCT
ejpam-3900	453	12	s.	s.	PROPN
ejpam-3900	453	13	khan	khan	PROPN
ejpam-3900	453	14	,	,	PUNCT
ejpam-3900	453	15	s.	s.	PROPN
ejpam-3900	453	16	araci	araci	PROPN
ejpam-3900	453	17	,	,	PUNCT
ejpam-3900	453	18	and	and	CCONJ
ejpam-3900	453	19	m.	m.	NOUN
ejpam-3900	453	20	acikgoz	acikgoz	VERB
ejpam-3900	453	21	.	.	PUNCT
ejpam-3900	454	1	a	a	DET
ejpam-3900	454	2	new	new	ADJ
ejpam-3900	454	3	approach	approach	NOUN
ejpam-3900	454	4	to	to	ADP
ejpam-3900	454	5	legendre	legendre	PROPN
ejpam-3900	454	6	-	-	PUNCT
ejpam-3900	454	7	truncated	truncate	VERB
ejpam-3900	454	8	-	-	PUNCT
ejpam-3900	454	9	exponential	exponential	NOUN
ejpam-3900	454	10	-	-	PUNCT
ejpam-3900	454	11	based	base	VERB
ejpam-3900	454	12	sheffer	sheffer	NOUN
ejpam-3900	454	13	sequences	sequence	NOUN
ejpam-3900	454	14	via	via	ADP
ejpam-3900	454	15	riordan	riordan	PROPN
ejpam-3900	454	16	arrays	array	VERB
ejpam-3900	454	17	.	.	PUNCT
ejpam-3900	455	1	appl	appl	PROPN
ejpam-3900	455	2	.	.	PROPN
ejpam-3900	455	3	math	math	PROPN
ejpam-3900	455	4	.	.	PUNCT
ejpam-3900	456	1	comput	comput	NOUN
ejpam-3900	456	2	.	.	PUNCT
ejpam-3900	456	3	,	,	PUNCT
ejpam-3900	456	4	369:124683	369:124683	NUM
ejpam-3900	456	5	,	,	PUNCT
ejpam-3900	456	6	2020	2020	NUM
ejpam-3900	456	7	.	.	PUNCT
ejpam-3900	457	1	[	[	X
ejpam-3900	457	2	13	13	NUM
ejpam-3900	457	3	]	]	X
ejpam-3900	457	4	h.m	h.m	PROPN
ejpam-3900	457	5	.	.	PROPN
ejpam-3900	457	6	srivastava	srivastava	PROPN
ejpam-3900	457	7	,	,	PUNCT
ejpam-3900	457	8	s.	s.	PROPN
ejpam-3900	457	9	khan	khan	PROPN
ejpam-3900	457	10	,	,	PUNCT
ejpam-3900	457	11	s.	s.	PROPN
ejpam-3900	457	12	araci	araci	PROPN
ejpam-3900	457	13	,	,	PUNCT
ejpam-3900	457	14	m.	m.	NOUN
ejpam-3900	457	15	acikgoz	acikgoz	ADJ
ejpam-3900	457	16	,	,	PUNCT
ejpam-3900	457	17	and	and	CCONJ
ejpam-3900	457	18	m.	m.	NOUN
ejpam-3900	457	19	riyasat	riyasat	NOUN
ejpam-3900	457	20	.	.	PUNCT
ejpam-3900	458	1	a	a	DET
ejpam-3900	458	2	general	general	ADJ
ejpam-3900	458	3	class	class	NOUN
ejpam-3900	458	4	of	of	ADP
ejpam-3900	458	5	the	the	DET
ejpam-3900	458	6	three	three	NUM
ejpam-3900	458	7	-	-	PUNCT
ejpam-3900	458	8	variable	variable	NOUN
ejpam-3900	458	9	unified	unify	VERB
ejpam-3900	458	10	apostol	apostol	NOUN
ejpam-3900	458	11	-	-	PUNCT
ejpam-3900	458	12	type	type	NOUN
ejpam-3900	458	13	q	q	NOUN
ejpam-3900	458	14	-	-	PUNCT
ejpam-3900	458	15	polynomials	polynomial	NOUN
ejpam-3900	458	16	and	and	CCONJ
ejpam-3900	458	17	multiple	multiple	ADJ
ejpam-3900	458	18	power	power	NOUN
ejpam-3900	458	19	q	q	NOUN
ejpam-3900	458	20	-	-	PUNCT
ejpam-3900	458	21	sums	sum	NOUN
ejpam-3900	458	22	.	.	PUNCT
ejpam-3900	459	1	bull	bull	NOUN
ejpam-3900	459	2	.	.	PUNCT
ejpam-3900	460	1	iran	iran	PROPN
ejpam-3900	460	2	.	.	PUNCT
ejpam-3900	461	1	math	math	NOUN
ejpam-3900	461	2	.	.	PUNCT
ejpam-3900	462	1	soc	soc	PROPN
ejpam-3900	462	2	.	.	PUNCT
ejpam-3900	462	3	,	,	PUNCT
ejpam-3900	462	4	46:519–542	46:519–542	PROPN
ejpam-3900	462	5	,	,	PUNCT
ejpam-3900	462	6	2020	2020	NUM
ejpam-3900	462	7	.	.	PUNCT