id	sid	tid	token	lemma	pos
ejpam-4441	1	1	european	european	PROPN
ejpam-4441	1	2	journal	journal	PROPN
ejpam-4441	1	3	of	of	ADP
ejpam-4441	1	4	pure	pure	ADJ
ejpam-4441	1	5	and	and	CCONJ
ejpam-4441	1	6	applied	apply	VERB
ejpam-4441	1	7	mathematics	mathematic	NOUN
ejpam-4441	1	8	vol	vol	NOUN
ejpam-4441	1	9	.	.	PROPN
ejpam-4441	2	1	15	15	NUM
ejpam-4441	2	2	,	,	PUNCT
ejpam-4441	2	3	no	no	INTJ
ejpam-4441	2	4	.	.	NOUN
ejpam-4441	2	5	3	3	NUM
ejpam-4441	2	6	,	,	PUNCT
ejpam-4441	2	7	2022	2022	NUM
ejpam-4441	2	8	,	,	PUNCT
ejpam-4441	2	9	1054	1054	NUM
ejpam-4441	2	10	-	-	SYM
ejpam-4441	2	11	1066	1066	NUM
ejpam-4441	2	12	issn	issn	PROPN
ejpam-4441	2	13	1307	1307	NUM
ejpam-4441	2	14	-	-	SYM
ejpam-4441	2	15	5543	5543	NUM
ejpam-4441	2	16	–	–	PUNCT
ejpam-4441	2	17	ejpam.com	ejpam.com	X
ejpam-4441	2	18	published	publish	VERB
ejpam-4441	2	19	by	by	ADP
ejpam-4441	2	20	new	new	PROPN
ejpam-4441	2	21	york	york	PROPN
ejpam-4441	2	22	business	business	PROPN
ejpam-4441	2	23	global	global	ADJ
ejpam-4441	2	24	some	some	DET
ejpam-4441	2	25	identities	identity	NOUN
ejpam-4441	2	26	on	on	ADP
ejpam-4441	2	27	λ	λ	PROPN
ejpam-4441	2	28	-analogues	-analogue	NOUN
ejpam-4441	2	29	of	of	ADP
ejpam-4441	2	30	r	r	NOUN
ejpam-4441	2	31	-	-	PUNCT
ejpam-4441	2	32	stirling	stirling	NOUN
ejpam-4441	2	33	numbers	number	NOUN
ejpam-4441	2	34	of	of	ADP
ejpam-4441	2	35	the	the	DET
ejpam-4441	2	36	second	second	ADJ
ejpam-4441	2	37	kind	kind	NOUN
ejpam-4441	2	38	dae	dae	NOUN
ejpam-4441	2	39	san	san	PROPN
ejpam-4441	2	40	kim1	kim1	PROPN
ejpam-4441	2	41	,	,	PUNCT
ejpam-4441	2	42	hye	hye	PROPN
ejpam-4441	2	43	kyung	kyung	PROPN
ejpam-4441	2	44	kim2	kim2	PROPN
ejpam-4441	2	45	*	*	PROPN
ejpam-4441	2	46	,	,	PUNCT
ejpam-4441	2	47	taekyun	taekyun	NOUN
ejpam-4441	2	48	kim3	kim3	PROPN
ejpam-4441	2	49	1	1	NUM
ejpam-4441	2	50	department	department	NOUN
ejpam-4441	2	51	of	of	ADP
ejpam-4441	2	52	mathematics	mathematics	PROPN
ejpam-4441	2	53	,	,	PUNCT
ejpam-4441	2	54	sogang	sogang	PROPN
ejpam-4441	2	55	university	university	PROPN
ejpam-4441	2	56	,	,	PUNCT
ejpam-4441	2	57	seoul	seoul	PROPN
ejpam-4441	2	58	121	121	NUM
ejpam-4441	2	59	-	-	SYM
ejpam-4441	2	60	742	742	NUM
ejpam-4441	2	61	,	,	PUNCT
ejpam-4441	2	62	republic	republic	NOUN
ejpam-4441	2	63	of	of	ADP
ejpam-4441	2	64	korea	korea	PROPN
ejpam-4441	2	65	2	2	PROPN
ejpam-4441	2	66	department	department	NOUN
ejpam-4441	2	67	of	of	ADP
ejpam-4441	2	68	mathematics	mathematics	PROPN
ejpam-4441	2	69	education	education	NOUN
ejpam-4441	2	70	,	,	PUNCT
ejpam-4441	2	71	daegu	daegu	PROPN
ejpam-4441	2	72	catholic	catholic	PROPN
ejpam-4441	2	73	university	university	PROPN
ejpam-4441	2	74	,	,	PUNCT
ejpam-4441	2	75	gyeongsan	gyeongsan	ADJ
ejpam-4441	2	76	38430	38430	NUM
ejpam-4441	2	77	,	,	PUNCT
ejpam-4441	2	78	republic	republic	NOUN
ejpam-4441	2	79	of	of	ADP
ejpam-4441	2	80	korea	korea	PROPN
ejpam-4441	2	81	3	3	PROPN
ejpam-4441	2	82	department	department	PROPN
ejpam-4441	2	83	of	of	ADP
ejpam-4441	2	84	mathematics	mathematic	NOUN
ejpam-4441	2	85	,	,	PUNCT
ejpam-4441	2	86	kwangwoon	kwangwoon	NOUN
ejpam-4441	2	87	university	university	NOUN
ejpam-4441	2	88	,	,	PUNCT
ejpam-4441	2	89	seoul	seoul	PROPN
ejpam-4441	2	90	139	139	NUM
ejpam-4441	2	91	-	-	SYM
ejpam-4441	2	92	701	701	NUM
ejpam-4441	2	93	,	,	PUNCT
ejpam-4441	2	94	republic	republic	NOUN
ejpam-4441	2	95	of	of	ADP
ejpam-4441	2	96	korea	korea	PROPN
ejpam-4441	2	97	abstract	abstract	PROPN
ejpam-4441	2	98	.	.	PUNCT
ejpam-4441	3	1	recently	recently	ADV
ejpam-4441	3	2	,	,	PUNCT
ejpam-4441	3	3	the	the	DET
ejpam-4441	3	4	λ	λ	PROPN
ejpam-4441	3	5	-analogues	-analogue	NOUN
ejpam-4441	3	6	of	of	ADP
ejpam-4441	3	7	r	r	NOUN
ejpam-4441	3	8	-	-	PUNCT
ejpam-4441	3	9	stirling	stirling	NOUN
ejpam-4441	3	10	numbers	number	NOUN
ejpam-4441	3	11	of	of	ADP
ejpam-4441	3	12	the	the	DET
ejpam-4441	3	13	first	first	ADJ
ejpam-4441	3	14	kind	kind	NOUN
ejpam-4441	3	15	were	be	AUX
ejpam-4441	3	16	studied	study	VERB
ejpam-4441	3	17	by	by	ADP
ejpam-4441	3	18	kim	kim	PROPN
ejpam-4441	3	19	-	-	PUNCT
ejpam-4441	3	20	kim	kim	PROPN
ejpam-4441	3	21	.	.	PUNCT
ejpam-4441	4	1	the	the	DET
ejpam-4441	4	2	aim	aim	NOUN
ejpam-4441	4	3	of	of	ADP
ejpam-4441	4	4	this	this	DET
ejpam-4441	4	5	paper	paper	NOUN
ejpam-4441	4	6	is	be	AUX
ejpam-4441	4	7	to	to	PART
ejpam-4441	4	8	introduce	introduce	VERB
ejpam-4441	4	9	the	the	DET
ejpam-4441	4	10	λ	λ	NOUN
ejpam-4441	4	11	-analogues	-analogue	NOUN
ejpam-4441	4	12	of	of	ADP
ejpam-4441	4	13	r	r	NOUN
ejpam-4441	4	14	-	-	PUNCT
ejpam-4441	4	15	stirling	stirling	NOUN
ejpam-4441	4	16	numbers	number	NOUN
ejpam-4441	4	17	of	of	ADP
ejpam-4441	4	18	the	the	DET
ejpam-4441	4	19	second	second	ADJ
ejpam-4441	4	20	kind	kind	NOUN
ejpam-4441	4	21	and	and	CCONJ
ejpam-4441	4	22	to	to	PART
ejpam-4441	4	23	investigate	investigate	VERB
ejpam-4441	4	24	some	some	DET
ejpam-4441	4	25	properties	property	NOUN
ejpam-4441	4	26	,	,	PUNCT
ejpam-4441	4	27	recurrence	recurrence	NOUN
ejpam-4441	4	28	relations	relation	NOUN
ejpam-4441	4	29	and	and	CCONJ
ejpam-4441	4	30	certain	certain	ADJ
ejpam-4441	4	31	identities	identity	NOUN
ejpam-4441	4	32	on	on	ADP
ejpam-4441	4	33	those	those	DET
ejpam-4441	4	34	numbers	number	NOUN
ejpam-4441	4	35	.	.	PUNCT
ejpam-4441	5	1	we	we	PRON
ejpam-4441	5	2	also	also	ADV
ejpam-4441	5	3	introduce	introduce	VERB
ejpam-4441	5	4	the	the	DET
ejpam-4441	5	5	λ	λ	PROPN
ejpam-4441	5	6	-analogues	-analogue	NOUN
ejpam-4441	5	7	of	of	ADP
ejpam-4441	5	8	whitney	whitney	NOUN
ejpam-4441	5	9	-	-	PUNCT
ejpam-4441	5	10	type	type	NOUN
ejpam-4441	5	11	r	r	NOUN
ejpam-4441	5	12	-	-	PUNCT
ejpam-4441	5	13	stirling	stirling	NOUN
ejpam-4441	5	14	numbers	number	NOUN
ejpam-4441	5	15	of	of	ADP
ejpam-4441	5	16	the	the	DET
ejpam-4441	5	17	second	second	ADJ
ejpam-4441	5	18	and	and	CCONJ
ejpam-4441	5	19	derive	derive	VERB
ejpam-4441	5	20	similar	similar	ADJ
ejpam-4441	5	21	results	result	NOUN
ejpam-4441	5	22	to	to	ADP
ejpam-4441	5	23	the	the	DET
ejpam-4441	5	24	case	case	NOUN
ejpam-4441	5	25	of	of	ADP
ejpam-4441	5	26	the	the	DET
ejpam-4441	5	27	λ	λ	PROPN
ejpam-4441	5	28	-analogues	-analogue	NOUN
ejpam-4441	5	29	of	of	ADP
ejpam-4441	5	30	r	r	NOUN
ejpam-4441	5	31	-	-	PUNCT
ejpam-4441	5	32	stirling	stirling	NOUN
ejpam-4441	5	33	numbers	number	NOUN
ejpam-4441	5	34	of	of	ADP
ejpam-4441	5	35	the	the	DET
ejpam-4441	5	36	second	second	ADJ
ejpam-4441	5	37	kind	kind	NOUN
ejpam-4441	5	38	.	.	PUNCT
ejpam-4441	6	1	in	in	ADP
ejpam-4441	6	2	addition	addition	NOUN
ejpam-4441	6	3	,	,	PUNCT
ejpam-4441	6	4	we	we	PRON
ejpam-4441	6	5	consider	consider	VERB
ejpam-4441	6	6	the	the	DET
ejpam-4441	6	7	λ	λ	NOUN
ejpam-4441	6	8	-analogues	-analogue	NOUN
ejpam-4441	6	9	of	of	ADP
ejpam-4441	6	10	dowling	dowle	VERB
ejpam-4441	6	11	polynomials	polynomial	NOUN
ejpam-4441	6	12	and	and	CCONJ
ejpam-4441	6	13	deduce	deduce	VERB
ejpam-4441	6	14	a	a	DET
ejpam-4441	6	15	dobinski	dobinski	ADJ
ejpam-4441	6	16	-	-	PUNCT
ejpam-4441	6	17	like	like	ADJ
ejpam-4441	6	18	formula	formula	NOUN
ejpam-4441	6	19	.	.	PUNCT
ejpam-4441	7	1	2020	2020	NUM
ejpam-4441	7	2	mathematics	mathematic	NOUN
ejpam-4441	7	3	subject	subject	NOUN
ejpam-4441	7	4	classifications	classification	NOUN
ejpam-4441	7	5	:	:	PUNCT
ejpam-4441	7	6	11b73	11b73	NUM
ejpam-4441	7	7	,	,	PUNCT
ejpam-4441	7	8	11b83	11b83	NUM
ejpam-4441	7	9	key	key	ADJ
ejpam-4441	7	10	words	word	NOUN
ejpam-4441	7	11	and	and	CCONJ
ejpam-4441	7	12	phrases	phrase	NOUN
ejpam-4441	7	13	:	:	PUNCT
ejpam-4441	7	14	λ	λ	NOUN
ejpam-4441	7	15	-anlogues	-anlogue	NOUN
ejpam-4441	7	16	of	of	ADP
ejpam-4441	7	17	r	r	NOUN
ejpam-4441	7	18	-	-	PUNCT
ejpam-4441	7	19	stirling	stirling	NOUN
ejpam-4441	7	20	numbers	number	NOUN
ejpam-4441	7	21	of	of	ADP
ejpam-4441	7	22	the	the	DET
ejpam-4441	7	23	second	second	ADJ
ejpam-4441	7	24	,	,	PUNCT
ejpam-4441	7	25	λ	λ	PROPN
ejpam-4441	7	26	-analogues	-analogue	NOUN
ejpam-4441	7	27	of	of	ADP
ejpam-4441	7	28	whitney	whitney	NOUN
ejpam-4441	7	29	-	-	PUNCT
ejpam-4441	7	30	type	type	NOUN
ejpam-4441	7	31	r	r	NOUN
ejpam-4441	7	32	-	-	PUNCT
ejpam-4441	7	33	stirling	stirling	NOUN
ejpam-4441	7	34	numbers	number	NOUN
ejpam-4441	7	35	of	of	ADP
ejpam-4441	7	36	the	the	DET
ejpam-4441	7	37	second	second	ADJ
ejpam-4441	7	38	,	,	PUNCT
ejpam-4441	7	39	λ	λ	PROPN
ejpam-4441	7	40	-analogues	-analogue	NOUN
ejpam-4441	7	41	of	of	ADP
ejpam-4441	7	42	dowling	dowle	VERB
ejpam-4441	7	43	polynomials	polynomial	NOUN
ejpam-4441	7	44	1	1	NUM
ejpam-4441	7	45	.	.	PUNCT
ejpam-4441	8	1	introduction	introduction	NOUN
ejpam-4441	8	2	carlitz	carlitz	NOUN
ejpam-4441	8	3	[	[	X
ejpam-4441	8	4	3	3	X
ejpam-4441	8	5	]	]	PUNCT
ejpam-4441	8	6	initiated	initiate	VERB
ejpam-4441	8	7	a	a	DET
ejpam-4441	8	8	study	study	NOUN
ejpam-4441	8	9	of	of	ADP
ejpam-4441	8	10	the	the	DET
ejpam-4441	8	11	degenerate	degenerate	ADJ
ejpam-4441	8	12	bernoulli	bernoulli	NOUN
ejpam-4441	8	13	and	and	CCONJ
ejpam-4441	8	14	euler	euler	NOUN
ejpam-4441	8	15	polynomials	polynomial	NOUN
ejpam-4441	8	16	and	and	CCONJ
ejpam-4441	8	17	numbers	number	NOUN
ejpam-4441	8	18	,	,	PUNCT
ejpam-4441	8	19	which	which	PRON
ejpam-4441	8	20	are	be	AUX
ejpam-4441	8	21	degenerate	degenerate	ADJ
ejpam-4441	8	22	versions	version	NOUN
ejpam-4441	8	23	of	of	ADP
ejpam-4441	8	24	the	the	DET
ejpam-4441	8	25	bernoulli	bernoulli	PROPN
ejpam-4441	8	26	and	and	CCONJ
ejpam-4441	8	27	euler	euler	NOUN
ejpam-4441	8	28	polynomials	polynomial	NOUN
ejpam-4441	8	29	and	and	CCONJ
ejpam-4441	8	30	numbers	number	NOUN
ejpam-4441	8	31	.	.	PUNCT
ejpam-4441	9	1	in	in	ADP
ejpam-4441	9	2	recent	recent	ADJ
ejpam-4441	9	3	years	year	NOUN
ejpam-4441	9	4	,	,	PUNCT
ejpam-4441	9	5	studying	study	VERB
ejpam-4441	9	6	degenerate	degenerate	ADJ
ejpam-4441	9	7	versions	version	NOUN
ejpam-4441	9	8	of	of	ADP
ejpam-4441	9	9	special	special	ADJ
ejpam-4441	9	10	numbers	number	NOUN
ejpam-4441	9	11	and	and	CCONJ
ejpam-4441	9	12	polynomials	polynomial	NOUN
ejpam-4441	9	13	regained	regain	VERB
ejpam-4441	9	14	interests	interest	NOUN
ejpam-4441	9	15	of	of	ADP
ejpam-4441	9	16	some	some	DET
ejpam-4441	9	17	mathematicians	mathematician	NOUN
ejpam-4441	9	18	.	.	PUNCT
ejpam-4441	10	1	they	they	PRON
ejpam-4441	10	2	have	have	AUX
ejpam-4441	10	3	been	be	AUX
ejpam-4441	10	4	explored	explore	VERB
ejpam-4441	10	5	with	with	ADP
ejpam-4441	10	6	various	various	ADJ
ejpam-4441	10	7	tools	tool	NOUN
ejpam-4441	10	8	and	and	CCONJ
ejpam-4441	10	9	many	many	ADJ
ejpam-4441	10	10	fascinating	fascinating	ADJ
ejpam-4441	10	11	results	result	NOUN
ejpam-4441	10	12	have	have	AUX
ejpam-4441	10	13	been	be	AUX
ejpam-4441	10	14	revealed	reveal	VERB
ejpam-4441	10	15	.	.	PUNCT
ejpam-4441	11	1	it	it	PRON
ejpam-4441	11	2	is	be	AUX
ejpam-4441	11	3	remakable	remakable	ADJ
ejpam-4441	11	4	that	that	SCONJ
ejpam-4441	11	5	this	this	DET
ejpam-4441	11	6	quest	quest	NOUN
ejpam-4441	11	7	for	for	ADP
ejpam-4441	11	8	degenerate	degenerate	ADJ
ejpam-4441	11	9	versions	version	NOUN
ejpam-4441	11	10	is	be	AUX
ejpam-4441	11	11	not	not	PART
ejpam-4441	11	12	just	just	ADV
ejpam-4441	11	13	restricted	restrict	VERB
ejpam-4441	11	14	to	to	ADP
ejpam-4441	11	15	polynomials	polynomial	NOUN
ejpam-4441	11	16	but	but	CCONJ
ejpam-4441	11	17	also	also	ADV
ejpam-4441	11	18	extended	extend	VERB
ejpam-4441	11	19	to	to	ADP
ejpam-4441	11	20	transcendental	transcendental	ADJ
ejpam-4441	11	21	functions	function	NOUN
ejpam-4441	11	22	,	,	PUNCT
ejpam-4441	11	23	like	like	ADP
ejpam-4441	11	24	gamma	gamma	NOUN
ejpam-4441	11	25	functions	function	NOUN
ejpam-4441	11	26	.	.	PUNCT
ejpam-4441	12	1	in	in	ADP
ejpam-4441	12	2	addition	addition	NOUN
ejpam-4441	12	3	,	,	PUNCT
ejpam-4441	12	4	it	it	PRON
ejpam-4441	12	5	also	also	ADV
ejpam-4441	12	6	led	lead	VERB
ejpam-4441	12	7	to	to	ADP
ejpam-4441	12	8	the	the	DET
ejpam-4441	12	9	introduction	introduction	NOUN
ejpam-4441	12	10	of	of	ADP
ejpam-4441	12	11	λ	λ	PROPN
ejpam-4441	12	12	-umbral	-umbral	ADJ
ejpam-4441	12	13	calculus	calculus	NOUN
ejpam-4441	12	14	and	and	CCONJ
ejpam-4441	12	15	λ	λ	NOUN
ejpam-4441	12	16	-sheffer	-sheffer	PROPN
ejpam-4441	12	17	sequences	sequence	NOUN
ejpam-4441	12	18	.	.	PUNCT
ejpam-4441	13	1	the	the	DET
ejpam-4441	13	2	degenerate	degenerate	ADJ
ejpam-4441	13	3	stirling	stirling	NOUN
ejpam-4441	13	4	numbers	number	NOUN
ejpam-4441	13	5	of	of	ADP
ejpam-4441	13	6	the	the	DET
ejpam-4441	13	7	first	first	ADJ
ejpam-4441	13	8	kind	kind	NOUN
ejpam-4441	13	9	and	and	CCONJ
ejpam-4441	13	10	of	of	ADP
ejpam-4441	13	11	the	the	DET
ejpam-4441	13	12	second	second	ADJ
ejpam-4441	13	13	kind	kind	NOUN
ejpam-4441	13	14	,	,	PUNCT
ejpam-4441	13	15	which	which	PRON
ejpam-4441	13	16	are	be	AUX
ejpam-4441	13	17	degenerate	degenerate	ADJ
ejpam-4441	13	18	versions	version	NOUN
ejpam-4441	13	19	of	of	ADP
ejpam-4441	13	20	the	the	DET
ejpam-4441	13	21	stirling	stirling	NOUN
ejpam-4441	13	22	numbers	number	NOUN
ejpam-4441	13	23	of	of	ADP
ejpam-4441	13	24	the	the	DET
ejpam-4441	13	25	first	first	ADJ
ejpam-4441	13	26	kind	kind	NOUN
ejpam-4441	13	27	and	and	CCONJ
ejpam-4441	13	28	of	of	ADP
ejpam-4441	13	29	the	the	DET
ejpam-4441	13	30	second	second	ADJ
ejpam-4441	13	31	kind	kind	NOUN
ejpam-4441	13	32	,	,	PUNCT
ejpam-4441	13	33	appear	appear	VERB
ejpam-4441	13	34	frequently	frequently	ADV
ejpam-4441	13	35	when	when	SCONJ
ejpam-4441	13	36	we	we	PRON
ejpam-4441	13	37	study	study	VERB
ejpam-4441	13	38	degenerate	degenerate	ADJ
ejpam-4441	13	39	versions	version	NOUN
ejpam-4441	13	40	of	of	ADP
ejpam-4441	13	41	some	some	DET
ejpam-4441	13	42	special	special	ADJ
ejpam-4441	13	43	numbers	number	NOUN
ejpam-4441	13	44	and	and	CCONJ
ejpam-4441	13	45	polynomials	polynomial	NOUN
ejpam-4441	13	46	.	.	PUNCT
ejpam-4441	14	1	they	they	PRON
ejpam-4441	14	2	arise	arise	VERB
ejpam-4441	14	3	naturally	naturally	ADV
ejpam-4441	14	4	when	when	SCONJ
ejpam-4441	14	5	we	we	PRON
ejpam-4441	14	6	replace	replace	VERB
ejpam-4441	14	7	the	the	DET
ejpam-4441	14	8	powers	power	NOUN
ejpam-4441	14	9	of	of	ADP
ejpam-4441	14	10	x	x	PUNCT
ejpam-4441	14	11	by	by	ADP
ejpam-4441	14	12	the	the	DET
ejpam-4441	14	13	generalized	generalized	ADJ
ejpam-4441	14	14	falling	fall	VERB
ejpam-4441	14	15	factorial	factorial	NOUN
ejpam-4441	14	16	polynomials	polynomial	NOUN
ejpam-4441	14	17	(	(	PUNCT
ejpam-4441	14	18	x)k	x)k	X
ejpam-4441	14	19	,	,	PUNCT
ejpam-4441	14	20	λ	λ	NOUN
ejpam-4441	14	21	in	in	ADP
ejpam-4441	14	22	the	the	DET
ejpam-4441	14	23	∗corresponding	∗corresponding	NOUN
ejpam-4441	14	24	author	author	NOUN
ejpam-4441	14	25	.	.	PUNCT
ejpam-4441	15	1	doi	doi	NOUN
ejpam-4441	15	2	:	:	PUNCT
ejpam-4441	15	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4441	https://doi.org/10.29020/nybg.ejpam.v15i3.4441	ADP
ejpam-4441	15	4	email	email	NOUN
ejpam-4441	15	5	addresses	address	NOUN
ejpam-4441	15	6	:	:	PUNCT
ejpam-4441	15	7	dskim@sogang.ac.kr	dskim@sogang.ac.kr	PROPN
ejpam-4441	15	8	(	(	PUNCT
ejpam-4441	15	9	d.	d.	PROPN
ejpam-4441	15	10	s.	s.	PROPN
ejpam-4441	15	11	kim	kim	PROPN
ejpam-4441	15	12	)	)	PUNCT
ejpam-4441	15	13	,	,	PUNCT
ejpam-4441	15	14	hkkim@cu.ac.kr	hkkim@cu.ac.kr	X
ejpam-4441	15	15	(	(	PUNCT
ejpam-4441	15	16	h.	h.	PROPN
ejpam-4441	15	17	k.	k.	PROPN
ejpam-4441	15	18	kim	kim	PROPN
ejpam-4441	15	19	)	)	PUNCT
ejpam-4441	15	20	,	,	PUNCT
ejpam-4441	15	21	tkkim@kw.ac.kr	tkkim@kw.ac.kr	X
ejpam-4441	15	22	(	(	PUNCT
ejpam-4441	15	23	t.	t.	PROPN
ejpam-4441	15	24	kim	kim	PROPN
ejpam-4441	15	25	)	)	PUNCT
ejpam-4441	15	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4441	15	27	1054	1054	NUM
ejpam-4441	16	1	©	©	PROPN
ejpam-4441	16	2	2022	2022	NUM
ejpam-4441	16	3	ejpam	ejpam	VERB
ejpam-4441	16	4	all	all	DET
ejpam-4441	16	5	rights	right	NOUN
ejpam-4441	16	6	reserved	reserve	VERB
ejpam-4441	16	7	.	.	PUNCT
ejpam-4441	17	1	d.	d.	PROPN
ejpam-4441	17	2	s.	s.	PROPN
ejpam-4441	17	3	kim	kim	PROPN
ejpam-4441	17	4	,	,	PUNCT
ejpam-4441	17	5	h.	h.	PROPN
ejpam-4441	17	6	k.	k.	PROPN
ejpam-4441	17	7	kim	kim	PROPN
ejpam-4441	17	8	,	,	PUNCT
ejpam-4441	17	9	t.	t.	PROPN
ejpam-4441	17	10	kim	kim	PROPN
ejpam-4441	17	11	/	/	SYM
ejpam-4441	17	12	eur	eur	PROPN
ejpam-4441	17	13	.	.	PUNCT
ejpam-4441	18	1	j.	j.	PROPN
ejpam-4441	18	2	pure	pure	PROPN
ejpam-4441	18	3	appl	appl	PROPN
ejpam-4441	18	4	.	.	PROPN
ejpam-4441	18	5	math	math	PROPN
ejpam-4441	18	6	,	,	PUNCT
ejpam-4441	18	7	15	15	NUM
ejpam-4441	18	8	(	(	PUNCT
ejpam-4441	18	9	3	3	NUM
ejpam-4441	18	10	)	)	PUNCT
ejpam-4441	18	11	(	(	PUNCT
ejpam-4441	18	12	2022	2022	NUM
ejpam-4441	18	13	)	)	PUNCT
ejpam-4441	18	14	,	,	PUNCT
ejpam-4441	18	15	1054	1054	NUM
ejpam-4441	18	16	-	-	SYM
ejpam-4441	18	17	1066	1066	NUM
ejpam-4441	18	18	1055	1055	NUM
ejpam-4441	18	19	defining	define	VERB
ejpam-4441	18	20	equations	equation	NOUN
ejpam-4441	18	21	of	of	ADP
ejpam-4441	18	22	the	the	DET
ejpam-4441	18	23	stirling	stirling	NOUN
ejpam-4441	18	24	numbers	number	NOUN
ejpam-4441	18	25	of	of	ADP
ejpam-4441	18	26	both	both	DET
ejpam-4441	18	27	kinds	kind	NOUN
ejpam-4441	18	28	(	(	PUNCT
ejpam-4441	18	29	see	see	VERB
ejpam-4441	18	30	(	(	PUNCT
ejpam-4441	18	31	1	1	NUM
ejpam-4441	18	32	)	)	PUNCT
ejpam-4441	18	33	)	)	PUNCT
ejpam-4441	18	34	,	,	PUNCT
ejpam-4441	18	35	while	while	SCONJ
ejpam-4441	18	36	the	the	DET
ejpam-4441	18	37	λ	λ	PROPN
ejpam-4441	18	38	-analogues	-analogue	NOUN
ejpam-4441	18	39	of	of	ADP
ejpam-4441	18	40	stirling	stirling	NOUN
ejpam-4441	18	41	numbers	number	NOUN
ejpam-4441	18	42	of	of	ADP
ejpam-4441	18	43	the	the	DET
ejpam-4441	18	44	first	first	ADJ
ejpam-4441	18	45	kind	kind	NOUN
ejpam-4441	18	46	and	and	CCONJ
ejpam-4441	18	47	of	of	ADP
ejpam-4441	18	48	the	the	DET
ejpam-4441	18	49	second	second	ADJ
ejpam-4441	18	50	kind	kind	NOUN
ejpam-4441	18	51	appear	appear	VERB
ejpam-4441	18	52	when	when	SCONJ
ejpam-4441	18	53	we	we	PRON
ejpam-4441	18	54	replace	replace	VERB
ejpam-4441	18	55	the	the	DET
ejpam-4441	18	56	falling	fall	VERB
ejpam-4441	18	57	factorials	factorial	NOUN
ejpam-4441	18	58	by	by	ADP
ejpam-4441	18	59	the	the	DET
ejpam-4441	18	60	generalized	generalized	ADJ
ejpam-4441	18	61	falling	fall	VERB
ejpam-4441	18	62	factorials	factorial	NOUN
ejpam-4441	18	63	.	.	PUNCT
ejpam-4441	19	1	the	the	DET
ejpam-4441	19	2	aim	aim	NOUN
ejpam-4441	19	3	of	of	ADP
ejpam-4441	19	4	this	this	DET
ejpam-4441	19	5	paper	paper	NOUN
ejpam-4441	19	6	is	be	AUX
ejpam-4441	19	7	to	to	PART
ejpam-4441	19	8	introduce	introduce	VERB
ejpam-4441	19	9	the	the	DET
ejpam-4441	19	10	λ	λ	NOUN
ejpam-4441	19	11	-analogues	-analogue	NOUN
ejpam-4441	19	12	of	of	ADP
ejpam-4441	19	13	r	r	NOUN
ejpam-4441	19	14	-	-	PUNCT
ejpam-4441	19	15	stirling	stirling	NOUN
ejpam-4441	19	16	numbers	number	NOUN
ejpam-4441	19	17	of	of	ADP
ejpam-4441	19	18	the	the	DET
ejpam-4441	19	19	second	second	ADJ
ejpam-4441	19	20	kind	kind	NOUN
ejpam-4441	19	21	and	and	CCONJ
ejpam-4441	19	22	to	to	PART
ejpam-4441	19	23	investigate	investigate	VERB
ejpam-4441	19	24	some	some	DET
ejpam-4441	19	25	properties	property	NOUN
ejpam-4441	19	26	,	,	PUNCT
ejpam-4441	19	27	recurrence	recurrence	NOUN
ejpam-4441	19	28	relations	relation	NOUN
ejpam-4441	19	29	and	and	CCONJ
ejpam-4441	19	30	certain	certain	ADJ
ejpam-4441	19	31	identities	identity	NOUN
ejpam-4441	19	32	on	on	ADP
ejpam-4441	19	33	those	those	DET
ejpam-4441	19	34	numbers	number	NOUN
ejpam-4441	19	35	.	.	PUNCT
ejpam-4441	20	1	we	we	PRON
ejpam-4441	20	2	also	also	ADV
ejpam-4441	20	3	introduce	introduce	VERB
ejpam-4441	20	4	the	the	DET
ejpam-4441	20	5	λ	λ	PROPN
ejpam-4441	20	6	-analogues	-analogue	NOUN
ejpam-4441	20	7	of	of	ADP
ejpam-4441	20	8	whitney	whitney	NOUN
ejpam-4441	20	9	-	-	PUNCT
ejpam-4441	20	10	type	type	NOUN
ejpam-4441	20	11	r	r	NOUN
ejpam-4441	20	12	-	-	PUNCT
ejpam-4441	20	13	stirling	stirling	NOUN
ejpam-4441	20	14	numbers	number	NOUN
ejpam-4441	20	15	of	of	ADP
ejpam-4441	20	16	the	the	DET
ejpam-4441	20	17	second	second	ADJ
ejpam-4441	20	18	and	and	CCONJ
ejpam-4441	20	19	derive	derive	VERB
ejpam-4441	20	20	similar	similar	ADJ
ejpam-4441	20	21	results	result	NOUN
ejpam-4441	20	22	to	to	ADP
ejpam-4441	20	23	the	the	DET
ejpam-4441	20	24	case	case	NOUN
ejpam-4441	20	25	of	of	ADP
ejpam-4441	20	26	the	the	DET
ejpam-4441	20	27	λ	λ	PROPN
ejpam-4441	20	28	-analogues	-analogue	NOUN
ejpam-4441	20	29	of	of	ADP
ejpam-4441	20	30	r	r	NOUN
ejpam-4441	20	31	-	-	PUNCT
ejpam-4441	20	32	stirling	stirling	NOUN
ejpam-4441	20	33	numbers	number	NOUN
ejpam-4441	20	34	of	of	ADP
ejpam-4441	20	35	the	the	DET
ejpam-4441	20	36	second	second	ADJ
ejpam-4441	20	37	kind	kind	NOUN
ejpam-4441	20	38	.	.	PUNCT
ejpam-4441	21	1	in	in	ADP
ejpam-4441	21	2	addition	addition	NOUN
ejpam-4441	21	3	,	,	PUNCT
ejpam-4441	21	4	we	we	PRON
ejpam-4441	21	5	consider	consider	VERB
ejpam-4441	21	6	the	the	DET
ejpam-4441	21	7	λ	λ	NOUN
ejpam-4441	21	8	-analogues	-analogue	NOUN
ejpam-4441	21	9	of	of	ADP
ejpam-4441	21	10	dowling	dowle	VERB
ejpam-4441	21	11	polynomials	polynomial	NOUN
ejpam-4441	21	12	,	,	PUNCT
ejpam-4441	21	13	which	which	PRON
ejpam-4441	21	14	are	be	AUX
ejpam-4441	21	15	a	a	DET
ejpam-4441	21	16	natural	natural	ADJ
ejpam-4441	21	17	extension	extension	NOUN
ejpam-4441	21	18	of	of	ADP
ejpam-4441	21	19	the	the	DET
ejpam-4441	21	20	analogues	analogue	NOUN
ejpam-4441	21	21	of	of	ADP
ejpam-4441	21	22	whitney	whitney	NOUN
ejpam-4441	21	23	-	-	PUNCT
ejpam-4441	21	24	type	type	NOUN
ejpam-4441	21	25	stirling	stirling	NOUN
ejpam-4441	21	26	numbers	number	NOUN
ejpam-4441	21	27	of	of	ADP
ejpam-4441	21	28	the	the	DET
ejpam-4441	21	29	second	second	ADJ
ejpam-4441	21	30	kind	kind	NOUN
ejpam-4441	21	31	,	,	PUNCT
ejpam-4441	21	32	and	and	CCONJ
ejpam-4441	21	33	deduce	deduce	VERB
ejpam-4441	21	34	a	a	DET
ejpam-4441	21	35	dobinski	dobinski	ADJ
ejpam-4441	21	36	-	-	PUNCT
ejpam-4441	21	37	like	like	ADJ
ejpam-4441	21	38	formula	formula	NOUN
ejpam-4441	21	39	.	.	PUNCT
ejpam-4441	22	1	the	the	DET
ejpam-4441	22	2	outline	outline	NOUN
ejpam-4441	22	3	of	of	ADP
ejpam-4441	22	4	this	this	DET
ejpam-4441	22	5	paper	paper	NOUN
ejpam-4441	22	6	is	be	AUX
ejpam-4441	22	7	as	as	SCONJ
ejpam-4441	22	8	follows	follow	VERB
ejpam-4441	22	9	.	.	PUNCT
ejpam-4441	23	1	in	in	ADP
ejpam-4441	23	2	section	section	NOUN
ejpam-4441	23	3	1	1	NUM
ejpam-4441	23	4	,	,	PUNCT
ejpam-4441	23	5	we	we	PRON
ejpam-4441	23	6	recall	recall	VERB
ejpam-4441	23	7	the	the	DET
ejpam-4441	23	8	generalized	generalized	ADJ
ejpam-4441	23	9	falling	fall	VERB
ejpam-4441	23	10	factorial	factorial	ADJ
ejpam-4441	23	11	sequence	sequence	NOUN
ejpam-4441	23	12	,	,	PUNCT
ejpam-4441	23	13	the	the	DET
ejpam-4441	23	14	degenerate	degenerate	ADJ
ejpam-4441	23	15	exponential	exponential	ADJ
ejpam-4441	23	16	functions	function	NOUN
ejpam-4441	23	17	,	,	PUNCT
ejpam-4441	23	18	the	the	DET
ejpam-4441	23	19	stirling	stirling	NOUN
ejpam-4441	23	20	numbers	number	NOUN
ejpam-4441	23	21	of	of	ADP
ejpam-4441	23	22	both	both	DET
ejpam-4441	23	23	kinds	kind	NOUN
ejpam-4441	23	24	,	,	PUNCT
ejpam-4441	23	25	the	the	DET
ejpam-4441	23	26	λ	λ	PROPN
ejpam-4441	23	27	-analogues	-analogue	NOUN
ejpam-4441	23	28	of	of	ADP
ejpam-4441	23	29	r	r	NOUN
ejpam-4441	23	30	-	-	PUNCT
ejpam-4441	23	31	stirling	stirling	NOUN
ejpam-4441	23	32	numbers	number	NOUN
ejpam-4441	23	33	of	of	ADP
ejpam-4441	23	34	the	the	DET
ejpam-4441	23	35	first	first	ADJ
ejpam-4441	23	36	kind	kind	NOUN
ejpam-4441	23	37	and	and	CCONJ
ejpam-4441	23	38	the	the	DET
ejpam-4441	23	39	λ	λ	PROPN
ejpam-4441	23	40	-analogues	-analogue	NOUN
ejpam-4441	23	41	of	of	ADP
ejpam-4441	23	42	unsigned	unsigned	ADJ
ejpam-4441	23	43	r	r	NOUN
ejpam-4441	23	44	-	-	PUNCT
ejpam-4441	23	45	stirling	stirling	NOUN
ejpam-4441	23	46	numbers	number	NOUN
ejpam-4441	23	47	of	of	ADP
ejpam-4441	23	48	the	the	DET
ejpam-4441	23	49	first	first	ADJ
ejpam-4441	23	50	kind	kind	NOUN
ejpam-4441	23	51	.	.	PUNCT
ejpam-4441	24	1	in	in	ADP
ejpam-4441	24	2	section	section	NOUN
ejpam-4441	24	3	2	2	NUM
ejpam-4441	24	4	,	,	PUNCT
ejpam-4441	24	5	we	we	PRON
ejpam-4441	24	6	introduce	introduce	VERB
ejpam-4441	24	7	the	the	DET
ejpam-4441	24	8	λ	λ	PROPN
ejpam-4441	24	9	-analogues	-analogue	NOUN
ejpam-4441	24	10	of	of	ADP
ejpam-4441	24	11	r	r	NOUN
ejpam-4441	24	12	-	-	PUNCT
ejpam-4441	24	13	stirling	stirling	NOUN
ejpam-4441	24	14	numbers	number	NOUN
ejpam-4441	24	15	of	of	ADP
ejpam-4441	24	16	the	the	DET
ejpam-4441	24	17	second	second	ADJ
ejpam-4441	24	18	as	as	SCONJ
ejpam-4441	24	19	the	the	DET
ejpam-4441	24	20	coefficients	coefficient	NOUN
ejpam-4441	24	21	appearing	appear	VERB
ejpam-4441	24	22	when	when	SCONJ
ejpam-4441	24	23	powers	power	NOUN
ejpam-4441	24	24	of	of	ADP
ejpam-4441	24	25	x+	x+	X
ejpam-4441	24	26	r	r	NOUN
ejpam-4441	24	27	are	be	AUX
ejpam-4441	24	28	expressed	express	VERB
ejpam-4441	24	29	in	in	ADP
ejpam-4441	24	30	terms	term	NOUN
ejpam-4441	24	31	of	of	ADP
ejpam-4441	24	32	the	the	DET
ejpam-4441	24	33	degenerate	degenerate	ADJ
ejpam-4441	24	34	falling	fall	VERB
ejpam-4441	24	35	factorial	factorial	ADJ
ejpam-4441	24	36	sequence	sequence	NOUN
ejpam-4441	24	37	.	.	PUNCT
ejpam-4441	25	1	in	in	ADP
ejpam-4441	25	2	the	the	DET
ejpam-4441	25	3	special	special	ADJ
ejpam-4441	25	4	case	case	NOUN
ejpam-4441	25	5	of	of	ADP
ejpam-4441	25	6	r	r	NOUN
ejpam-4441	25	7	=	=	SYM
ejpam-4441	25	8	0	0	NUM
ejpam-4441	25	9	,	,	PUNCT
ejpam-4441	25	10	we	we	PRON
ejpam-4441	25	11	get	get	VERB
ejpam-4441	25	12	the	the	DET
ejpam-4441	25	13	λ	λ	PROPN
ejpam-4441	25	14	-analogues	-analogue	NOUN
ejpam-4441	25	15	of	of	ADP
ejpam-4441	25	16	stirling	stirling	NOUN
ejpam-4441	25	17	numbers	number	NOUN
ejpam-4441	25	18	of	of	ADP
ejpam-4441	25	19	the	the	DET
ejpam-4441	25	20	second	second	ADJ
ejpam-4441	25	21	kind	kind	NOUN
ejpam-4441	25	22	.	.	PUNCT
ejpam-4441	26	1	in	in	ADP
ejpam-4441	26	2	theorem	theorem	NOUN
ejpam-4441	26	3	1	1	NUM
ejpam-4441	26	4	,	,	PUNCT
ejpam-4441	26	5	we	we	PRON
ejpam-4441	26	6	obtain	obtain	VERB
ejpam-4441	26	7	the	the	DET
ejpam-4441	26	8	generating	generate	VERB
ejpam-4441	26	9	function	function	NOUN
ejpam-4441	26	10	of	of	ADP
ejpam-4441	26	11	the	the	DET
ejpam-4441	26	12	λ	λ	PROPN
ejpam-4441	26	13	-analogues	-analogue	NOUN
ejpam-4441	26	14	of	of	ADP
ejpam-4441	26	15	r	r	NOUN
ejpam-4441	26	16	-	-	PUNCT
ejpam-4441	26	17	stirling	stirling	NOUN
ejpam-4441	26	18	numbers	number	NOUN
ejpam-4441	26	19	of	of	ADP
ejpam-4441	26	20	the	the	DET
ejpam-4441	26	21	second	second	NOUN
ejpam-4441	26	22	.	.	PUNCT
ejpam-4441	27	1	we	we	PRON
ejpam-4441	27	2	express	express	VERB
ejpam-4441	27	3	those	those	DET
ejpam-4441	27	4	numbers	number	NOUN
ejpam-4441	27	5	in	in	ADP
ejpam-4441	27	6	terms	term	NOUN
ejpam-4441	27	7	of	of	ADP
ejpam-4441	27	8	the	the	DET
ejpam-4441	27	9	forward	forward	ADJ
ejpam-4441	27	10	difference	difference	NOUN
ejpam-4441	27	11	operator	operator	NOUN
ejpam-4441	27	12	in	in	ADP
ejpam-4441	27	13	theorem	theorem	NOUN
ejpam-4441	27	14	2	2	NUM
ejpam-4441	27	15	.	.	PUNCT
ejpam-4441	27	16	in	in	ADP
ejpam-4441	27	17	theorems	theorem	NOUN
ejpam-4441	27	18	3	3	NUM
ejpam-4441	27	19	and	and	CCONJ
ejpam-4441	27	20	6	6	NUM
ejpam-4441	27	21	,	,	PUNCT
ejpam-4441	27	22	we	we	PRON
ejpam-4441	27	23	find	find	VERB
ejpam-4441	27	24	an	an	DET
ejpam-4441	27	25	expression	expression	NOUN
ejpam-4441	27	26	of	of	ADP
ejpam-4441	27	27	the	the	DET
ejpam-4441	27	28	analogues	analogue	NOUN
ejpam-4441	27	29	of	of	ADP
ejpam-4441	27	30	r	r	NOUN
ejpam-4441	27	31	-	-	PUNCT
ejpam-4441	27	32	stirling	stirling	NOUN
ejpam-4441	27	33	numbers	number	NOUN
ejpam-4441	27	34	of	of	ADP
ejpam-4441	27	35	the	the	DET
ejpam-4441	27	36	second	second	ADJ
ejpam-4441	27	37	kind	kind	NOUN
ejpam-4441	27	38	in	in	ADP
ejpam-4441	27	39	terms	term	NOUN
ejpam-4441	27	40	of	of	ADP
ejpam-4441	27	41	the	the	DET
ejpam-4441	27	42	analogues	analogue	NOUN
ejpam-4441	27	43	of	of	ADP
ejpam-4441	27	44	stirling	stirling	NOUN
ejpam-4441	27	45	numbers	number	NOUN
ejpam-4441	27	46	of	of	ADP
ejpam-4441	27	47	the	the	DET
ejpam-4441	27	48	second	second	ADJ
ejpam-4441	27	49	kind	kind	NOUN
ejpam-4441	27	50	and	and	CCONJ
ejpam-4441	27	51	vice	vice	ADV
ejpam-4441	27	52	versa	versa	ADV
ejpam-4441	27	53	.	.	PUNCT
ejpam-4441	28	1	in	in	ADP
ejpam-4441	28	2	theorems	theorem	NOUN
ejpam-4441	28	3	4	4	NUM
ejpam-4441	28	4	and	and	CCONJ
ejpam-4441	28	5	5	5	NUM
ejpam-4441	28	6	,	,	PUNCT
ejpam-4441	28	7	we	we	PRON
ejpam-4441	28	8	get	get	VERB
ejpam-4441	28	9	recurrence	recurrence	NOUN
ejpam-4441	28	10	relations	relation	NOUN
ejpam-4441	28	11	for	for	ADP
ejpam-4441	28	12	the	the	DET
ejpam-4441	28	13	analogues	analogue	NOUN
ejpam-4441	28	14	of	of	ADP
ejpam-4441	28	15	r	r	NOUN
ejpam-4441	28	16	-	-	PUNCT
ejpam-4441	28	17	stirling	stirling	NOUN
ejpam-4441	28	18	numbers	number	NOUN
ejpam-4441	28	19	of	of	ADP
ejpam-4441	28	20	the	the	DET
ejpam-4441	28	21	second	second	ADJ
ejpam-4441	28	22	kind	kind	NOUN
ejpam-4441	28	23	.	.	PUNCT
ejpam-4441	29	1	in	in	ADP
ejpam-4441	29	2	theorem	theorem	NOUN
ejpam-4441	29	3	7	7	NUM
ejpam-4441	29	4	,	,	PUNCT
ejpam-4441	29	5	we	we	PRON
ejpam-4441	29	6	derive	derive	VERB
ejpam-4441	29	7	an	an	DET
ejpam-4441	29	8	identity	identity	NOUN
ejpam-4441	29	9	connecting	connect	VERB
ejpam-4441	29	10	the	the	DET
ejpam-4441	29	11	analogues	analogue	NOUN
ejpam-4441	29	12	of	of	ADP
ejpam-4441	29	13	r	r	NOUN
ejpam-4441	29	14	-	-	PUNCT
ejpam-4441	29	15	stirling	stirling	NOUN
ejpam-4441	29	16	numbers	number	NOUN
ejpam-4441	29	17	of	of	ADP
ejpam-4441	29	18	the	the	DET
ejpam-4441	29	19	second	second	ADJ
ejpam-4441	29	20	kind	kind	NOUN
ejpam-4441	29	21	and	and	CCONJ
ejpam-4441	29	22	some	some	DET
ejpam-4441	29	23	values	value	NOUN
ejpam-4441	29	24	of	of	ADP
ejpam-4441	29	25	the	the	DET
ejpam-4441	29	26	higher	high	ADJ
ejpam-4441	29	27	order	order	NOUN
ejpam-4441	29	28	bernoulli	bernoulli	NOUN
ejpam-4441	29	29	polynomials	polynomial	NOUN
ejpam-4441	29	30	.	.	PUNCT
ejpam-4441	30	1	in	in	ADP
ejpam-4441	30	2	section	section	NOUN
ejpam-4441	30	3	3	3	NUM
ejpam-4441	30	4	,	,	PUNCT
ejpam-4441	30	5	introduced	introduce	VERB
ejpam-4441	30	6	are	be	AUX
ejpam-4441	30	7	the	the	DET
ejpam-4441	30	8	λ	λ	PROPN
ejpam-4441	30	9	-analogues	-analogue	NOUN
ejpam-4441	30	10	of	of	ADP
ejpam-4441	30	11	whitney	whitney	NOUN
ejpam-4441	30	12	-	-	PUNCT
ejpam-4441	30	13	type	type	NOUN
ejpam-4441	30	14	r	r	NOUN
ejpam-4441	30	15	-	-	PUNCT
ejpam-4441	30	16	stirling	stirling	NOUN
ejpam-4441	30	17	numbers	number	NOUN
ejpam-4441	30	18	of	of	ADP
ejpam-4441	30	19	the	the	DET
ejpam-4441	30	20	second	second	NOUN
ejpam-4441	30	21	.	.	PUNCT
ejpam-4441	31	1	in	in	ADP
ejpam-4441	31	2	case	case	NOUN
ejpam-4441	31	3	of	of	ADP
ejpam-4441	31	4	r	r	NOUN
ejpam-4441	31	5	=	=	SYM
ejpam-4441	31	6	1	1	NUM
ejpam-4441	31	7	,	,	PUNCT
ejpam-4441	31	8	we	we	PRON
ejpam-4441	31	9	get	get	VERB
ejpam-4441	31	10	the	the	DET
ejpam-4441	31	11	λ	λ	PROPN
ejpam-4441	31	12	-analogues	-analogue	NOUN
ejpam-4441	31	13	of	of	ADP
ejpam-4441	31	14	whitney	whitney	NOUN
ejpam-4441	31	15	-	-	PUNCT
ejpam-4441	31	16	type	type	NOUN
ejpam-4441	31	17	stirling	stirling	NOUN
ejpam-4441	31	18	numbers	number	NOUN
ejpam-4441	31	19	of	of	ADP
ejpam-4441	31	20	the	the	DET
ejpam-4441	31	21	second	second	NOUN
ejpam-4441	31	22	.	.	PUNCT
ejpam-4441	32	1	the	the	DET
ejpam-4441	32	2	generating	generate	VERB
ejpam-4441	32	3	function	function	NOUN
ejpam-4441	32	4	of	of	ADP
ejpam-4441	32	5	those	those	DET
ejpam-4441	32	6	numbers	number	NOUN
ejpam-4441	32	7	are	be	AUX
ejpam-4441	32	8	derived	derive	VERB
ejpam-4441	32	9	in	in	ADP
ejpam-4441	32	10	theorem	theorem	NOUN
ejpam-4441	32	11	12	12	NUM
ejpam-4441	32	12	.	.	PUNCT
ejpam-4441	33	1	in	in	ADP
ejpam-4441	33	2	theorem	theorem	NOUN
ejpam-4441	33	3	13	13	NUM
ejpam-4441	33	4	,	,	PUNCT
ejpam-4441	33	5	we	we	PRON
ejpam-4441	33	6	obtain	obtain	VERB
ejpam-4441	33	7	an	an	DET
ejpam-4441	33	8	identity	identity	NOUN
ejpam-4441	33	9	relating	relate	VERB
ejpam-4441	33	10	the	the	DET
ejpam-4441	33	11	λ	λ	PROPN
ejpam-4441	33	12	-analogues	-analogue	NOUN
ejpam-4441	33	13	of	of	ADP
ejpam-4441	33	14	whitney	whitney	NOUN
ejpam-4441	33	15	-	-	PUNCT
ejpam-4441	33	16	type	type	NOUN
ejpam-4441	33	17	r	r	NOUN
ejpam-4441	33	18	-	-	PUNCT
ejpam-4441	33	19	stirling	stirling	NOUN
ejpam-4441	33	20	numbers	number	NOUN
ejpam-4441	33	21	of	of	ADP
ejpam-4441	33	22	the	the	DET
ejpam-4441	33	23	second	second	ADJ
ejpam-4441	33	24	,	,	PUNCT
ejpam-4441	33	25	the	the	DET
ejpam-4441	33	26	λ	λ	PROPN
ejpam-4441	33	27	-analogues	-analogue	NOUN
ejpam-4441	33	28	of	of	ADP
ejpam-4441	33	29	whitney	whitney	NOUN
ejpam-4441	33	30	-	-	PUNCT
ejpam-4441	33	31	type	type	NOUN
ejpam-4441	33	32	stirling	stirling	NOUN
ejpam-4441	33	33	numbers	number	NOUN
ejpam-4441	33	34	of	of	ADP
ejpam-4441	33	35	the	the	DET
ejpam-4441	33	36	second	second	ADJ
ejpam-4441	33	37	and	and	CCONJ
ejpam-4441	33	38	some	some	DET
ejpam-4441	33	39	values	value	NOUN
ejpam-4441	33	40	of	of	ADP
ejpam-4441	33	41	higher	high	ADJ
ejpam-4441	33	42	order	order	NOUN
ejpam-4441	33	43	bernoulli	bernoulli	NOUN
ejpam-4441	33	44	numbers	number	NOUN
ejpam-4441	33	45	.	.	PUNCT
ejpam-4441	34	1	we	we	PRON
ejpam-4441	34	2	introduce	introduce	VERB
ejpam-4441	34	3	the	the	DET
ejpam-4441	34	4	λ	λ	PROPN
ejpam-4441	34	5	-analogues	-analogue	NOUN
ejpam-4441	34	6	of	of	ADP
ejpam-4441	34	7	dowling	dowle	VERB
ejpam-4441	34	8	polynomials	polynomial	NOUN
ejpam-4441	34	9	,	,	PUNCT
ejpam-4441	34	10	and	and	CCONJ
ejpam-4441	34	11	deduce	deduce	VERB
ejpam-4441	34	12	the	the	DET
ejpam-4441	34	13	generating	generate	VERB
ejpam-4441	34	14	function	function	NOUN
ejpam-4441	34	15	and	and	CCONJ
ejpam-4441	34	16	dobinski	dobinski	ADJ
ejpam-4441	34	17	-	-	PUNCT
ejpam-4441	34	18	like	like	ADJ
ejpam-4441	34	19	formula	formula	NOUN
ejpam-4441	34	20	in	in	ADP
ejpam-4441	34	21	theorems	theorem	NOUN
ejpam-4441	34	22	10	10	NUM
ejpam-4441	34	23	and	and	CCONJ
ejpam-4441	34	24	11	11	NUM
ejpam-4441	34	25	,	,	PUNCT
ejpam-4441	34	26	respectively	respectively	ADV
ejpam-4441	34	27	.	.	PUNCT
ejpam-4441	35	1	in	in	ADP
ejpam-4441	35	2	the	the	DET
ejpam-4441	35	3	rest	rest	NOUN
ejpam-4441	35	4	of	of	ADP
ejpam-4441	35	5	this	this	DET
ejpam-4441	35	6	section	section	NOUN
ejpam-4441	35	7	,	,	PUNCT
ejpam-4441	35	8	we	we	PRON
ejpam-4441	35	9	recall	recall	VERB
ejpam-4441	35	10	the	the	DET
ejpam-4441	35	11	facts	fact	NOUN
ejpam-4441	35	12	that	that	PRON
ejpam-4441	35	13	are	be	AUX
ejpam-4441	35	14	needed	need	VERB
ejpam-4441	35	15	in	in	ADP
ejpam-4441	35	16	this	this	DET
ejpam-4441	35	17	paper	paper	NOUN
ejpam-4441	35	18	.	.	PUNCT
ejpam-4441	36	1	throughout	throughout	ADP
ejpam-4441	36	2	this	this	DET
ejpam-4441	36	3	paper	paper	NOUN
ejpam-4441	36	4	,	,	PUNCT
ejpam-4441	36	5	let	let	VERB
ejpam-4441	36	6	λ	λ	PRON
ejpam-4441	36	7	be	be	AUX
ejpam-4441	36	8	any	any	DET
ejpam-4441	36	9	nonzero	nonzero	ADJ
ejpam-4441	36	10	real	real	ADJ
ejpam-4441	36	11	number	number	NOUN
ejpam-4441	36	12	.	.	PUNCT
ejpam-4441	37	1	the	the	DET
ejpam-4441	37	2	generalized	generalized	ADJ
ejpam-4441	37	3	falling	fall	VERB
ejpam-4441	37	4	factorial	factorial	NOUN
ejpam-4441	37	5	sequence	sequence	NOUN
ejpam-4441	37	6	is	be	AUX
ejpam-4441	37	7	defined	define	VERB
ejpam-4441	37	8	by	by	ADP
ejpam-4441	37	9	(	(	PUNCT
ejpam-4441	37	10	x)0,λ	x)0,λ	NOUN
ejpam-4441	37	11	=	=	SYM
ejpam-4441	37	12	1	1	NUM
ejpam-4441	37	13	,	,	PUNCT
ejpam-4441	37	14	(	(	PUNCT
ejpam-4441	37	15	x)n	x)n	PROPN
ejpam-4441	37	16	,	,	PUNCT
ejpam-4441	37	17	λ	λ	PROPN
ejpam-4441	37	18	=	=	PUNCT
ejpam-4441	37	19	x(x−λ	x(x−λ	PROPN
ejpam-4441	37	20	)	)	PUNCT
ejpam-4441	37	21	·	·	PUNCT
ejpam-4441	37	22	·	·	PUNCT
ejpam-4441	38	1	·	·	PUNCT
ejpam-4441	38	2	(	(	PUNCT
ejpam-4441	38	3	x−	x−	PROPN
ejpam-4441	38	4	(	(	PUNCT
ejpam-4441	38	5	n−1)λ	n−1)λ	PROPN
ejpam-4441	38	6	)	)	PUNCT
ejpam-4441	38	7	,	,	PUNCT
ejpam-4441	38	8	(	(	PUNCT
ejpam-4441	38	9	n	n	CCONJ
ejpam-4441	38	10	≥	≥	NOUN
ejpam-4441	38	11	1	1	NUM
ejpam-4441	38	12	)	)	PUNCT
ejpam-4441	38	13	,	,	PUNCT
ejpam-4441	38	14	(	(	PUNCT
ejpam-4441	38	15	see	see	VERB
ejpam-4441	38	16	[	[	X
ejpam-4441	38	17	2	2	NUM
ejpam-4441	38	18	]	]	PUNCT
ejpam-4441	38	19	,	,	PUNCT
ejpam-4441	38	20	[	[	X
ejpam-4441	38	21	5	5	NUM
ejpam-4441	38	22	]	]	PUNCT
ejpam-4441	38	23	,	,	PUNCT
ejpam-4441	38	24	[	[	X
ejpam-4441	38	25	7	7	NUM
ejpam-4441	38	26	]	]	PUNCT
ejpam-4441	38	27	,	,	PUNCT
ejpam-4441	38	28	[	[	X
ejpam-4441	38	29	8	8	NUM
ejpam-4441	38	30	]	]	PUNCT
ejpam-4441	38	31	,	,	PUNCT
ejpam-4441	38	32	[	[	X
ejpam-4441	38	33	11	11	NUM
ejpam-4441	38	34	]	]	PUNCT
ejpam-4441	38	35	,	,	PUNCT
ejpam-4441	38	36	[	[	X
ejpam-4441	38	37	10	10	NUM
ejpam-4441	38	38	]	]	NUM
ejpam-4441	38	39	)	)	PUNCT
ejpam-4441	38	40	.	.	PUNCT
ejpam-4441	39	1	(	(	PUNCT
ejpam-4441	39	2	1	1	X
ejpam-4441	39	3	)	)	PUNCT
ejpam-4441	39	4	it	it	PRON
ejpam-4441	39	5	is	be	AUX
ejpam-4441	39	6	known	know	VERB
ejpam-4441	39	7	that	that	SCONJ
ejpam-4441	39	8	the	the	DET
ejpam-4441	39	9	degenerate	degenerate	ADJ
ejpam-4441	39	10	exponential	exponential	ADJ
ejpam-4441	39	11	functions	function	NOUN
ejpam-4441	39	12	are	be	AUX
ejpam-4441	39	13	defined	define	VERB
ejpam-4441	39	14	by	by	ADP
ejpam-4441	39	15	ex	ex	ADJ
ejpam-4441	39	16	λ	λ	PROPN
ejpam-4441	39	17	(	(	PUNCT
ejpam-4441	39	18	t	t	PROPN
ejpam-4441	39	19	)	)	PUNCT
ejpam-4441	39	20	=	=	PUNCT
ejpam-4441	40	1	(	(	PUNCT
ejpam-4441	40	2	1+λ	1+λ	NUM
ejpam-4441	40	3	t	t	NOUN
ejpam-4441	40	4	)	)	PUNCT
ejpam-4441	41	1	x	x	X
ejpam-4441	42	1	λ	λ	NOUN
ejpam-4441	42	2	=	=	SYM
ejpam-4441	42	3	∞	∞	NUM
ejpam-4441	42	4	∑	∑	SYM
ejpam-4441	42	5	n=0	n=0	NUM
ejpam-4441	42	6	(	(	PUNCT
ejpam-4441	42	7	x)n	x)n	PROPN
ejpam-4441	42	8	,	,	PUNCT
ejpam-4441	42	9	λ	λ	PROPN
ejpam-4441	42	10	tn	tn	NOUN
ejpam-4441	42	11	n	n	X
ejpam-4441	42	12	!	!	PROPN
ejpam-4441	42	13	,	,	PUNCT
ejpam-4441	42	14	(	(	PUNCT
ejpam-4441	42	15	see	see	VERB
ejpam-4441	42	16	[	[	X
ejpam-4441	42	17	3	3	NUM
ejpam-4441	42	18	]	]	PUNCT
ejpam-4441	42	19	,	,	PUNCT
ejpam-4441	42	20	[	[	X
ejpam-4441	42	21	6	6	NUM
ejpam-4441	42	22	]	]	PUNCT
ejpam-4441	42	23	,	,	PUNCT
ejpam-4441	43	1	[	[	X
ejpam-4441	43	2	9	9	NUM
ejpam-4441	43	3	]	]	NUM
ejpam-4441	43	4	)	)	PUNCT
ejpam-4441	43	5	.	.	PUNCT
ejpam-4441	44	1	(	(	PUNCT
ejpam-4441	44	2	2	2	X
ejpam-4441	44	3	)	)	PUNCT
ejpam-4441	44	4	when	when	SCONJ
ejpam-4441	44	5	x	x	PROPN
ejpam-4441	44	6	=	=	SYM
ejpam-4441	44	7	1	1	NUM
ejpam-4441	44	8	,	,	PUNCT
ejpam-4441	44	9	we	we	PRON
ejpam-4441	44	10	use	use	VERB
ejpam-4441	44	11	the	the	DET
ejpam-4441	44	12	notation	notation	NOUN
ejpam-4441	44	13	as	as	ADP
ejpam-4441	44	14	eλ	eλ	PROPN
ejpam-4441	44	15	(	(	PUNCT
ejpam-4441	44	16	t	t	NOUN
ejpam-4441	44	17	)	)	PUNCT
ejpam-4441	44	18	=	=	SYM
ejpam-4441	44	19	e1	e1	PROPN
ejpam-4441	44	20	λ	λ	PROPN
ejpam-4441	44	21	(	(	PUNCT
ejpam-4441	44	22	t	t	PROPN
ejpam-4441	44	23	)	)	PUNCT
ejpam-4441	44	24	.	.	PUNCT
ejpam-4441	45	1	for	for	ADP
ejpam-4441	45	2	n	n	PRON
ejpam-4441	45	3	≥	≥	NOUN
ejpam-4441	45	4	0	0	NUM
ejpam-4441	45	5	,	,	PUNCT
ejpam-4441	45	6	the	the	DET
ejpam-4441	45	7	stirling	stirling	NOUN
ejpam-4441	45	8	numbers	number	NOUN
ejpam-4441	45	9	of	of	ADP
ejpam-4441	45	10	the	the	DET
ejpam-4441	45	11	first	first	ADJ
ejpam-4441	45	12	kind	kind	NOUN
ejpam-4441	45	13	are	be	AUX
ejpam-4441	45	14	defined	define	VERB
ejpam-4441	45	15	by	by	ADP
ejpam-4441	45	16	(	(	PUNCT
ejpam-4441	45	17	x)n	x)n	PUNCT
ejpam-4441	45	18	=	=	SYM
ejpam-4441	45	19	n	n	PROPN
ejpam-4441	45	20	∑	∑	ADP
ejpam-4441	45	21	k=0	k=0	PROPN
ejpam-4441	45	22	s1(n	s1(n	PROPN
ejpam-4441	45	23	,	,	PUNCT
ejpam-4441	45	24	k)xk	k)xk	PROPN
ejpam-4441	45	25	,	,	PUNCT
ejpam-4441	45	26	(	(	PUNCT
ejpam-4441	45	27	see	see	VERB
ejpam-4441	45	28	[	[	X
ejpam-4441	45	29	1	1	NUM
ejpam-4441	45	30	]	]	PUNCT
ejpam-4441	45	31	,	,	PUNCT
ejpam-4441	46	1	[	[	X
ejpam-4441	46	2	2	2	NUM
ejpam-4441	46	3	]	]	PUNCT
ejpam-4441	46	4	,	,	PUNCT
ejpam-4441	46	5	[	[	X
ejpam-4441	46	6	4	4	NUM
ejpam-4441	46	7	]	]	PUNCT
ejpam-4441	46	8	,	,	PUNCT
ejpam-4441	46	9	[	[	X
ejpam-4441	46	10	6	6	NUM
ejpam-4441	46	11	]	]	PUNCT
ejpam-4441	46	12	,	,	PUNCT
ejpam-4441	46	13	[	[	X
ejpam-4441	46	14	12	12	NUM
ejpam-4441	46	15	]	]	PUNCT
ejpam-4441	46	16	,	,	PUNCT
ejpam-4441	46	17	[	[	X
ejpam-4441	46	18	14	14	NUM
ejpam-4441	46	19	]	]	SYM
ejpam-4441	46	20	)	)	PUNCT
ejpam-4441	47	1	,	,	PUNCT
ejpam-4441	47	2	(	(	PUNCT
ejpam-4441	47	3	3	3	X
ejpam-4441	47	4	)	)	PUNCT
ejpam-4441	47	5	d.	d.	PROPN
ejpam-4441	47	6	s.	s.	PROPN
ejpam-4441	47	7	kim	kim	PROPN
ejpam-4441	47	8	,	,	PUNCT
ejpam-4441	47	9	h.	h.	PROPN
ejpam-4441	47	10	k.	k.	PROPN
ejpam-4441	47	11	kim	kim	PROPN
ejpam-4441	47	12	,	,	PUNCT
ejpam-4441	47	13	t.	t.	PROPN
ejpam-4441	47	14	kim	kim	PROPN
ejpam-4441	47	15	/	/	SYM
ejpam-4441	47	16	eur	eur	PROPN
ejpam-4441	47	17	.	.	PUNCT
ejpam-4441	48	1	j.	j.	PROPN
ejpam-4441	48	2	pure	pure	PROPN
ejpam-4441	48	3	appl	appl	PROPN
ejpam-4441	48	4	.	.	PROPN
ejpam-4441	48	5	math	math	PROPN
ejpam-4441	48	6	,	,	PUNCT
ejpam-4441	48	7	15	15	NUM
ejpam-4441	48	8	(	(	PUNCT
ejpam-4441	48	9	3	3	NUM
ejpam-4441	48	10	)	)	PUNCT
ejpam-4441	48	11	(	(	PUNCT
ejpam-4441	48	12	2022	2022	NUM
ejpam-4441	48	13	)	)	PUNCT
ejpam-4441	48	14	,	,	PUNCT
ejpam-4441	48	15	1054	1054	NUM
ejpam-4441	48	16	-	-	SYM
ejpam-4441	48	17	1066	1066	NUM
ejpam-4441	48	18	1056	1056	NUM
ejpam-4441	48	19	where	where	SCONJ
ejpam-4441	48	20	the	the	DET
ejpam-4441	48	21	falling	fall	VERB
ejpam-4441	48	22	factorial	factorial	ADJ
ejpam-4441	48	23	sequence	sequence	NOUN
ejpam-4441	48	24	is	be	AUX
ejpam-4441	48	25	given	give	VERB
ejpam-4441	48	26	by	by	ADP
ejpam-4441	48	27	(	(	PUNCT
ejpam-4441	48	28	x)0	x)0	X
ejpam-4441	48	29	=	=	SYM
ejpam-4441	48	30	1	1	NUM
ejpam-4441	48	31	,	,	PUNCT
ejpam-4441	48	32	(	(	PUNCT
ejpam-4441	48	33	x)n	x)n	PUNCT
ejpam-4441	48	34	=	=	SYM
ejpam-4441	48	35	x(x−1	x(x−1	X
ejpam-4441	48	36	)	)	PUNCT
ejpam-4441	48	37	·	·	PUNCT
ejpam-4441	48	38	·	·	PUNCT
ejpam-4441	48	39	·	·	PUNCT
ejpam-4441	48	40	(	(	PUNCT
ejpam-4441	48	41	x−n+1	x−n+1	PROPN
ejpam-4441	48	42	)	)	PUNCT
ejpam-4441	48	43	,	,	PUNCT
ejpam-4441	48	44	(	(	PUNCT
ejpam-4441	48	45	n	n	X
ejpam-4441	48	46	≥	≥	NOUN
ejpam-4441	48	47	1	1	NUM
ejpam-4441	48	48	)	)	PUNCT
ejpam-4441	48	49	.	.	PUNCT
ejpam-4441	49	1	as	as	ADP
ejpam-4441	49	2	the	the	DET
ejpam-4441	49	3	inversion	inversion	NOUN
ejpam-4441	49	4	formula	formula	NOUN
ejpam-4441	49	5	of	of	ADP
ejpam-4441	49	6	(	(	PUNCT
ejpam-4441	49	7	3	3	NUM
ejpam-4441	49	8	)	)	PUNCT
ejpam-4441	49	9	,	,	PUNCT
ejpam-4441	49	10	the	the	DET
ejpam-4441	49	11	stirling	stirling	NOUN
ejpam-4441	49	12	numbers	number	NOUN
ejpam-4441	49	13	of	of	ADP
ejpam-4441	49	14	the	the	DET
ejpam-4441	49	15	second	second	ADJ
ejpam-4441	49	16	kind	kind	NOUN
ejpam-4441	49	17	are	be	AUX
ejpam-4441	49	18	defined	define	VERB
ejpam-4441	49	19	as	as	ADP
ejpam-4441	49	20	xn	xn	PROPN
ejpam-4441	49	21	=	=	PROPN
ejpam-4441	49	22	n	n	PROPN
ejpam-4441	49	23	∑	∑	PUNCT
ejpam-4441	49	24	k=0	k=0	PROPN
ejpam-4441	49	25	{	{	PUNCT
ejpam-4441	49	26	n	n	NOUN
ejpam-4441	49	27	k	k	NOUN
ejpam-4441	49	28	}	}	PUNCT
ejpam-4441	49	29	(	(	PUNCT
ejpam-4441	49	30	x)k	x)k	X
ejpam-4441	49	31	,	,	PUNCT
ejpam-4441	49	32	(	(	PUNCT
ejpam-4441	49	33	see	see	VERB
ejpam-4441	49	34	[	[	X
ejpam-4441	49	35	4	4	NUM
ejpam-4441	49	36	]	]	PUNCT
ejpam-4441	49	37	,	,	PUNCT
ejpam-4441	49	38	[	[	X
ejpam-4441	49	39	8	8	NUM
ejpam-4441	49	40	]	]	PUNCT
ejpam-4441	49	41	,	,	PUNCT
ejpam-4441	49	42	[	[	X
ejpam-4441	49	43	11	11	NUM
ejpam-4441	49	44	]	]	PUNCT
ejpam-4441	49	45	,	,	PUNCT
ejpam-4441	50	1	[	[	X
ejpam-4441	50	2	12	12	NUM
ejpam-4441	50	3	]	]	PUNCT
ejpam-4441	50	4	,	,	PUNCT
ejpam-4441	51	1	[	[	X
ejpam-4441	51	2	14	14	NUM
ejpam-4441	51	3	]	]	PUNCT
ejpam-4441	51	4	,	,	PUNCT
ejpam-4441	51	5	[	[	X
ejpam-4441	51	6	13	13	NUM
ejpam-4441	51	7	]	]	NUM
ejpam-4441	51	8	)	)	PUNCT
ejpam-4441	51	9	.	.	PUNCT
ejpam-4441	52	1	(	(	PUNCT
ejpam-4441	52	2	4	4	X
ejpam-4441	52	3	)	)	PUNCT
ejpam-4441	52	4	the	the	DET
ejpam-4441	52	5	λ	λ	PROPN
ejpam-4441	52	6	-analogues	-analogue	NOUN
ejpam-4441	52	7	of	of	ADP
ejpam-4441	52	8	stirling	stirling	NOUN
ejpam-4441	52	9	numbers	number	NOUN
ejpam-4441	52	10	of	of	ADP
ejpam-4441	52	11	the	the	DET
ejpam-4441	52	12	first	first	ADJ
ejpam-4441	52	13	kind	kind	NOUN
ejpam-4441	52	14	are	be	AUX
ejpam-4441	52	15	defined	define	VERB
ejpam-4441	52	16	by	by	ADP
ejpam-4441	52	17	(	(	PUNCT
ejpam-4441	52	18	x)n	x)n	PROPN
ejpam-4441	52	19	,	,	PUNCT
ejpam-4441	52	20	λ	λ	X
ejpam-4441	52	21	=	=	SYM
ejpam-4441	52	22	n	n	PROPN
ejpam-4441	52	23	∑	∑	ADP
ejpam-4441	53	1	k=0	k=0	PROPN
ejpam-4441	53	2	s1,λ	s1,λ	PROPN
ejpam-4441	53	3	(	(	PUNCT
ejpam-4441	53	4	n	n	CCONJ
ejpam-4441	53	5	,	,	PUNCT
ejpam-4441	53	6	k)x	k)x	X
ejpam-4441	53	7	k	k	NOUN
ejpam-4441	53	8	,	,	PUNCT
ejpam-4441	53	9	(	(	PUNCT
ejpam-4441	53	10	n	n	CCONJ
ejpam-4441	53	11	≥	≥	NOUN
ejpam-4441	53	12	0	0	NUM
ejpam-4441	53	13	)	)	PUNCT
ejpam-4441	53	14	,	,	PUNCT
ejpam-4441	53	15	(	(	PUNCT
ejpam-4441	53	16	see	see	VERB
ejpam-4441	53	17	[	[	X
ejpam-4441	53	18	8	8	NUM
ejpam-4441	53	19	]	]	NUM
ejpam-4441	53	20	)	)	PUNCT
ejpam-4441	53	21	.	.	PUNCT
ejpam-4441	54	1	(	(	PUNCT
ejpam-4441	54	2	5	5	NUM
ejpam-4441	54	3	)	)	PUNCT
ejpam-4441	54	4	for	for	ADP
ejpam-4441	54	5	r	r	NOUN
ejpam-4441	54	6	∈	∈	PROPN
ejpam-4441	54	7	n∪{0	n∪{0	NOUN
ejpam-4441	54	8	}	}	PUNCT
ejpam-4441	54	9	,	,	PUNCT
ejpam-4441	54	10	the	the	DET
ejpam-4441	54	11	λ	λ	PROPN
ejpam-4441	54	12	-analogues	-analogue	NOUN
ejpam-4441	54	13	of	of	ADP
ejpam-4441	54	14	r	r	NOUN
ejpam-4441	54	15	-	-	PUNCT
ejpam-4441	54	16	stirling	stirling	NOUN
ejpam-4441	54	17	numbers	number	NOUN
ejpam-4441	54	18	of	of	ADP
ejpam-4441	54	19	the	the	DET
ejpam-4441	54	20	first	first	ADJ
ejpam-4441	54	21	kind	kind	NOUN
ejpam-4441	54	22	are	be	AUX
ejpam-4441	54	23	defined	define	VERB
ejpam-4441	54	24	by	by	ADP
ejpam-4441	54	25	(	(	PUNCT
ejpam-4441	54	26	x+	x+	ADJ
ejpam-4441	54	27	r)n	r)n	NOUN
ejpam-4441	54	28	,	,	PUNCT
ejpam-4441	54	29	λ	λ	PROPN
ejpam-4441	54	30	=	=	SYM
ejpam-4441	54	31	n	n	PROPN
ejpam-4441	54	32	∑	∑	ADP
ejpam-4441	54	33	k=0	k=0	PROPN
ejpam-4441	54	34	s(r)1,λ	s(r)1,λ	X
ejpam-4441	54	35	(	(	PUNCT
ejpam-4441	54	36	n	n	CCONJ
ejpam-4441	54	37	,	,	PUNCT
ejpam-4441	54	38	k)x	k)x	X
ejpam-4441	54	39	k	k	NOUN
ejpam-4441	54	40	,	,	PUNCT
ejpam-4441	54	41	(	(	PUNCT
ejpam-4441	54	42	see	see	VERB
ejpam-4441	54	43	[	[	X
ejpam-4441	54	44	8	8	NUM
ejpam-4441	54	45	]	]	NUM
ejpam-4441	54	46	)	)	PUNCT
ejpam-4441	54	47	.	.	PUNCT
ejpam-4441	55	1	(	(	PUNCT
ejpam-4441	55	2	6	6	NUM
ejpam-4441	55	3	)	)	PUNCT
ejpam-4441	55	4	also	also	ADV
ejpam-4441	55	5	,	,	PUNCT
ejpam-4441	55	6	the	the	DET
ejpam-4441	55	7	λ	λ	PROPN
ejpam-4441	55	8	-analogues	-analogue	NOUN
ejpam-4441	55	9	of	of	ADP
ejpam-4441	55	10	unsigned	unsigned	ADJ
ejpam-4441	55	11	r	r	NOUN
ejpam-4441	55	12	-	-	PUNCT
ejpam-4441	55	13	stirling	stirling	NOUN
ejpam-4441	55	14	numbers	number	NOUN
ejpam-4441	55	15	of	of	ADP
ejpam-4441	55	16	the	the	DET
ejpam-4441	55	17	first	first	ADJ
ejpam-4441	55	18	kind	kind	NOUN
ejpam-4441	55	19	are	be	AUX
ejpam-4441	55	20	given	give	VERB
ejpam-4441	55	21	by	by	ADP
ejpam-4441	55	22	⟨x+	⟨x+	NOUN
ejpam-4441	55	23	r⟩n	r⟩n	NOUN
ejpam-4441	55	24	,	,	PUNCT
ejpam-4441	55	25	λ	λ	X
ejpam-4441	55	26	=	=	SYM
ejpam-4441	55	27	n	n	PROPN
ejpam-4441	55	28	∑	∑	PUNCT
ejpam-4441	55	29	k=0	k=0	PUNCT
ejpam-4441	55	30	[	[	PUNCT
ejpam-4441	55	31	n+	n+	ADP
ejpam-4441	55	32	r	r	NOUN
ejpam-4441	55	33	k+	k+	NOUN
ejpam-4441	55	34	r	r	NOUN
ejpam-4441	55	35	]	]	PUNCT
ejpam-4441	55	36	r	r	X
ejpam-4441	55	37	,	,	PUNCT
ejpam-4441	55	38	λ	λ	PROPN
ejpam-4441	55	39	xk	xk	PROPN
ejpam-4441	55	40	,	,	PUNCT
ejpam-4441	55	41	(	(	PUNCT
ejpam-4441	55	42	n	n	CCONJ
ejpam-4441	55	43	≥	≥	NOUN
ejpam-4441	55	44	0	0	NUM
ejpam-4441	55	45	)	)	PUNCT
ejpam-4441	56	1	,	,	PUNCT
ejpam-4441	56	2	(	(	PUNCT
ejpam-4441	56	3	see	see	VERB
ejpam-4441	56	4	[	[	X
ejpam-4441	56	5	8	8	NUM
ejpam-4441	56	6	]	]	NUM
ejpam-4441	56	7	)	)	PUNCT
ejpam-4441	56	8	.	.	PUNCT
ejpam-4441	57	1	(	(	PUNCT
ejpam-4441	57	2	7	7	X
ejpam-4441	57	3	)	)	PUNCT
ejpam-4441	57	4	note	note	NOUN
ejpam-4441	57	5	that	that	SCONJ
ejpam-4441	57	6	lim	lim	PROPN
ejpam-4441	57	7	λ→1	λ→1	X
ejpam-4441	57	8	[	[	PUNCT
ejpam-4441	57	9	n+	n+	ADP
ejpam-4441	57	10	r	r	NOUN
ejpam-4441	57	11	k+	k+	NOUN
ejpam-4441	57	12	r	r	NOUN
ejpam-4441	57	13	]	]	PUNCT
ejpam-4441	57	14	r	r	NOUN
ejpam-4441	57	15	,	,	PUNCT
ejpam-4441	57	16	λ	λ	X
ejpam-4441	57	17	=	=	PUNCT
ejpam-4441	57	18	[	[	PUNCT
ejpam-4441	57	19	n+	n+	NOUN
ejpam-4441	57	20	r	r	NOUN
ejpam-4441	57	21	k+	k+	NOUN
ejpam-4441	57	22	r	r	NOUN
ejpam-4441	57	23	]	]	PUNCT
ejpam-4441	57	24	r	r	NOUN
ejpam-4441	57	25	are	be	AUX
ejpam-4441	57	26	the	the	DET
ejpam-4441	57	27	ordinary	ordinary	ADJ
ejpam-4441	57	28	unsigned	unsigned	ADJ
ejpam-4441	57	29	r	r	NOUN
ejpam-4441	57	30	-	-	PUNCT
ejpam-4441	57	31	stirling	stirling	NOUN
ejpam-4441	57	32	numbers	number	NOUN
ejpam-4441	57	33	of	of	ADP
ejpam-4441	57	34	the	the	DET
ejpam-4441	57	35	first	first	ADJ
ejpam-4441	57	36	kind	kind	NOUN
ejpam-4441	57	37	.	.	PUNCT
ejpam-4441	58	1	2	2	X
ejpam-4441	58	2	.	.	X
ejpam-4441	58	3	λ	λ	X
ejpam-4441	58	4	-analogues	-analogue	NOUN
ejpam-4441	58	5	of	of	ADP
ejpam-4441	58	6	r	r	NOUN
ejpam-4441	58	7	-	-	PUNCT
ejpam-4441	58	8	stirling	stirling	NOUN
ejpam-4441	58	9	numbers	number	NOUN
ejpam-4441	58	10	of	of	ADP
ejpam-4441	58	11	the	the	DET
ejpam-4441	58	12	second	second	ADJ
ejpam-4441	58	13	kind	kind	NOUN
ejpam-4441	58	14	first	first	ADV
ejpam-4441	58	15	,	,	PUNCT
ejpam-4441	58	16	we	we	PRON
ejpam-4441	58	17	consider	consider	VERB
ejpam-4441	58	18	the	the	DET
ejpam-4441	58	19	λ	λ	PROPN
ejpam-4441	58	20	-analogues	-analogue	NOUN
ejpam-4441	58	21	of	of	ADP
ejpam-4441	58	22	stirling	stirling	NOUN
ejpam-4441	58	23	numbers	number	NOUN
ejpam-4441	58	24	of	of	ADP
ejpam-4441	58	25	the	the	DET
ejpam-4441	58	26	second	second	ADJ
ejpam-4441	58	27	kind	kind	NOUN
ejpam-4441	58	28	as	as	ADP
ejpam-4441	58	29	the	the	DET
ejpam-4441	58	30	inversion	inversion	NOUN
ejpam-4441	58	31	formula	formula	NOUN
ejpam-4441	58	32	of	of	ADP
ejpam-4441	58	33	(	(	PUNCT
ejpam-4441	58	34	5	5	NUM
ejpam-4441	58	35	)	)	PUNCT
ejpam-4441	58	36	,	,	PUNCT
ejpam-4441	58	37	which	which	PRON
ejpam-4441	58	38	are	be	AUX
ejpam-4441	58	39	defined	define	VERB
ejpam-4441	58	40	by	by	ADP
ejpam-4441	58	41	xn	xn	PROPN
ejpam-4441	58	42	=	=	PROPN
ejpam-4441	59	1	n	n	PROPN
ejpam-4441	59	2	∑	∑	PUNCT
ejpam-4441	59	3	k=0	k=0	PROPN
ejpam-4441	59	4	{	{	PUNCT
ejpam-4441	59	5	n	n	NOUN
ejpam-4441	59	6	k	k	ADJ
ejpam-4441	59	7	}	}	PUNCT
ejpam-4441	59	8	λ	λ	PROPN
ejpam-4441	59	9	(	(	PUNCT
ejpam-4441	59	10	x)k	x)k	X
ejpam-4441	59	11	,	,	PUNCT
ejpam-4441	59	12	λ	λ	PROPN
ejpam-4441	59	13	,	,	PUNCT
ejpam-4441	59	14	(	(	PUNCT
ejpam-4441	59	15	n	n	CCONJ
ejpam-4441	59	16	≥	≥	NOUN
ejpam-4441	59	17	0	0	NUM
ejpam-4441	59	18	)	)	PUNCT
ejpam-4441	59	19	.	.	PUNCT
ejpam-4441	60	1	(	(	PUNCT
ejpam-4441	60	2	8)	8)	NUM
ejpam-4441	60	3	from	from	ADP
ejpam-4441	60	4	(	(	PUNCT
ejpam-4441	60	5	8)	8)	NUM
ejpam-4441	60	6	,	,	PUNCT
ejpam-4441	60	7	we	we	PRON
ejpam-4441	60	8	note	note	VERB
ejpam-4441	60	9	that	that	SCONJ
ejpam-4441	60	10	ext	ext	NOUN
ejpam-4441	60	11	=	=	SYM
ejpam-4441	60	12	∞	∞	PROPN
ejpam-4441	60	13	∑	∑	PROPN
ejpam-4441	60	14	n=0	n=0	PROPN
ejpam-4441	60	15	tn	tn	NOUN
ejpam-4441	60	16	n	n	NOUN
ejpam-4441	60	17	!	!	PUNCT
ejpam-4441	60	18	xn	xn	PUNCT
ejpam-4441	61	1	=	=	SYM
ejpam-4441	61	2	∞	∞	NUM
ejpam-4441	61	3	∑	∑	PROPN
ejpam-4441	61	4	n=0	n=0	PROPN
ejpam-4441	61	5	tn	tn	NOUN
ejpam-4441	61	6	n	n	NOUN
ejpam-4441	61	7	!	!	PUNCT
ejpam-4441	62	1	n	n	CCONJ
ejpam-4441	62	2	∑	∑	ADV
ejpam-4441	62	3	k=0	k=0	PROPN
ejpam-4441	62	4	{	{	PUNCT
ejpam-4441	62	5	n	n	NOUN
ejpam-4441	62	6	k	k	ADJ
ejpam-4441	62	7	}	}	PUNCT
ejpam-4441	62	8	λ	λ	PROPN
ejpam-4441	62	9	(	(	PUNCT
ejpam-4441	62	10	x)k	x)k	X
ejpam-4441	62	11	,	,	PUNCT
ejpam-4441	62	12	λ	λ	X
ejpam-4441	62	13	=	=	SYM
ejpam-4441	62	14	∞	∞	NUM
ejpam-4441	62	15	∑	∑	PUNCT
ejpam-4441	62	16	k=0	k=0	PROPN
ejpam-4441	62	17	(	(	PUNCT
ejpam-4441	62	18	∞	∞	PROPN
ejpam-4441	62	19	∑	∑	PUNCT
ejpam-4441	62	20	n	n	CCONJ
ejpam-4441	62	21	=	=	SYM
ejpam-4441	62	22	k	k	X
ejpam-4441	62	23	{	{	PUNCT
ejpam-4441	62	24	n	n	NOUN
ejpam-4441	62	25	k	k	ADJ
ejpam-4441	62	26	}	}	PUNCT
ejpam-4441	62	27	λ	λ	PROPN
ejpam-4441	62	28	tn	tn	NOUN
ejpam-4441	62	29	n	n	X
ejpam-4441	62	30	!	!	PUNCT
ejpam-4441	62	31	)	)	PUNCT
ejpam-4441	63	1	(	(	PUNCT
ejpam-4441	63	2	x)k	x)k	X
ejpam-4441	63	3	,	,	PUNCT
ejpam-4441	63	4	λ	λ	INTJ
ejpam-4441	63	5	.	.	PUNCT
ejpam-4441	64	1	(	(	PUNCT
ejpam-4441	64	2	9	9	NUM
ejpam-4441	64	3	)	)	PUNCT
ejpam-4441	64	4	on	on	ADP
ejpam-4441	64	5	the	the	DET
ejpam-4441	64	6	other	other	ADJ
ejpam-4441	64	7	hand	hand	NOUN
ejpam-4441	64	8	,	,	PUNCT
ejpam-4441	64	9	by	by	ADP
ejpam-4441	64	10	(	(	PUNCT
ejpam-4441	64	11	1	1	NUM
ejpam-4441	64	12	)	)	PUNCT
ejpam-4441	64	13	,	,	PUNCT
ejpam-4441	64	14	we	we	PRON
ejpam-4441	64	15	get	get	VERB
ejpam-4441	64	16	ext	ext	NOUN
ejpam-4441	65	1	=	=	PUNCT
ejpam-4441	66	1	(	(	PUNCT
ejpam-4441	66	2	eλ	eλ	NOUN
ejpam-4441	66	3	t	t	PROPN
ejpam-4441	66	4	−1	−1	NOUN
ejpam-4441	66	5	+	+	PROPN
ejpam-4441	66	6	1	1	NUM
ejpam-4441	66	7	)	)	PUNCT
ejpam-4441	66	8	x	x	SYM
ejpam-4441	67	1	λ	λ	NOUN
ejpam-4441	67	2	=	=	SYM
ejpam-4441	67	3	∞	∞	PROPN
ejpam-4441	67	4	∑	∑	PUNCT
ejpam-4441	67	5	k=0	k=0	PROPN
ejpam-4441	67	6	(	(	PUNCT
ejpam-4441	67	7	x	x	PUNCT
ejpam-4441	67	8	λ	λ	X
ejpam-4441	67	9	k	k	PROPN
ejpam-4441	67	10	)	)	PUNCT
ejpam-4441	67	11	(	(	PUNCT
ejpam-4441	67	12	eλ	eλ	PROPN
ejpam-4441	67	13	t	t	X
ejpam-4441	67	14	−1)k	−1)k	PROPN
ejpam-4441	67	15	(	(	PUNCT
ejpam-4441	67	16	10	10	NUM
ejpam-4441	67	17	)	)	PUNCT
ejpam-4441	67	18	d.	d.	PROPN
ejpam-4441	67	19	s.	s.	PROPN
ejpam-4441	67	20	kim	kim	PROPN
ejpam-4441	67	21	,	,	PUNCT
ejpam-4441	67	22	h.	h.	PROPN
ejpam-4441	67	23	k.	k.	PROPN
ejpam-4441	67	24	kim	kim	PROPN
ejpam-4441	67	25	,	,	PUNCT
ejpam-4441	67	26	t.	t.	PROPN
ejpam-4441	67	27	kim	kim	PROPN
ejpam-4441	67	28	/	/	SYM
ejpam-4441	67	29	eur	eur	PROPN
ejpam-4441	67	30	.	.	PUNCT
ejpam-4441	68	1	j.	j.	PROPN
ejpam-4441	68	2	pure	pure	PROPN
ejpam-4441	68	3	appl	appl	PROPN
ejpam-4441	68	4	.	.	PROPN
ejpam-4441	68	5	math	math	PROPN
ejpam-4441	68	6	,	,	PUNCT
ejpam-4441	68	7	15	15	NUM
ejpam-4441	68	8	(	(	PUNCT
ejpam-4441	68	9	3	3	NUM
ejpam-4441	68	10	)	)	PUNCT
ejpam-4441	68	11	(	(	PUNCT
ejpam-4441	68	12	2022	2022	NUM
ejpam-4441	68	13	)	)	PUNCT
ejpam-4441	68	14	,	,	PUNCT
ejpam-4441	68	15	1054	1054	NUM
ejpam-4441	68	16	-	-	SYM
ejpam-4441	68	17	1066	1066	NUM
ejpam-4441	68	18	1057	1057	NUM
ejpam-4441	69	1	=	=	SYM
ejpam-4441	69	2	∞	∞	NUM
ejpam-4441	69	3	∑	∑	PUNCT
ejpam-4441	69	4	k=0	k=0	PUNCT
ejpam-4441	69	5	λ	λ	PROPN
ejpam-4441	69	6	−k	−k	NOUN
ejpam-4441	69	7	1	1	NUM
ejpam-4441	69	8	k	k	NOUN
ejpam-4441	69	9	!	!	PUNCT
ejpam-4441	70	1	(	(	PUNCT
ejpam-4441	70	2	eλ	eλ	PROPN
ejpam-4441	70	3	t	t	PROPN
ejpam-4441	70	4	−1	−1	NOUN
ejpam-4441	70	5	)	)	PUNCT
ejpam-4441	71	1	k	k	PROPN
ejpam-4441	71	2	(	(	PUNCT
ejpam-4441	71	3	x)k	x)k	X
ejpam-4441	71	4	,	,	PUNCT
ejpam-4441	71	5	λ	λ	INTJ
ejpam-4441	71	6	.	.	PUNCT
ejpam-4441	72	1	from	from	ADP
ejpam-4441	72	2	(	(	PUNCT
ejpam-4441	72	3	9	9	NUM
ejpam-4441	72	4	)	)	PUNCT
ejpam-4441	72	5	and	and	CCONJ
ejpam-4441	72	6	(	(	PUNCT
ejpam-4441	72	7	10	10	NUM
ejpam-4441	72	8	)	)	PUNCT
ejpam-4441	72	9	,	,	PUNCT
ejpam-4441	72	10	we	we	PRON
ejpam-4441	72	11	note	note	VERB
ejpam-4441	72	12	that	that	SCONJ
ejpam-4441	72	13	1	1	NUM
ejpam-4441	72	14	λ	λ	SYM
ejpam-4441	72	15	k	k	PROPN
ejpam-4441	72	16	1	1	NUM
ejpam-4441	72	17	k	k	NOUN
ejpam-4441	72	18	!	!	PUNCT
ejpam-4441	73	1	(	(	PUNCT
ejpam-4441	73	2	eλ	eλ	PROPN
ejpam-4441	73	3	t	t	PROPN
ejpam-4441	73	4	−1	−1	NOUN
ejpam-4441	73	5	)	)	PUNCT
ejpam-4441	74	1	k	k	X
ejpam-4441	74	2	=	=	SYM
ejpam-4441	74	3	∞	∞	NUM
ejpam-4441	74	4	∑	∑	PUNCT
ejpam-4441	74	5	n	n	CCONJ
ejpam-4441	74	6	=	=	SYM
ejpam-4441	74	7	k	k	X
ejpam-4441	74	8	{	{	PUNCT
ejpam-4441	74	9	n	n	NOUN
ejpam-4441	74	10	k	k	ADJ
ejpam-4441	74	11	}	}	PUNCT
ejpam-4441	74	12	λ	λ	PROPN
ejpam-4441	74	13	tn	tn	NOUN
ejpam-4441	74	14	n	n	X
ejpam-4441	74	15	!	!	PUNCT
ejpam-4441	74	16	.	.	PUNCT
ejpam-4441	75	1	(	(	PUNCT
ejpam-4441	75	2	11	11	X
ejpam-4441	75	3	)	)	PUNCT
ejpam-4441	75	4	note	note	NOUN
ejpam-4441	75	5	that	that	SCONJ
ejpam-4441	75	6	lim	lim	PROPN
ejpam-4441	75	7	λ→0	λ→0	PUNCT
ejpam-4441	75	8	{	{	PUNCT
ejpam-4441	75	9	n	n	PROPN
ejpam-4441	75	10	k	k	ADJ
ejpam-4441	75	11	}	}	PUNCT
ejpam-4441	75	12	λ	λ	PROPN
ejpam-4441	75	13	=	=	SYM
ejpam-4441	75	14	{	{	PUNCT
ejpam-4441	75	15	n	n	CCONJ
ejpam-4441	75	16	k	k	PROPN
ejpam-4441	75	17	}	}	PUNCT
ejpam-4441	75	18	are	be	AUX
ejpam-4441	75	19	the	the	DET
ejpam-4441	75	20	stirling	stirling	NOUN
ejpam-4441	75	21	numbers	number	NOUN
ejpam-4441	75	22	of	of	ADP
ejpam-4441	75	23	the	the	DET
ejpam-4441	75	24	second	second	ADJ
ejpam-4441	75	25	kind	kind	NOUN
ejpam-4441	75	26	which	which	PRON
ejpam-4441	75	27	are	be	AUX
ejpam-4441	75	28	defined	define	VERB
ejpam-4441	75	29	by	by	ADP
ejpam-4441	75	30	xn	xn	PROPN
ejpam-4441	75	31	=	=	PROPN
ejpam-4441	75	32	n	n	PROPN
ejpam-4441	75	33	∑	∑	PUNCT
ejpam-4441	75	34	k=0	k=0	PROPN
ejpam-4441	75	35	{	{	PUNCT
ejpam-4441	75	36	n	n	NOUN
ejpam-4441	75	37	k	k	NOUN
ejpam-4441	75	38	}	}	PUNCT
ejpam-4441	75	39	(	(	PUNCT
ejpam-4441	75	40	x)k	x)k	X
ejpam-4441	75	41	,	,	PUNCT
ejpam-4441	75	42	(	(	PUNCT
ejpam-4441	75	43	n	n	X
ejpam-4441	75	44	≥	≥	NOUN
ejpam-4441	75	45	0	0	NUM
ejpam-4441	75	46	)	)	PUNCT
ejpam-4441	75	47	.	.	PUNCT
ejpam-4441	76	1	for	for	ADP
ejpam-4441	76	2	r	r	PROPN
ejpam-4441	76	3	∈	∈	PROPN
ejpam-4441	76	4	n∪	n∪	PROPN
ejpam-4441	76	5	{	{	PUNCT
ejpam-4441	76	6	0	0	NUM
ejpam-4441	76	7	}	}	PUNCT
ejpam-4441	76	8	,	,	PUNCT
ejpam-4441	76	9	we	we	PRON
ejpam-4441	76	10	consider	consider	VERB
ejpam-4441	76	11	the	the	DET
ejpam-4441	76	12	λ	λ	NOUN
ejpam-4441	76	13	-analogues	-analogue	NOUN
ejpam-4441	76	14	of	of	ADP
ejpam-4441	76	15	r	r	NOUN
ejpam-4441	76	16	-	-	PUNCT
ejpam-4441	76	17	stirling	stirling	NOUN
ejpam-4441	76	18	numbers	number	NOUN
ejpam-4441	76	19	of	of	ADP
ejpam-4441	76	20	the	the	DET
ejpam-4441	76	21	second	second	ADJ
ejpam-4441	76	22	kind	kind	NOUN
ejpam-4441	76	23	as	as	ADP
ejpam-4441	76	24	the	the	DET
ejpam-4441	76	25	inversion	inversion	NOUN
ejpam-4441	76	26	formula	formula	NOUN
ejpam-4441	76	27	of	of	ADP
ejpam-4441	76	28	(	(	PUNCT
ejpam-4441	76	29	6	6	NUM
ejpam-4441	76	30	)	)	PUNCT
ejpam-4441	76	31	which	which	PRON
ejpam-4441	76	32	are	be	AUX
ejpam-4441	76	33	defined	define	VERB
ejpam-4441	76	34	by	by	ADP
ejpam-4441	76	35	(	(	PUNCT
ejpam-4441	76	36	x+	x+	X
ejpam-4441	76	37	r)n	r)n	X
ejpam-4441	76	38	=	=	SYM
ejpam-4441	76	39	n	n	X
ejpam-4441	76	40	∑	∑	PUNCT
ejpam-4441	76	41	k=0	k=0	PROPN
ejpam-4441	76	42	{	{	PUNCT
ejpam-4441	76	43	n+	n+	ADP
ejpam-4441	76	44	r	r	NOUN
ejpam-4441	76	45	k+	k+	NOUN
ejpam-4441	76	46	r	r	NOUN
ejpam-4441	76	47	}	}	PUNCT
ejpam-4441	76	48	r	r	NOUN
ejpam-4441	76	49	,	,	PUNCT
ejpam-4441	76	50	λ	λ	PROPN
ejpam-4441	76	51	(	(	PUNCT
ejpam-4441	76	52	x)k	x)k	X
ejpam-4441	76	53	,	,	PUNCT
ejpam-4441	76	54	λ	λ	PROPN
ejpam-4441	76	55	,	,	PUNCT
ejpam-4441	76	56	(	(	PUNCT
ejpam-4441	76	57	n	n	CCONJ
ejpam-4441	76	58	≥	≥	NOUN
ejpam-4441	76	59	0	0	NUM
ejpam-4441	76	60	)	)	PUNCT
ejpam-4441	76	61	.	.	PUNCT
ejpam-4441	77	1	(	(	PUNCT
ejpam-4441	77	2	12	12	NUM
ejpam-4441	77	3	)	)	PUNCT
ejpam-4441	77	4	from	from	ADP
ejpam-4441	77	5	(	(	PUNCT
ejpam-4441	77	6	12	12	NUM
ejpam-4441	77	7	)	)	PUNCT
ejpam-4441	77	8	,	,	PUNCT
ejpam-4441	77	9	we	we	PRON
ejpam-4441	77	10	note	note	VERB
ejpam-4441	77	11	that	that	SCONJ
ejpam-4441	77	12	e(x+r)t	e(x+r)t	ADJ
ejpam-4441	78	1	=	=	PUNCT
ejpam-4441	78	2	∞	∞	NUM
ejpam-4441	78	3	∑	∑	PUNCT
ejpam-4441	78	4	n=0	n=0	NUM
ejpam-4441	78	5	(	(	PUNCT
ejpam-4441	78	6	x+	x+	X
ejpam-4441	78	7	r)n	r)n	X
ejpam-4441	78	8	tn	tn	NOUN
ejpam-4441	78	9	n	n	X
ejpam-4441	78	10	!	!	PUNCT
ejpam-4441	79	1	=	=	SYM
ejpam-4441	80	1	∞	∞	NUM
ejpam-4441	80	2	∑	∑	SYM
ejpam-4441	80	3	n=0	n=0	NUM
ejpam-4441	80	4	(	(	PUNCT
ejpam-4441	80	5	n	n	CCONJ
ejpam-4441	80	6	∑	∑	ADP
ejpam-4441	80	7	k=0	k=0	PROPN
ejpam-4441	80	8	{	{	PUNCT
ejpam-4441	80	9	n+	n+	ADP
ejpam-4441	80	10	r	r	NOUN
ejpam-4441	80	11	k+	k+	NOUN
ejpam-4441	80	12	r	r	NOUN
ejpam-4441	80	13	}	}	PUNCT
ejpam-4441	80	14	r	r	NOUN
ejpam-4441	80	15	,	,	PUNCT
ejpam-4441	80	16	λ	λ	PROPN
ejpam-4441	80	17	(	(	PUNCT
ejpam-4441	80	18	x)k	x)k	X
ejpam-4441	80	19	,	,	PUNCT
ejpam-4441	80	20	λ	λ	PROPN
ejpam-4441	80	21	)	)	PUNCT
ejpam-4441	80	22	tn	tn	PROPN
ejpam-4441	80	23	n	n	PROPN
ejpam-4441	80	24	!	!	PUNCT
ejpam-4441	81	1	(	(	PUNCT
ejpam-4441	81	2	13	13	NUM
ejpam-4441	81	3	)	)	PUNCT
ejpam-4441	81	4	=	=	SYM
ejpam-4441	82	1	∞	∞	PROPN
ejpam-4441	82	2	∑	∑	PUNCT
ejpam-4441	82	3	k=0	k=0	PROPN
ejpam-4441	82	4	(	(	PUNCT
ejpam-4441	82	5	∞	∞	PROPN
ejpam-4441	82	6	∑	∑	PUNCT
ejpam-4441	82	7	n	n	CCONJ
ejpam-4441	82	8	=	=	SYM
ejpam-4441	82	9	k	k	X
ejpam-4441	82	10	{	{	PUNCT
ejpam-4441	82	11	n+	n+	ADP
ejpam-4441	82	12	r	r	NOUN
ejpam-4441	82	13	k+	k+	NOUN
ejpam-4441	82	14	r	r	NOUN
ejpam-4441	82	15	}	}	PUNCT
ejpam-4441	82	16	r	r	NOUN
ejpam-4441	82	17	,	,	PUNCT
ejpam-4441	82	18	λ	λ	PROPN
ejpam-4441	82	19	tn	tn	NOUN
ejpam-4441	82	20	n	n	X
ejpam-4441	82	21	!	!	PUNCT
ejpam-4441	82	22	)	)	PUNCT
ejpam-4441	83	1	(	(	PUNCT
ejpam-4441	83	2	x)k	x)k	X
ejpam-4441	83	3	,	,	PUNCT
ejpam-4441	83	4	λ	λ	INTJ
ejpam-4441	83	5	.	.	PUNCT
ejpam-4441	84	1	on	on	ADP
ejpam-4441	84	2	the	the	DET
ejpam-4441	84	3	other	other	ADJ
ejpam-4441	84	4	hand	hand	NOUN
ejpam-4441	84	5	,	,	PUNCT
ejpam-4441	84	6	by	by	ADP
ejpam-4441	84	7	(	(	PUNCT
ejpam-4441	84	8	1	1	NUM
ejpam-4441	84	9	)	)	PUNCT
ejpam-4441	84	10	,	,	PUNCT
ejpam-4441	84	11	we	we	PRON
ejpam-4441	84	12	get	get	VERB
ejpam-4441	84	13	e(x+r)t	e(x+r)t	ADJ
ejpam-4441	84	14	=	=	PUNCT
ejpam-4441	84	15	ertext	ertext	NOUN
ejpam-4441	84	16	=	=	PUNCT
ejpam-4441	84	17	ert(eλ	ert(eλ	NOUN
ejpam-4441	84	18	t	t	NOUN
ejpam-4441	84	19	−1	−1	NOUN
ejpam-4441	84	20	+	+	NOUN
ejpam-4441	84	21	1	1	NUM
ejpam-4441	84	22	)	)	PUNCT
ejpam-4441	84	23	x	x	SYM
ejpam-4441	85	1	λ	λ	X
ejpam-4441	85	2	(	(	PUNCT
ejpam-4441	85	3	14	14	NUM
ejpam-4441	85	4	)	)	PUNCT
ejpam-4441	85	5	=	=	PRON
ejpam-4441	85	6	ert	ert	X
ejpam-4441	85	7	∞	∞	PROPN
ejpam-4441	85	8	∑	∑	X
ejpam-4441	85	9	k=0	k=0	PROPN
ejpam-4441	85	10	(	(	PUNCT
ejpam-4441	85	11	x	x	PUNCT
ejpam-4441	85	12	λ	λ	X
ejpam-4441	85	13	k	k	PROPN
ejpam-4441	85	14	)	)	PUNCT
ejpam-4441	85	15	(	(	PUNCT
ejpam-4441	85	16	eλ	eλ	PROPN
ejpam-4441	85	17	t	t	X
ejpam-4441	85	18	−1)k	−1)k	PROPN
ejpam-4441	85	19	=	=	SYM
ejpam-4441	86	1	∞	∞	NUM
ejpam-4441	86	2	∑	∑	PUNCT
ejpam-4441	86	3	k=0	k=0	PROPN
ejpam-4441	86	4	1	1	NUM
ejpam-4441	86	5	k	k	NOUN
ejpam-4441	86	6	(	(	PUNCT
ejpam-4441	86	7	eλ	eλ	PROPN
ejpam-4441	86	8	t	t	X
ejpam-4441	86	9	−1)kert	−1)kert	PROPN
ejpam-4441	86	10	1	1	NUM
ejpam-4441	86	11	λ	λ	X
ejpam-4441	86	12	k	k	PROPN
ejpam-4441	86	13	(	(	PUNCT
ejpam-4441	86	14	x)k	x)k	X
ejpam-4441	86	15	,	,	PUNCT
ejpam-4441	86	16	λ	λ	INTJ
ejpam-4441	86	17	.	.	PUNCT
ejpam-4441	87	1	from	from	ADP
ejpam-4441	87	2	(	(	PUNCT
ejpam-4441	87	3	13	13	NUM
ejpam-4441	87	4	)	)	PUNCT
ejpam-4441	87	5	and	and	CCONJ
ejpam-4441	87	6	(	(	PUNCT
ejpam-4441	87	7	14	14	NUM
ejpam-4441	87	8	)	)	PUNCT
ejpam-4441	87	9	,	,	PUNCT
ejpam-4441	87	10	we	we	PRON
ejpam-4441	87	11	note	note	VERB
ejpam-4441	87	12	that	that	SCONJ
ejpam-4441	87	13	1	1	NUM
ejpam-4441	87	14	λ	λ	SYM
ejpam-4441	87	15	k	k	PROPN
ejpam-4441	87	16	1	1	NUM
ejpam-4441	87	17	k	k	NOUN
ejpam-4441	87	18	!	!	PUNCT
ejpam-4441	88	1	(	(	PUNCT
ejpam-4441	88	2	eλ	eλ	PROPN
ejpam-4441	88	3	t	t	PROPN
ejpam-4441	88	4	−1	−1	NOUN
ejpam-4441	88	5	)	)	PUNCT
ejpam-4441	89	1	kert	kert	PROPN
ejpam-4441	89	2	=	=	PUNCT
ejpam-4441	89	3	∞	∞	PROPN
ejpam-4441	89	4	∑	∑	PUNCT
ejpam-4441	89	5	n	n	CCONJ
ejpam-4441	89	6	=	=	SYM
ejpam-4441	89	7	k	k	X
ejpam-4441	89	8	{	{	PUNCT
ejpam-4441	89	9	n+	n+	ADP
ejpam-4441	89	10	r	r	NOUN
ejpam-4441	89	11	k+	k+	NOUN
ejpam-4441	89	12	r	r	NOUN
ejpam-4441	89	13	}	}	PUNCT
ejpam-4441	89	14	r	r	NOUN
ejpam-4441	89	15	,	,	PUNCT
ejpam-4441	89	16	λ	λ	PROPN
ejpam-4441	89	17	tn	tn	NOUN
ejpam-4441	89	18	n	n	X
ejpam-4441	89	19	!	!	PUNCT
ejpam-4441	89	20	.	.	PUNCT
ejpam-4441	90	1	(	(	PUNCT
ejpam-4441	90	2	15	15	NUM
ejpam-4441	90	3	)	)	PUNCT
ejpam-4441	90	4	theorem	theorem	NOUN
ejpam-4441	90	5	1	1	NUM
ejpam-4441	90	6	.	.	PUNCT
ejpam-4441	91	1	the	the	DET
ejpam-4441	91	2	generating	generate	VERB
ejpam-4441	91	3	function	function	NOUN
ejpam-4441	91	4	of	of	ADP
ejpam-4441	91	5	the	the	DET
ejpam-4441	91	6	λ	λ	PROPN
ejpam-4441	91	7	-analogues	-analogue	NOUN
ejpam-4441	91	8	of	of	ADP
ejpam-4441	91	9	r	r	NOUN
ejpam-4441	91	10	-	-	PUNCT
ejpam-4441	91	11	stirling	stirling	NOUN
ejpam-4441	91	12	numbers	number	NOUN
ejpam-4441	91	13	of	of	ADP
ejpam-4441	91	14	the	the	DET
ejpam-4441	91	15	second	second	ADJ
ejpam-4441	91	16	kind	kind	NOUN
ejpam-4441	91	17	is	be	AUX
ejpam-4441	91	18	given	give	VERB
ejpam-4441	91	19	by	by	ADP
ejpam-4441	91	20	1	1	NUM
ejpam-4441	91	21	λ	λ	SYM
ejpam-4441	91	22	k	k	PROPN
ejpam-4441	91	23	1	1	NUM
ejpam-4441	91	24	k	k	NOUN
ejpam-4441	91	25	!	!	PUNCT
ejpam-4441	92	1	(	(	PUNCT
ejpam-4441	92	2	eλ	eλ	PROPN
ejpam-4441	92	3	t	t	PROPN
ejpam-4441	92	4	−1	−1	NOUN
ejpam-4441	92	5	)	)	PUNCT
ejpam-4441	93	1	kert	kert	PROPN
ejpam-4441	93	2	=	=	PUNCT
ejpam-4441	93	3	∞	∞	PROPN
ejpam-4441	93	4	∑	∑	PUNCT
ejpam-4441	93	5	n	n	CCONJ
ejpam-4441	93	6	=	=	SYM
ejpam-4441	93	7	k	k	X
ejpam-4441	93	8	{	{	PUNCT
ejpam-4441	93	9	n+	n+	ADP
ejpam-4441	93	10	r	r	NOUN
ejpam-4441	93	11	k+	k+	NOUN
ejpam-4441	93	12	r	r	NOUN
ejpam-4441	93	13	}	}	PUNCT
ejpam-4441	93	14	r	r	NOUN
ejpam-4441	93	15	,	,	PUNCT
ejpam-4441	93	16	λ	λ	PROPN
ejpam-4441	93	17	tn	tn	NOUN
ejpam-4441	93	18	n	n	X
ejpam-4441	93	19	!	!	PUNCT
ejpam-4441	93	20	,	,	PUNCT
ejpam-4441	93	21	(	(	PUNCT
ejpam-4441	93	22	k	k	X
ejpam-4441	93	23	≥	≥	PROPN
ejpam-4441	93	24	0	0	NUM
ejpam-4441	93	25	)	)	PUNCT
ejpam-4441	93	26	.	.	PUNCT
ejpam-4441	94	1	note	note	VERB
ejpam-4441	94	2	that	that	SCONJ
ejpam-4441	94	3	lim	lim	PROPN
ejpam-4441	94	4	λ→1	λ→1	X
ejpam-4441	94	5	{	{	PUNCT
ejpam-4441	94	6	n+	n+	ADP
ejpam-4441	94	7	r	r	NOUN
ejpam-4441	94	8	k+	k+	NOUN
ejpam-4441	94	9	r	r	NOUN
ejpam-4441	94	10	}	}	PUNCT
ejpam-4441	94	11	r	r	NOUN
ejpam-4441	94	12	,	,	PUNCT
ejpam-4441	94	13	λ	λ	NOUN
ejpam-4441	94	14	=	=	SYM
ejpam-4441	94	15	{	{	PUNCT
ejpam-4441	94	16	n+	n+	ADP
ejpam-4441	94	17	r	r	NOUN
ejpam-4441	94	18	k+	k+	NOUN
ejpam-4441	94	19	r	r	NOUN
ejpam-4441	94	20	}	}	PUNCT
ejpam-4441	94	21	r	r	NOUN
ejpam-4441	94	22	are	be	AUX
ejpam-4441	94	23	the	the	DET
ejpam-4441	94	24	ordinary	ordinary	ADJ
ejpam-4441	94	25	r	r	NOUN
ejpam-4441	94	26	-	-	PUNCT
ejpam-4441	94	27	stirling	stirling	NOUN
ejpam-4441	94	28	numbers	number	NOUN
ejpam-4441	94	29	of	of	ADP
ejpam-4441	94	30	the	the	DET
ejpam-4441	94	31	second	second	ADJ
ejpam-4441	94	32	kind	kind	NOUN
ejpam-4441	94	33	which	which	PRON
ejpam-4441	94	34	are	be	AUX
ejpam-4441	94	35	defined	define	VERB
ejpam-4441	94	36	by	by	ADP
ejpam-4441	94	37	(	(	PUNCT
ejpam-4441	94	38	x+	x+	X
ejpam-4441	94	39	r)n	r)n	X
ejpam-4441	94	40	=	=	SYM
ejpam-4441	94	41	n	n	X
ejpam-4441	94	42	∑	∑	PUNCT
ejpam-4441	94	43	k=0	k=0	PROPN
ejpam-4441	94	44	{	{	PUNCT
ejpam-4441	94	45	n+	n+	ADP
ejpam-4441	94	46	r	r	NOUN
ejpam-4441	94	47	k+	k+	NOUN
ejpam-4441	94	48	r	r	NOUN
ejpam-4441	94	49	}	}	PUNCT
ejpam-4441	94	50	r	r	NOUN
ejpam-4441	94	51	(	(	PUNCT
ejpam-4441	94	52	x)k	x)k	NOUN
ejpam-4441	94	53	,	,	PUNCT
ejpam-4441	94	54	(	(	PUNCT
ejpam-4441	94	55	n	n	X
ejpam-4441	94	56	≥	≥	NOUN
ejpam-4441	94	57	0	0	NUM
ejpam-4441	94	58	)	)	PUNCT
ejpam-4441	94	59	,	,	PUNCT
ejpam-4441	94	60	(	(	PUNCT
ejpam-4441	94	61	see	see	VERB
ejpam-4441	94	62	[	[	X
ejpam-4441	94	63	11	11	NUM
ejpam-4441	94	64	]	]	SYM
ejpam-4441	94	65	]	]	PUNCT
ejpam-4441	94	66	)	)	PUNCT
ejpam-4441	94	67	.	.	PUNCT
ejpam-4441	95	1	d.	d.	PROPN
ejpam-4441	95	2	s.	s.	PROPN
ejpam-4441	95	3	kim	kim	PROPN
ejpam-4441	95	4	,	,	PUNCT
ejpam-4441	95	5	h.	h.	PROPN
ejpam-4441	95	6	k.	k.	PROPN
ejpam-4441	95	7	kim	kim	PROPN
ejpam-4441	95	8	,	,	PUNCT
ejpam-4441	95	9	t.	t.	PROPN
ejpam-4441	95	10	kim	kim	PROPN
ejpam-4441	95	11	/	/	SYM
ejpam-4441	95	12	eur	eur	PROPN
ejpam-4441	95	13	.	.	PUNCT
ejpam-4441	96	1	j.	j.	PROPN
ejpam-4441	96	2	pure	pure	PROPN
ejpam-4441	96	3	appl	appl	PROPN
ejpam-4441	96	4	.	.	PROPN
ejpam-4441	96	5	math	math	PROPN
ejpam-4441	96	6	,	,	PUNCT
ejpam-4441	96	7	15	15	NUM
ejpam-4441	96	8	(	(	PUNCT
ejpam-4441	96	9	3	3	NUM
ejpam-4441	96	10	)	)	PUNCT
ejpam-4441	96	11	(	(	PUNCT
ejpam-4441	96	12	2022	2022	NUM
ejpam-4441	96	13	)	)	PUNCT
ejpam-4441	96	14	,	,	PUNCT
ejpam-4441	96	15	1054	1054	NUM
ejpam-4441	96	16	-	-	SYM
ejpam-4441	96	17	1066	1066	NUM
ejpam-4441	96	18	1058	1058	NUM
ejpam-4441	96	19	let	let	VERB
ejpam-4441	96	20	△	△	PROPN
ejpam-4441	96	21	be	be	AUX
ejpam-4441	96	22	the	the	DET
ejpam-4441	96	23	difference	difference	NOUN
ejpam-4441	96	24	operator	operator	NOUN
ejpam-4441	96	25	with	with	ADP
ejpam-4441	96	26	△	△	PROPN
ejpam-4441	96	27	f	f	X
ejpam-4441	96	28	(	(	PUNCT
ejpam-4441	96	29	x	x	X
ejpam-4441	96	30	)	)	PUNCT
ejpam-4441	97	1	=	=	SYM
ejpam-4441	97	2	f	f	PROPN
ejpam-4441	97	3	(	(	PUNCT
ejpam-4441	97	4	x+1)−	x+1)−	PROPN
ejpam-4441	97	5	f	f	PROPN
ejpam-4441	97	6	(	(	PUNCT
ejpam-4441	97	7	x	x	NOUN
ejpam-4441	97	8	)	)	PUNCT
ejpam-4441	97	9	.	.	PUNCT
ejpam-4441	98	1	then	then	ADV
ejpam-4441	98	2	we	we	PRON
ejpam-4441	98	3	have	have	VERB
ejpam-4441	98	4	△	△	PROPN
ejpam-4441	98	5	k	k	PROPN
ejpam-4441	98	6	f	f	X
ejpam-4441	98	7	(	(	PUNCT
ejpam-4441	98	8	x	x	X
ejpam-4441	98	9	)	)	PUNCT
ejpam-4441	98	10	=	=	SYM
ejpam-4441	99	1	k	k	X
ejpam-4441	99	2	∑	∑	PUNCT
ejpam-4441	99	3	l=0	l=0	PROPN
ejpam-4441	99	4	(	(	PUNCT
ejpam-4441	99	5	k	k	NOUN
ejpam-4441	99	6	l	l	NOUN
ejpam-4441	99	7	)	)	PUNCT
ejpam-4441	100	1	(	(	PUNCT
ejpam-4441	100	2	−1)k−l	−1)k−l	NOUN
ejpam-4441	100	3	f	f	X
ejpam-4441	100	4	(	(	PUNCT
ejpam-4441	100	5	x+	x+	PROPN
ejpam-4441	100	6	l	l	NOUN
ejpam-4441	100	7	)	)	PUNCT
ejpam-4441	100	8	.	.	PUNCT
ejpam-4441	101	1	(	(	PUNCT
ejpam-4441	101	2	16	16	NUM
ejpam-4441	101	3	)	)	PUNCT
ejpam-4441	101	4	from	from	ADP
ejpam-4441	101	5	theorem	theorem	ADJ
ejpam-4441	101	6	1	1	NUM
ejpam-4441	101	7	,	,	PUNCT
ejpam-4441	101	8	we	we	PRON
ejpam-4441	101	9	note	note	VERB
ejpam-4441	101	10	that	that	SCONJ
ejpam-4441	101	11	∞	∞	PROPN
ejpam-4441	101	12	∑	∑	PUNCT
ejpam-4441	101	13	n	n	CCONJ
ejpam-4441	101	14	=	=	SYM
ejpam-4441	101	15	k	k	X
ejpam-4441	101	16	{	{	PUNCT
ejpam-4441	101	17	n+	n+	ADP
ejpam-4441	101	18	r	r	NOUN
ejpam-4441	101	19	k+	k+	NOUN
ejpam-4441	101	20	r	r	NOUN
ejpam-4441	101	21	}	}	PUNCT
ejpam-4441	101	22	r	r	NOUN
ejpam-4441	101	23	,	,	PUNCT
ejpam-4441	101	24	λ	λ	PROPN
ejpam-4441	101	25	tn	tn	NOUN
ejpam-4441	101	26	n	n	NOUN
ejpam-4441	101	27	!	!	PUNCT
ejpam-4441	102	1	=	=	SYM
ejpam-4441	102	2	1	1	NUM
ejpam-4441	102	3	λ	λ	SYM
ejpam-4441	102	4	k	k	PROPN
ejpam-4441	102	5	1	1	NUM
ejpam-4441	102	6	k	k	NOUN
ejpam-4441	102	7	!	!	PUNCT
ejpam-4441	103	1	(	(	PUNCT
ejpam-4441	103	2	eλ	eλ	PROPN
ejpam-4441	103	3	t	t	PROPN
ejpam-4441	103	4	−1	−1	NOUN
ejpam-4441	103	5	)	)	PUNCT
ejpam-4441	104	1	kert	kert	PROPN
ejpam-4441	104	2	(	(	PUNCT
ejpam-4441	104	3	17	17	NUM
ejpam-4441	104	4	)	)	PUNCT
ejpam-4441	104	5	=	=	SYM
ejpam-4441	104	6	1	1	NUM
ejpam-4441	104	7	λ	λ	SYM
ejpam-4441	104	8	k	k	PROPN
ejpam-4441	104	9	1	1	NUM
ejpam-4441	104	10	k	k	NOUN
ejpam-4441	104	11	!	!	PUNCT
ejpam-4441	105	1	k	k	X
ejpam-4441	106	1	∑	∑	PUNCT
ejpam-4441	106	2	l=0	l=0	PROPN
ejpam-4441	106	3	(	(	PUNCT
ejpam-4441	106	4	k	k	NOUN
ejpam-4441	106	5	l	l	NOUN
ejpam-4441	106	6	)	)	PUNCT
ejpam-4441	107	1	(	(	PUNCT
ejpam-4441	107	2	−1)k−le(lλ+r)t	−1)k−le(lλ+r)t	PROPN
ejpam-4441	107	3	=	=	SYM
ejpam-4441	107	4	∞	∞	NUM
ejpam-4441	107	5	∑	∑	SYM
ejpam-4441	107	6	n=0	n=0	NUM
ejpam-4441	107	7	(	(	PUNCT
ejpam-4441	107	8	1	1	NUM
ejpam-4441	107	9	λ	λ	SYM
ejpam-4441	107	10	k	k	PROPN
ejpam-4441	107	11	1	1	NUM
ejpam-4441	107	12	k	k	NOUN
ejpam-4441	107	13	!	!	PUNCT
ejpam-4441	108	1	k	k	X
ejpam-4441	109	1	∑	∑	PUNCT
ejpam-4441	109	2	l=0	l=0	PROPN
ejpam-4441	109	3	(	(	PUNCT
ejpam-4441	109	4	k	k	NOUN
ejpam-4441	109	5	l	l	NOUN
ejpam-4441	109	6	)	)	PUNCT
ejpam-4441	109	7	(	(	PUNCT
ejpam-4441	109	8	−1)k−l(lλ	−1)k−l(lλ	NOUN
ejpam-4441	109	9	+	+	CCONJ
ejpam-4441	109	10	r)n	r)n	X
ejpam-4441	109	11	)	)	PUNCT
ejpam-4441	109	12	tn	tn	PROPN
ejpam-4441	109	13	n	n	PROPN
ejpam-4441	109	14	!	!	PUNCT
ejpam-4441	109	15	.	.	PUNCT
ejpam-4441	110	1	let	let	VERB
ejpam-4441	110	2	us	we	PRON
ejpam-4441	110	3	take	take	VERB
ejpam-4441	110	4	f	f	PROPN
ejpam-4441	110	5	(	(	PUNCT
ejpam-4441	110	6	x	x	NOUN
ejpam-4441	110	7	)	)	PUNCT
ejpam-4441	110	8	=	=	SYM
ejpam-4441	111	1	(	(	PUNCT
ejpam-4441	111	2	x	x	PART
ejpam-4441	111	3	λ	λ	NOUN
ejpam-4441	111	4	)	)	PUNCT
ejpam-4441	111	5	n	n	CCONJ
ejpam-4441	111	6	in	in	ADP
ejpam-4441	111	7	(	(	PUNCT
ejpam-4441	111	8	8)	8)	NUM
ejpam-4441	111	9	.	.	PUNCT
ejpam-4441	112	1	then	then	ADV
ejpam-4441	112	2	we	we	PRON
ejpam-4441	112	3	have	have	VERB
ejpam-4441	112	4	△	△	NOUN
ejpam-4441	112	5	k	k	X
ejpam-4441	112	6	(	(	PUNCT
ejpam-4441	112	7	r	r	NOUN
ejpam-4441	112	8	λ	λ	PROPN
ejpam-4441	112	9	)	)	PUNCT
ejpam-4441	112	10	n	n	NOUN
ejpam-4441	112	11	=	=	SYM
ejpam-4441	112	12	k	k	X
ejpam-4441	112	13	∑	∑	PUNCT
ejpam-4441	112	14	l=0	l=0	PROPN
ejpam-4441	112	15	(	(	PUNCT
ejpam-4441	112	16	k	k	NOUN
ejpam-4441	112	17	l	l	NOUN
ejpam-4441	112	18	)	)	PUNCT
ejpam-4441	112	19	(	(	PUNCT
ejpam-4441	112	20	−1)k−l	−1)k−l	X
ejpam-4441	112	21	(	(	PUNCT
ejpam-4441	112	22	l	l	NOUN
ejpam-4441	112	23	+	+	CCONJ
ejpam-4441	112	24	r	r	NOUN
ejpam-4441	112	25	λ	λ	NOUN
ejpam-4441	112	26	)	)	PUNCT
ejpam-4441	112	27	n	n	CCONJ
ejpam-4441	112	28	(	(	PUNCT
ejpam-4441	112	29	18	18	NUM
ejpam-4441	112	30	)	)	PUNCT
ejpam-4441	112	31	=	=	SYM
ejpam-4441	113	1	k	k	X
ejpam-4441	113	2	∑	∑	PUNCT
ejpam-4441	113	3	l=0	l=0	PROPN
ejpam-4441	113	4	(	(	PUNCT
ejpam-4441	113	5	k	k	NOUN
ejpam-4441	113	6	l	l	NOUN
ejpam-4441	113	7	)	)	PUNCT
ejpam-4441	113	8	(	(	PUNCT
ejpam-4441	113	9	−1)k−l(λ	−1)k−l(λ	NUM
ejpam-4441	113	10	l	l	NOUN
ejpam-4441	113	11	+	+	NOUN
ejpam-4441	113	12	r)n	r)n	X
ejpam-4441	113	13	λ	λ	NOUN
ejpam-4441	113	14	−n	−n	NOUN
ejpam-4441	113	15	.	.	PUNCT
ejpam-4441	114	1	by	by	ADP
ejpam-4441	114	2	(	(	PUNCT
ejpam-4441	114	3	17	17	NUM
ejpam-4441	114	4	)	)	PUNCT
ejpam-4441	114	5	and	and	CCONJ
ejpam-4441	114	6	(	(	PUNCT
ejpam-4441	114	7	18	18	NUM
ejpam-4441	114	8	)	)	PUNCT
ejpam-4441	114	9	,	,	PUNCT
ejpam-4441	114	10	we	we	PRON
ejpam-4441	114	11	get	get	VERB
ejpam-4441	114	12	∞	∞	PROPN
ejpam-4441	114	13	∑	∑	PUNCT
ejpam-4441	114	14	n	n	PROPN
ejpam-4441	114	15	=	=	SYM
ejpam-4441	114	16	k	k	X
ejpam-4441	114	17	{	{	PUNCT
ejpam-4441	114	18	n+	n+	ADP
ejpam-4441	114	19	r	r	NOUN
ejpam-4441	114	20	k+	k+	NOUN
ejpam-4441	114	21	r	r	NOUN
ejpam-4441	114	22	}	}	PUNCT
ejpam-4441	114	23	r	r	NOUN
ejpam-4441	114	24	,	,	PUNCT
ejpam-4441	114	25	λ	λ	PROPN
ejpam-4441	114	26	tn	tn	NOUN
ejpam-4441	114	27	n	n	NOUN
ejpam-4441	114	28	!	!	PUNCT
ejpam-4441	115	1	=	=	SYM
ejpam-4441	116	1	∞	∞	NUM
ejpam-4441	116	2	∑	∑	PUNCT
ejpam-4441	116	3	n=0	n=0	PROPN
ejpam-4441	116	4	λ	λ	PROPN
ejpam-4441	116	5	n−k	n−k	NOUN
ejpam-4441	116	6	1	1	NUM
ejpam-4441	116	7	k	k	X
ejpam-4441	116	8	!	!	PUNCT
ejpam-4441	116	9	△	△	PROPN
ejpam-4441	117	1	k	k	PROPN
ejpam-4441	117	2	(	(	PUNCT
ejpam-4441	117	3	r	r	NOUN
ejpam-4441	117	4	λ	λ	PROPN
ejpam-4441	117	5	)	)	PUNCT
ejpam-4441	117	6	n	n	PROPN
ejpam-4441	117	7	tn	tn	PROPN
ejpam-4441	117	8	n	n	X
ejpam-4441	117	9	!	!	PUNCT
ejpam-4441	117	10	.	.	PUNCT
ejpam-4441	118	1	(	(	PUNCT
ejpam-4441	118	2	19	19	NUM
ejpam-4441	118	3	)	)	PUNCT
ejpam-4441	118	4	theorem	theorem	NOUN
ejpam-4441	118	5	2	2	NUM
ejpam-4441	118	6	.	.	X
ejpam-4441	118	7	for	for	ADP
ejpam-4441	118	8	k	k	PROPN
ejpam-4441	118	9	≥	≥	PROPN
ejpam-4441	118	10	0	0	NUM
ejpam-4441	118	11	,	,	PUNCT
ejpam-4441	118	12	we	we	PRON
ejpam-4441	118	13	have	have	VERB
ejpam-4441	118	14	λ	λ	PROPN
ejpam-4441	118	15	n−k	n−k	NOUN
ejpam-4441	118	16	1	1	NUM
ejpam-4441	118	17	k	k	X
ejpam-4441	118	18	!	!	PUNCT
ejpam-4441	118	19	△	△	PROPN
ejpam-4441	119	1	k	k	PROPN
ejpam-4441	119	2	(	(	PUNCT
ejpam-4441	119	3	r	r	NOUN
ejpam-4441	119	4	λ	λ	PROPN
ejpam-4441	119	5	)	)	PUNCT
ejpam-4441	119	6	n	n	NOUN
ejpam-4441	119	7	=	=	PRON
ejpam-4441	119	8	{	{	PUNCT
ejpam-4441	119	9	{	{	PUNCT
ejpam-4441	119	10	n+r	n+r	X
ejpam-4441	119	11	k+r	k+r	X
ejpam-4441	119	12	}	}	PUNCT
ejpam-4441	119	13	r	r	PROPN
ejpam-4441	119	14	,	,	PUNCT
ejpam-4441	119	15	λ	λ	INTJ
ejpam-4441	119	16	,	,	PUNCT
ejpam-4441	119	17	if	if	SCONJ
ejpam-4441	119	18	n	n	PRON
ejpam-4441	119	19	≥	≥	X
ejpam-4441	119	20	k	k	NOUN
ejpam-4441	119	21	,	,	PUNCT
ejpam-4441	119	22	0	0	NUM
ejpam-4441	119	23	,	,	PUNCT
ejpam-4441	119	24	if	if	SCONJ
ejpam-4441	119	25	0	0	NUM
ejpam-4441	119	26	≤	≤	NUM
ejpam-4441	119	27	n	n	ADP
ejpam-4441	119	28	<	<	X
ejpam-4441	119	29	k.	k.	X
ejpam-4441	119	30	by	by	ADP
ejpam-4441	119	31	theorem	theorem	NOUN
ejpam-4441	119	32	1	1	NUM
ejpam-4441	119	33	,	,	PUNCT
ejpam-4441	119	34	we	we	PRON
ejpam-4441	119	35	get	get	VERB
ejpam-4441	119	36	∞	∞	PROPN
ejpam-4441	119	37	∑	∑	PUNCT
ejpam-4441	119	38	n	n	PROPN
ejpam-4441	119	39	=	=	SYM
ejpam-4441	119	40	k	k	X
ejpam-4441	119	41	{	{	PUNCT
ejpam-4441	119	42	n+	n+	ADP
ejpam-4441	119	43	r	r	NOUN
ejpam-4441	119	44	k+	k+	NOUN
ejpam-4441	119	45	r	r	NOUN
ejpam-4441	119	46	}	}	PUNCT
ejpam-4441	119	47	r	r	NOUN
ejpam-4441	119	48	,	,	PUNCT
ejpam-4441	119	49	λ	λ	PROPN
ejpam-4441	119	50	tn	tn	NOUN
ejpam-4441	119	51	n	n	NOUN
ejpam-4441	119	52	!	!	PUNCT
ejpam-4441	120	1	=	=	SYM
ejpam-4441	120	2	1	1	NUM
ejpam-4441	120	3	λ	λ	SYM
ejpam-4441	120	4	k	k	PROPN
ejpam-4441	120	5	1	1	NUM
ejpam-4441	120	6	k	k	NOUN
ejpam-4441	120	7	!	!	PUNCT
ejpam-4441	121	1	(	(	PUNCT
ejpam-4441	121	2	eλ	eλ	PROPN
ejpam-4441	121	3	t	t	PROPN
ejpam-4441	121	4	−1	−1	NOUN
ejpam-4441	121	5	)	)	PUNCT
ejpam-4441	122	1	kert	kert	PROPN
ejpam-4441	122	2	(	(	PUNCT
ejpam-4441	122	3	20	20	NUM
ejpam-4441	122	4	)	)	PUNCT
ejpam-4441	122	5	=	=	SYM
ejpam-4441	123	1	∞	∞	NUM
ejpam-4441	123	2	∑	∑	PUNCT
ejpam-4441	123	3	l	l	X
ejpam-4441	123	4	=	=	SYM
ejpam-4441	123	5	k	k	X
ejpam-4441	123	6	{	{	PUNCT
ejpam-4441	123	7	l	l	NOUN
ejpam-4441	123	8	k	k	PROPN
ejpam-4441	123	9	}	}	PUNCT
ejpam-4441	123	10	λ	λ	PROPN
ejpam-4441	123	11	t	t	NOUN
ejpam-4441	123	12	l	l	NOUN
ejpam-4441	123	13	l	l	NOUN
ejpam-4441	123	14	!	!	PUNCT
ejpam-4441	124	1	∞	∞	PROPN
ejpam-4441	124	2	∑	∑	PUNCT
ejpam-4441	124	3	m=0	m=0	PROPN
ejpam-4441	124	4	rm	rm	PROPN
ejpam-4441	124	5	tm	tm	PROPN
ejpam-4441	124	6	m	m	PROPN
ejpam-4441	124	7	!	!	PUNCT
ejpam-4441	125	1	=	=	SYM
ejpam-4441	125	2	∞	∞	NUM
ejpam-4441	125	3	∑	∑	PUNCT
ejpam-4441	125	4	n	n	PROPN
ejpam-4441	125	5	=	=	SYM
ejpam-4441	125	6	k	k	X
ejpam-4441	125	7	(	(	PUNCT
ejpam-4441	125	8	n	n	CCONJ
ejpam-4441	125	9	∑	∑	PROPN
ejpam-4441	125	10	l	l	X
ejpam-4441	125	11	=	=	SYM
ejpam-4441	125	12	k	k	X
ejpam-4441	125	13	{	{	PUNCT
ejpam-4441	125	14	l	l	NOUN
ejpam-4441	125	15	k	k	X
ejpam-4441	125	16	}	}	PUNCT
ejpam-4441	125	17	λ	λ	X
ejpam-4441	125	18	rn−l	rn−l	X
ejpam-4441	125	19	(	(	PUNCT
ejpam-4441	125	20	n	n	X
ejpam-4441	125	21	l	l	NOUN
ejpam-4441	125	22	)	)	PUNCT
ejpam-4441	125	23	)	)	PUNCT
ejpam-4441	125	24	tn	tn	PROPN
ejpam-4441	125	25	n	n	PROPN
ejpam-4441	125	26	!	!	PUNCT
ejpam-4441	125	27	.	.	PUNCT
ejpam-4441	126	1	therefore	therefore	ADV
ejpam-4441	126	2	,	,	PUNCT
ejpam-4441	126	3	by	by	ADP
ejpam-4441	126	4	comparing	compare	VERB
ejpam-4441	126	5	the	the	DET
ejpam-4441	126	6	coefficients	coefficient	NOUN
ejpam-4441	126	7	on	on	ADP
ejpam-4441	126	8	both	both	DET
ejpam-4441	126	9	sides	side	NOUN
ejpam-4441	126	10	of	of	ADP
ejpam-4441	126	11	(	(	PUNCT
ejpam-4441	126	12	20	20	NUM
ejpam-4441	126	13	)	)	PUNCT
ejpam-4441	126	14	,	,	PUNCT
ejpam-4441	126	15	we	we	PRON
ejpam-4441	126	16	obtain	obtain	VERB
ejpam-4441	126	17	the	the	DET
ejpam-4441	126	18	following	follow	VERB
ejpam-4441	126	19	theorem	theorem	PROPN
ejpam-4441	126	20	.	.	PROPN
ejpam-4441	127	1	d.	d.	PROPN
ejpam-4441	127	2	s.	s.	PROPN
ejpam-4441	127	3	kim	kim	PROPN
ejpam-4441	127	4	,	,	PUNCT
ejpam-4441	127	5	h.	h.	PROPN
ejpam-4441	127	6	k.	k.	PROPN
ejpam-4441	127	7	kim	kim	PROPN
ejpam-4441	127	8	,	,	PUNCT
ejpam-4441	127	9	t.	t.	PROPN
ejpam-4441	127	10	kim	kim	PROPN
ejpam-4441	127	11	/	/	SYM
ejpam-4441	127	12	eur	eur	PROPN
ejpam-4441	127	13	.	.	PUNCT
ejpam-4441	128	1	j.	j.	PROPN
ejpam-4441	128	2	pure	pure	PROPN
ejpam-4441	128	3	appl	appl	PROPN
ejpam-4441	128	4	.	.	PROPN
ejpam-4441	128	5	math	math	PROPN
ejpam-4441	128	6	,	,	PUNCT
ejpam-4441	128	7	15	15	NUM
ejpam-4441	128	8	(	(	PUNCT
ejpam-4441	128	9	3	3	NUM
ejpam-4441	128	10	)	)	PUNCT
ejpam-4441	128	11	(	(	PUNCT
ejpam-4441	128	12	2022	2022	NUM
ejpam-4441	128	13	)	)	PUNCT
ejpam-4441	128	14	,	,	PUNCT
ejpam-4441	128	15	1054	1054	NUM
ejpam-4441	128	16	-	-	SYM
ejpam-4441	128	17	1066	1066	NUM
ejpam-4441	128	18	1059	1059	NUM
ejpam-4441	128	19	theorem	theorem	NOUN
ejpam-4441	128	20	3	3	NUM
ejpam-4441	128	21	.	.	NOUN
ejpam-4441	128	22	for	for	ADP
ejpam-4441	128	23	n	n	PRON
ejpam-4441	128	24	,	,	PUNCT
ejpam-4441	128	25	k	k	PROPN
ejpam-4441	128	26	∈	∈	PROPN
ejpam-4441	128	27	z	z	PROPN
ejpam-4441	128	28	with	with	ADP
ejpam-4441	128	29	n	n	PRON
ejpam-4441	128	30	≥	≥	NOUN
ejpam-4441	128	31	k	k	X
ejpam-4441	128	32	≥	≥	PROPN
ejpam-4441	128	33	0	0	NUM
ejpam-4441	128	34	,	,	PUNCT
ejpam-4441	128	35	we	we	PRON
ejpam-4441	128	36	have	have	VERB
ejpam-4441	128	37	{	{	PUNCT
ejpam-4441	128	38	n+	n+	ADP
ejpam-4441	128	39	r	r	NOUN
ejpam-4441	128	40	k+	k+	NOUN
ejpam-4441	128	41	r	r	NOUN
ejpam-4441	128	42	}	}	PUNCT
ejpam-4441	128	43	r	r	NOUN
ejpam-4441	128	44	,	,	PUNCT
ejpam-4441	128	45	λ	λ	NOUN
ejpam-4441	128	46	=	=	SYM
ejpam-4441	128	47	n	n	PROPN
ejpam-4441	128	48	∑	∑	PROPN
ejpam-4441	128	49	l	l	X
ejpam-4441	128	50	=	=	X
ejpam-4441	128	51	k	k	X
ejpam-4441	128	52	(	(	PUNCT
ejpam-4441	128	53	n	n	NOUN
ejpam-4441	128	54	l	l	NOUN
ejpam-4441	128	55	)	)	PUNCT
ejpam-4441	128	56	{	{	PUNCT
ejpam-4441	128	57	l	l	NOUN
ejpam-4441	128	58	k	k	NOUN
ejpam-4441	128	59	}	}	PUNCT
ejpam-4441	128	60	λ	λ	X
ejpam-4441	128	61	rn−l	rn−l	ADJ
ejpam-4441	128	62	.	.	PUNCT
ejpam-4441	129	1	for	for	ADP
ejpam-4441	129	2	n	n	PRON
ejpam-4441	129	3	≥	≥	NUM
ejpam-4441	129	4	1	1	NUM
ejpam-4441	129	5	,	,	PUNCT
ejpam-4441	129	6	we	we	PRON
ejpam-4441	129	7	have	have	VERB
ejpam-4441	129	8	(	(	PUNCT
ejpam-4441	129	9	x+	x+	X
ejpam-4441	129	10	r)n+1	r)n+1	PROPN
ejpam-4441	129	11	=	=	SYM
ejpam-4441	129	12	(	(	PUNCT
ejpam-4441	129	13	x+	x+	X
ejpam-4441	129	14	r)n(x+	r)n(x+	PROPN
ejpam-4441	129	15	r	r	NOUN
ejpam-4441	129	16	)	)	PUNCT
ejpam-4441	129	17	=	=	SYM
ejpam-4441	129	18	n	n	PROPN
ejpam-4441	129	19	∑	∑	PUNCT
ejpam-4441	129	20	k=0	k=0	PROPN
ejpam-4441	129	21	{	{	PUNCT
ejpam-4441	129	22	n+	n+	ADP
ejpam-4441	129	23	r	r	NOUN
ejpam-4441	129	24	k+	k+	NOUN
ejpam-4441	129	25	r	r	NOUN
ejpam-4441	129	26	}	}	PUNCT
ejpam-4441	129	27	r	r	NOUN
ejpam-4441	129	28	,	,	PUNCT
ejpam-4441	129	29	λ	λ	X
ejpam-4441	129	30	(	(	PUNCT
ejpam-4441	129	31	x+	x+	X
ejpam-4441	129	32	r)(x)k	r)(x)k	NOUN
ejpam-4441	129	33	,	,	PUNCT
ejpam-4441	129	34	λ	λ	X
ejpam-4441	129	35	=	=	SYM
ejpam-4441	129	36	n	n	PROPN
ejpam-4441	129	37	∑	∑	ADP
ejpam-4441	129	38	k=0	k=0	PROPN
ejpam-4441	129	39	{	{	PUNCT
ejpam-4441	129	40	n+	n+	ADP
ejpam-4441	129	41	r	r	NOUN
ejpam-4441	129	42	k+	k+	NOUN
ejpam-4441	129	43	r	r	NOUN
ejpam-4441	129	44	}	}	PUNCT
ejpam-4441	129	45	r	r	NOUN
ejpam-4441	129	46	,	,	PUNCT
ejpam-4441	129	47	λ	λ	PROPN
ejpam-4441	129	48	(	(	PUNCT
ejpam-4441	129	49	x−	x−	PROPN
ejpam-4441	129	50	kλ	kλ	PROPN
ejpam-4441	129	51	+	+	PROPN
ejpam-4441	129	52	kλ	kλ	PROPN
ejpam-4441	129	53	+	+	CCONJ
ejpam-4441	129	54	r)(x)k	r)(x)k	NOUN
ejpam-4441	129	55	,	,	PUNCT
ejpam-4441	129	56	λ	λ	PROPN
ejpam-4441	129	57	(	(	PUNCT
ejpam-4441	129	58	21	21	NUM
ejpam-4441	129	59	)	)	PUNCT
ejpam-4441	129	60	=	=	SYM
ejpam-4441	130	1	n	n	PROPN
ejpam-4441	130	2	∑	∑	PUNCT
ejpam-4441	130	3	k=0	k=0	PROPN
ejpam-4441	130	4	{	{	PUNCT
ejpam-4441	130	5	n+	n+	ADP
ejpam-4441	130	6	r	r	NOUN
ejpam-4441	130	7	k+	k+	NOUN
ejpam-4441	130	8	r	r	NOUN
ejpam-4441	130	9	}	}	PUNCT
ejpam-4441	130	10	r	r	NOUN
ejpam-4441	130	11	,	,	PUNCT
ejpam-4441	130	12	λ	λ	X
ejpam-4441	130	13	(	(	PUNCT
ejpam-4441	130	14	x)k+1,λ	x)k+1,λ	X
ejpam-4441	130	15	+	+	CCONJ
ejpam-4441	130	16	n	n	X
ejpam-4441	130	17	∑	∑	ADV
ejpam-4441	130	18	k=0	k=0	PROPN
ejpam-4441	130	19	{	{	PUNCT
ejpam-4441	130	20	n+	n+	ADP
ejpam-4441	130	21	r	r	NOUN
ejpam-4441	130	22	k+	k+	NOUN
ejpam-4441	130	23	r	r	NOUN
ejpam-4441	130	24	}	}	PUNCT
ejpam-4441	130	25	r	r	NOUN
ejpam-4441	130	26	,	,	PUNCT
ejpam-4441	130	27	λ	λ	PROPN
ejpam-4441	130	28	(	(	PUNCT
ejpam-4441	130	29	x)k	x)k	X
ejpam-4441	130	30	,	,	PUNCT
ejpam-4441	130	31	λ	λ	PROPN
ejpam-4441	130	32	(	(	PUNCT
ejpam-4441	130	33	λk+	λk+	NOUN
ejpam-4441	130	34	r	r	NOUN
ejpam-4441	130	35	)	)	PUNCT
ejpam-4441	130	36	=	=	SYM
ejpam-4441	131	1	n+1	n+1	PROPN
ejpam-4441	131	2	∑	∑	PUNCT
ejpam-4441	131	3	k=1	k=1	X
ejpam-4441	131	4	{	{	PUNCT
ejpam-4441	131	5	n+	n+	INTJ
ejpam-4441	131	6	r	r	NOUN
ejpam-4441	131	7	k−1	k−1	PROPN
ejpam-4441	131	8	+	+	PROPN
ejpam-4441	131	9	r	r	NOUN
ejpam-4441	131	10	}	}	PUNCT
ejpam-4441	131	11	r	r	NOUN
ejpam-4441	131	12	,	,	PUNCT
ejpam-4441	131	13	λ	λ	PROPN
ejpam-4441	131	14	(	(	PUNCT
ejpam-4441	131	15	x)k	x)k	X
ejpam-4441	131	16	,	,	PUNCT
ejpam-4441	131	17	λ	λ	X
ejpam-4441	131	18	+	+	CCONJ
ejpam-4441	131	19	n	n	CCONJ
ejpam-4441	131	20	∑	∑	ADP
ejpam-4441	131	21	k=0	k=0	PROPN
ejpam-4441	131	22	(	(	PUNCT
ejpam-4441	131	23	λk+	λk+	NOUN
ejpam-4441	131	24	r	r	NOUN
ejpam-4441	131	25	)	)	PUNCT
ejpam-4441	131	26	{	{	PUNCT
ejpam-4441	131	27	n+	n+	ADP
ejpam-4441	131	28	r	r	NOUN
ejpam-4441	131	29	k+	k+	NOUN
ejpam-4441	131	30	r	r	NOUN
ejpam-4441	131	31	}	}	PUNCT
ejpam-4441	131	32	r	r	NOUN
ejpam-4441	131	33	,	,	PUNCT
ejpam-4441	131	34	λ	λ	PROPN
ejpam-4441	131	35	(	(	PUNCT
ejpam-4441	131	36	x)k	x)k	X
ejpam-4441	131	37	,	,	PUNCT
ejpam-4441	131	38	λ	λ	X
ejpam-4441	131	39	=	=	SYM
ejpam-4441	131	40	n+1	n+1	PROPN
ejpam-4441	131	41	∑	∑	PUNCT
ejpam-4441	131	42	k=0	k=0	X
ejpam-4441	131	43	(	(	PUNCT
ejpam-4441	131	44	{	{	PUNCT
ejpam-4441	131	45	n+	n+	ADP
ejpam-4441	131	46	r	r	NOUN
ejpam-4441	131	47	k−1	k−1	PROPN
ejpam-4441	131	48	+	+	PROPN
ejpam-4441	131	49	r	r	NOUN
ejpam-4441	131	50	}	}	PUNCT
ejpam-4441	131	51	r	r	NOUN
ejpam-4441	131	52	,	,	PUNCT
ejpam-4441	131	53	λ	λ	X
ejpam-4441	131	54	+	+	PROPN
ejpam-4441	131	55	(	(	PUNCT
ejpam-4441	131	56	λk+	λk+	NOUN
ejpam-4441	131	57	r	r	NOUN
ejpam-4441	131	58	)	)	PUNCT
ejpam-4441	131	59	{	{	PUNCT
ejpam-4441	131	60	n+	n+	ADP
ejpam-4441	131	61	r	r	NOUN
ejpam-4441	131	62	k+	k+	NOUN
ejpam-4441	131	63	r	r	NOUN
ejpam-4441	131	64	}	}	PUNCT
ejpam-4441	131	65	r	r	NOUN
ejpam-4441	131	66	,	,	PUNCT
ejpam-4441	131	67	λ	λ	PROPN
ejpam-4441	131	68	)	)	PUNCT
ejpam-4441	131	69	(	(	PUNCT
ejpam-4441	131	70	x)k	x)k	X
ejpam-4441	131	71	,	,	PUNCT
ejpam-4441	131	72	λ	λ	INTJ
ejpam-4441	131	73	.	.	PUNCT
ejpam-4441	132	1	on	on	ADP
ejpam-4441	132	2	the	the	DET
ejpam-4441	132	3	other	other	ADJ
ejpam-4441	132	4	hand	hand	NOUN
ejpam-4441	132	5	,	,	PUNCT
ejpam-4441	132	6	by	by	ADP
ejpam-4441	132	7	(	(	PUNCT
ejpam-4441	132	8	12	12	NUM
ejpam-4441	132	9	)	)	PUNCT
ejpam-4441	132	10	,	,	PUNCT
ejpam-4441	132	11	we	we	PRON
ejpam-4441	132	12	get	get	VERB
ejpam-4441	132	13	(	(	PUNCT
ejpam-4441	132	14	x+	x+	X
ejpam-4441	132	15	r)n+1	r)n+1	PROPN
ejpam-4441	133	1	=	=	SYM
ejpam-4441	133	2	n+1	n+1	PROPN
ejpam-4441	133	3	∑	∑	PUNCT
ejpam-4441	133	4	k=0	k=0	X
ejpam-4441	133	5	{	{	PUNCT
ejpam-4441	133	6	n+1	n+1	NUM
ejpam-4441	133	7	+	+	NOUN
ejpam-4441	133	8	r	r	NOUN
ejpam-4441	133	9	k+	k+	NOUN
ejpam-4441	133	10	r	r	NOUN
ejpam-4441	133	11	}	}	PUNCT
ejpam-4441	133	12	r	r	NOUN
ejpam-4441	133	13	,	,	PUNCT
ejpam-4441	133	14	λ	λ	PROPN
ejpam-4441	133	15	(	(	PUNCT
ejpam-4441	133	16	x)k	x)k	X
ejpam-4441	133	17	,	,	PUNCT
ejpam-4441	133	18	λ	λ	INTJ
ejpam-4441	133	19	.	.	PUNCT
ejpam-4441	134	1	(	(	PUNCT
ejpam-4441	134	2	22	22	NUM
ejpam-4441	134	3	)	)	PUNCT
ejpam-4441	134	4	therefore	therefore	ADV
ejpam-4441	134	5	,	,	PUNCT
ejpam-4441	134	6	by	by	ADP
ejpam-4441	134	7	(	(	PUNCT
ejpam-4441	134	8	21	21	NUM
ejpam-4441	134	9	)	)	PUNCT
ejpam-4441	134	10	and	and	CCONJ
ejpam-4441	134	11	(	(	PUNCT
ejpam-4441	134	12	22	22	NUM
ejpam-4441	134	13	)	)	PUNCT
ejpam-4441	134	14	,	,	PUNCT
ejpam-4441	134	15	we	we	PRON
ejpam-4441	134	16	obtain	obtain	VERB
ejpam-4441	134	17	the	the	DET
ejpam-4441	134	18	following	follow	VERB
ejpam-4441	134	19	theorem	theorem	VERB
ejpam-4441	134	20	.	.	PUNCT
ejpam-4441	134	21	theorem	theorem	NOUN
ejpam-4441	134	22	4	4	NUM
ejpam-4441	134	23	.	.	NOUN
ejpam-4441	134	24	for	for	ADP
ejpam-4441	134	25	n	n	PRON
ejpam-4441	134	26	,	,	PUNCT
ejpam-4441	134	27	k	k	PROPN
ejpam-4441	134	28	∈	∈	PROPN
ejpam-4441	134	29	z	z	PROPN
ejpam-4441	134	30	with	with	ADP
ejpam-4441	134	31	n	n	PRON
ejpam-4441	134	32	≥	≥	NOUN
ejpam-4441	134	33	k	k	X
ejpam-4441	134	34	≥	≥	NUM
ejpam-4441	134	35	1	1	NUM
ejpam-4441	134	36	,	,	PUNCT
ejpam-4441	134	37	we	we	PRON
ejpam-4441	134	38	have	have	VERB
ejpam-4441	134	39	{	{	PUNCT
ejpam-4441	134	40	n+1	n+1	NOUN
ejpam-4441	134	41	+	+	NOUN
ejpam-4441	134	42	r	r	NOUN
ejpam-4441	134	43	k+	k+	NOUN
ejpam-4441	134	44	r	r	NOUN
ejpam-4441	134	45	}	}	PUNCT
ejpam-4441	134	46	r	r	NOUN
ejpam-4441	134	47	,	,	PUNCT
ejpam-4441	134	48	λ	λ	NOUN
ejpam-4441	134	49	=	=	SYM
ejpam-4441	134	50	{	{	PUNCT
ejpam-4441	134	51	n+	n+	ADP
ejpam-4441	134	52	r	r	NOUN
ejpam-4441	134	53	k−1	k−1	PROPN
ejpam-4441	134	54	+	+	PROPN
ejpam-4441	134	55	r	r	NOUN
ejpam-4441	134	56	}	}	PUNCT
ejpam-4441	134	57	r	r	NOUN
ejpam-4441	134	58	,	,	PUNCT
ejpam-4441	134	59	λ	λ	X
ejpam-4441	134	60	+	+	PROPN
ejpam-4441	134	61	(	(	PUNCT
ejpam-4441	134	62	λk+	λk+	NOUN
ejpam-4441	134	63	r	r	NOUN
ejpam-4441	134	64	)	)	PUNCT
ejpam-4441	134	65	{	{	PUNCT
ejpam-4441	134	66	n+	n+	ADP
ejpam-4441	134	67	r	r	NOUN
ejpam-4441	134	68	k+	k+	NOUN
ejpam-4441	134	69	r	r	NOUN
ejpam-4441	134	70	}	}	PUNCT
ejpam-4441	134	71	r	r	NOUN
ejpam-4441	134	72	,	,	PUNCT
ejpam-4441	134	73	λ	λ	INTJ
ejpam-4441	134	74	.	.	PUNCT
ejpam-4441	135	1	now	now	ADV
ejpam-4441	135	2	,	,	PUNCT
ejpam-4441	135	3	we	we	PRON
ejpam-4441	135	4	observe	observe	VERB
ejpam-4441	135	5	that	that	SCONJ
ejpam-4441	135	6	1	1	NUM
ejpam-4441	135	7	λ	λ	SYM
ejpam-4441	135	8	k	k	PROPN
ejpam-4441	135	9	1	1	NUM
ejpam-4441	135	10	k	k	NOUN
ejpam-4441	135	11	!	!	PUNCT
ejpam-4441	136	1	(	(	PUNCT
ejpam-4441	136	2	eλ	eλ	PROPN
ejpam-4441	136	3	t	t	PROPN
ejpam-4441	136	4	−1	−1	NOUN
ejpam-4441	136	5	)	)	PUNCT
ejpam-4441	137	1	k	k	PROPN
ejpam-4441	137	2	1	1	NUM
ejpam-4441	137	3	λ	λ	SYM
ejpam-4441	137	4	m	m	VERB
ejpam-4441	137	5	1	1	NUM
ejpam-4441	137	6	m	m	NOUN
ejpam-4441	137	7	!	!	PUNCT
ejpam-4441	138	1	(	(	PUNCT
ejpam-4441	138	2	eλ	eλ	PROPN
ejpam-4441	138	3	t	t	PROPN
ejpam-4441	138	4	−1	−1	NOUN
ejpam-4441	138	5	)	)	PUNCT
ejpam-4441	138	6	mert	mert	PROPN
ejpam-4441	138	7	(	(	PUNCT
ejpam-4441	138	8	23	23	NUM
ejpam-4441	138	9	)	)	PUNCT
ejpam-4441	138	10	=	=	SYM
ejpam-4441	139	1	1	1	NUM
ejpam-4441	139	2	λ	λ	SYM
ejpam-4441	139	3	k+m	k+m	PROPN
ejpam-4441	139	4	1	1	NUM
ejpam-4441	139	5	(	(	PUNCT
ejpam-4441	139	6	k+m	k+m	NUM
ejpam-4441	139	7	)	)	PUNCT
ejpam-4441	139	8	!	!	PUNCT
ejpam-4441	140	1	(	(	PUNCT
ejpam-4441	140	2	eλ	eλ	PROPN
ejpam-4441	140	3	t	t	PROPN
ejpam-4441	140	4	−1)k+mert	−1)k+mert	PROPN
ejpam-4441	140	5	(	(	PUNCT
ejpam-4441	140	6	k+m	k+m	NUM
ejpam-4441	140	7	)	)	PUNCT
ejpam-4441	140	8	!	!	PUNCT
ejpam-4441	141	1	k!m	k!m	X
ejpam-4441	141	2	!	!	PUNCT
ejpam-4441	141	3	=	=	PUNCT
ejpam-4441	142	1	(	(	PUNCT
ejpam-4441	142	2	k+m	k+m	PROPN
ejpam-4441	142	3	k	k	X
ejpam-4441	142	4	)	)	PUNCT
ejpam-4441	142	5	∞	∞	PROPN
ejpam-4441	142	6	∑	∑	PUNCT
ejpam-4441	142	7	n	n	CCONJ
ejpam-4441	142	8	=	=	SYM
ejpam-4441	142	9	m+k	m+k	X
ejpam-4441	142	10	{	{	PUNCT
ejpam-4441	142	11	n+	n+	ADP
ejpam-4441	142	12	r	r	NOUN
ejpam-4441	142	13	k+m+	k+m+	NOUN
ejpam-4441	142	14	r	r	NOUN
ejpam-4441	142	15	}	}	PUNCT
ejpam-4441	142	16	r	r	NOUN
ejpam-4441	142	17	,	,	PUNCT
ejpam-4441	142	18	λ	λ	PROPN
ejpam-4441	142	19	tn	tn	NOUN
ejpam-4441	142	20	n	n	X
ejpam-4441	142	21	!	!	PUNCT
ejpam-4441	142	22	.	.	PUNCT
ejpam-4441	143	1	on	on	ADP
ejpam-4441	143	2	the	the	DET
ejpam-4441	143	3	other	other	ADJ
ejpam-4441	143	4	hand	hand	NOUN
ejpam-4441	143	5	,	,	PUNCT
ejpam-4441	143	6	by	by	ADP
ejpam-4441	143	7	(	(	PUNCT
ejpam-4441	143	8	15	15	NUM
ejpam-4441	143	9	)	)	PUNCT
ejpam-4441	143	10	,	,	PUNCT
ejpam-4441	143	11	we	we	PRON
ejpam-4441	143	12	get	get	VERB
ejpam-4441	143	13	1	1	NUM
ejpam-4441	143	14	λ	λ	NOUN
ejpam-4441	143	15	k	k	PROPN
ejpam-4441	143	16	1	1	NUM
ejpam-4441	143	17	k	k	NOUN
ejpam-4441	143	18	!	!	PUNCT
ejpam-4441	144	1	(	(	PUNCT
ejpam-4441	144	2	eλ	eλ	PROPN
ejpam-4441	144	3	t	t	PROPN
ejpam-4441	144	4	−1	−1	NOUN
ejpam-4441	144	5	)	)	PUNCT
ejpam-4441	145	1	k	k	PROPN
ejpam-4441	145	2	1	1	NUM
ejpam-4441	145	3	λ	λ	SYM
ejpam-4441	145	4	m	m	VERB
ejpam-4441	145	5	1	1	NUM
ejpam-4441	145	6	m	m	NOUN
ejpam-4441	145	7	!	!	PUNCT
ejpam-4441	146	1	(	(	PUNCT
ejpam-4441	146	2	eλ	eλ	PROPN
ejpam-4441	146	3	t	t	PROPN
ejpam-4441	146	4	−1)mert	−1)mert	PROPN
ejpam-4441	146	5	(	(	PUNCT
ejpam-4441	146	6	24	24	NUM
ejpam-4441	146	7	)	)	PUNCT
ejpam-4441	146	8	d.	d.	PROPN
ejpam-4441	146	9	s.	s.	PROPN
ejpam-4441	146	10	kim	kim	PROPN
ejpam-4441	146	11	,	,	PUNCT
ejpam-4441	146	12	h.	h.	PROPN
ejpam-4441	146	13	k.	k.	PROPN
ejpam-4441	146	14	kim	kim	PROPN
ejpam-4441	146	15	,	,	PUNCT
ejpam-4441	146	16	t.	t.	PROPN
ejpam-4441	146	17	kim	kim	PROPN
ejpam-4441	146	18	/	/	SYM
ejpam-4441	146	19	eur	eur	PROPN
ejpam-4441	146	20	.	.	PUNCT
ejpam-4441	147	1	j.	j.	PROPN
ejpam-4441	147	2	pure	pure	PROPN
ejpam-4441	147	3	appl	appl	PROPN
ejpam-4441	147	4	.	.	PROPN
ejpam-4441	147	5	math	math	PROPN
ejpam-4441	147	6	,	,	PUNCT
ejpam-4441	147	7	15	15	NUM
ejpam-4441	147	8	(	(	PUNCT
ejpam-4441	147	9	3	3	NUM
ejpam-4441	147	10	)	)	PUNCT
ejpam-4441	147	11	(	(	PUNCT
ejpam-4441	147	12	2022	2022	NUM
ejpam-4441	147	13	)	)	PUNCT
ejpam-4441	147	14	,	,	PUNCT
ejpam-4441	147	15	1054	1054	NUM
ejpam-4441	147	16	-	-	SYM
ejpam-4441	147	17	1066	1066	NUM
ejpam-4441	147	18	1060	1060	NUM
ejpam-4441	147	19	=	=	SYM
ejpam-4441	148	1	∞	∞	NUM
ejpam-4441	148	2	∑	∑	PUNCT
ejpam-4441	148	3	l	l	X
ejpam-4441	148	4	=	=	SYM
ejpam-4441	148	5	k	k	X
ejpam-4441	148	6	{	{	PUNCT
ejpam-4441	148	7	l	l	NOUN
ejpam-4441	148	8	k	k	PROPN
ejpam-4441	148	9	}	}	PUNCT
ejpam-4441	148	10	λ	λ	PROPN
ejpam-4441	148	11	t	t	NOUN
ejpam-4441	148	12	l	l	NOUN
ejpam-4441	148	13	l	l	NOUN
ejpam-4441	148	14	!	!	PUNCT
ejpam-4441	149	1	∞	∞	PROPN
ejpam-4441	149	2	∑	∑	PUNCT
ejpam-4441	149	3	j	j	X
ejpam-4441	149	4	=	=	VERB
ejpam-4441	149	5	m	m	PROPN
ejpam-4441	149	6	{	{	PUNCT
ejpam-4441	149	7	j+	j+	NUM
ejpam-4441	149	8	r	r	NOUN
ejpam-4441	149	9	m+	m+	NUM
ejpam-4441	149	10	r	r	NOUN
ejpam-4441	149	11	}	}	PUNCT
ejpam-4441	149	12	r	r	NOUN
ejpam-4441	149	13	,	,	PUNCT
ejpam-4441	149	14	λ	λ	PROPN
ejpam-4441	149	15	t	t	PROPN
ejpam-4441	149	16	j	j	PROPN
ejpam-4441	149	17	j	j	PROPN
ejpam-4441	149	18	!	!	PUNCT
ejpam-4441	149	19	=	=	SYM
ejpam-4441	150	1	∞	∞	NUM
ejpam-4441	150	2	∑	∑	PUNCT
ejpam-4441	150	3	n	n	CCONJ
ejpam-4441	150	4	=	=	NOUN
ejpam-4441	150	5	m+k	m+k	NOUN
ejpam-4441	150	6	n−m	n−m	PROPN
ejpam-4441	150	7	∑	∑	PUNCT
ejpam-4441	150	8	l	l	X
ejpam-4441	150	9	=	=	SYM
ejpam-4441	150	10	k	k	X
ejpam-4441	150	11	{	{	PUNCT
ejpam-4441	150	12	l	l	NOUN
ejpam-4441	150	13	k	k	PROPN
ejpam-4441	150	14	}	}	PUNCT
ejpam-4441	150	15	λ	λ	PROPN
ejpam-4441	150	16	{	{	PUNCT
ejpam-4441	150	17	n−	n−	NOUN
ejpam-4441	150	18	l	l	NOUN
ejpam-4441	151	1	+	+	CCONJ
ejpam-4441	151	2	r	r	X
ejpam-4441	151	3	m+	m+	NOUN
ejpam-4441	151	4	r	r	NOUN
ejpam-4441	151	5	}	}	PUNCT
ejpam-4441	151	6	r	r	NOUN
ejpam-4441	151	7	,	,	PUNCT
ejpam-4441	151	8	λ	λ	X
ejpam-4441	151	9	(	(	PUNCT
ejpam-4441	151	10	n	n	X
ejpam-4441	151	11	l	l	NOUN
ejpam-4441	151	12	)	)	PUNCT
ejpam-4441	151	13	tn	tn	PROPN
ejpam-4441	151	14	n	n	PROPN
ejpam-4441	151	15	!	!	PUNCT
ejpam-4441	151	16	.	.	PUNCT
ejpam-4441	152	1	therefore	therefore	ADV
ejpam-4441	152	2	,	,	PUNCT
ejpam-4441	152	3	by	by	ADP
ejpam-4441	152	4	(	(	PUNCT
ejpam-4441	152	5	23	23	NUM
ejpam-4441	152	6	)	)	PUNCT
ejpam-4441	152	7	and	and	CCONJ
ejpam-4441	152	8	(	(	PUNCT
ejpam-4441	152	9	24	24	NUM
ejpam-4441	152	10	)	)	PUNCT
ejpam-4441	152	11	,	,	PUNCT
ejpam-4441	152	12	we	we	PRON
ejpam-4441	152	13	obtain	obtain	VERB
ejpam-4441	152	14	the	the	DET
ejpam-4441	152	15	following	follow	VERB
ejpam-4441	152	16	theorem	theorem	VERB
ejpam-4441	152	17	.	.	PUNCT
ejpam-4441	152	18	theorem	theorem	NOUN
ejpam-4441	152	19	5	5	NUM
ejpam-4441	152	20	.	.	NOUN
ejpam-4441	152	21	for	for	ADP
ejpam-4441	152	22	m	m	PROPN
ejpam-4441	152	23	,	,	PUNCT
ejpam-4441	152	24	n	n	CCONJ
ejpam-4441	152	25	,	,	PUNCT
ejpam-4441	152	26	k	k	X
ejpam-4441	152	27	≥	≥	X
ejpam-4441	152	28	0	0	NUM
ejpam-4441	152	29	with	with	ADP
ejpam-4441	152	30	n	n	PRON
ejpam-4441	152	31	≥	≥	NUM
ejpam-4441	152	32	m+	m+	NUM
ejpam-4441	153	1	k	k	NOUN
ejpam-4441	153	2	,	,	PUNCT
ejpam-4441	153	3	we	we	PRON
ejpam-4441	153	4	have	have	VERB
ejpam-4441	153	5	(	(	PUNCT
ejpam-4441	153	6	m+	m+	NOUN
ejpam-4441	153	7	k	k	PROPN
ejpam-4441	153	8	k	k	PROPN
ejpam-4441	153	9	)	)	PUNCT
ejpam-4441	153	10	{	{	PUNCT
ejpam-4441	154	1	n+	n+	NUM
ejpam-4441	154	2	r	r	NOUN
ejpam-4441	154	3	k+m+	k+m+	NOUN
ejpam-4441	154	4	r	r	NOUN
ejpam-4441	154	5	}	}	PUNCT
ejpam-4441	154	6	r	r	NOUN
ejpam-4441	154	7	,	,	PUNCT
ejpam-4441	154	8	λ	λ	NOUN
ejpam-4441	154	9	=	=	SYM
ejpam-4441	154	10	n−m	n−m	X
ejpam-4441	154	11	∑	∑	PUNCT
ejpam-4441	154	12	l	l	X
ejpam-4441	154	13	=	=	X
ejpam-4441	154	14	k	k	X
ejpam-4441	154	15	(	(	PUNCT
ejpam-4441	154	16	n	n	NOUN
ejpam-4441	154	17	l	l	NOUN
ejpam-4441	154	18	)	)	PUNCT
ejpam-4441	154	19	{	{	PUNCT
ejpam-4441	154	20	l	l	NOUN
ejpam-4441	154	21	k	k	PROPN
ejpam-4441	154	22	}	}	PUNCT
ejpam-4441	154	23	λ	λ	PROPN
ejpam-4441	154	24	{	{	PUNCT
ejpam-4441	154	25	n−	n−	NOUN
ejpam-4441	154	26	l	l	NOUN
ejpam-4441	155	1	+	+	CCONJ
ejpam-4441	155	2	r	r	X
ejpam-4441	155	3	m+	m+	NOUN
ejpam-4441	155	4	r	r	NOUN
ejpam-4441	155	5	}	}	PUNCT
ejpam-4441	155	6	r	r	NOUN
ejpam-4441	155	7	,	,	PUNCT
ejpam-4441	155	8	λ	λ	PROPN
ejpam-4441	155	9	.	.	PUNCT
ejpam-4441	156	1	from	from	ADP
ejpam-4441	156	2	the	the	DET
ejpam-4441	156	3	definition	definition	NOUN
ejpam-4441	156	4	of	of	ADP
ejpam-4441	156	5	the	the	DET
ejpam-4441	156	6	λ	λ	PROPN
ejpam-4441	156	7	-analogues	-analogue	NOUN
ejpam-4441	156	8	of	of	ADP
ejpam-4441	156	9	the	the	DET
ejpam-4441	156	10	stirling	stirling	NOUN
ejpam-4441	156	11	numbers	number	NOUN
ejpam-4441	156	12	of	of	ADP
ejpam-4441	156	13	the	the	DET
ejpam-4441	156	14	second	second	ADJ
ejpam-4441	156	15	kind	kind	NOUN
ejpam-4441	156	16	,	,	PUNCT
ejpam-4441	156	17	we	we	PRON
ejpam-4441	156	18	have	have	VERB
ejpam-4441	156	19	∞	∞	PROPN
ejpam-4441	156	20	∑	∑	PUNCT
ejpam-4441	156	21	n	n	CCONJ
ejpam-4441	156	22	=	=	SYM
ejpam-4441	156	23	k	k	X
ejpam-4441	156	24	{	{	PUNCT
ejpam-4441	156	25	n	n	NOUN
ejpam-4441	156	26	k	k	ADJ
ejpam-4441	156	27	}	}	PUNCT
ejpam-4441	156	28	λ	λ	PROPN
ejpam-4441	156	29	tn	tn	NOUN
ejpam-4441	156	30	n	n	NOUN
ejpam-4441	156	31	!	!	PUNCT
ejpam-4441	157	1	=	=	SYM
ejpam-4441	157	2	1	1	NUM
ejpam-4441	157	3	λ	λ	SYM
ejpam-4441	157	4	k	k	PROPN
ejpam-4441	157	5	1	1	NUM
ejpam-4441	157	6	k	k	NOUN
ejpam-4441	157	7	!	!	PUNCT
ejpam-4441	158	1	(	(	PUNCT
ejpam-4441	158	2	et	et	NOUN
ejpam-4441	158	3	−1	−1	NOUN
ejpam-4441	158	4	)	)	PUNCT
ejpam-4441	159	1	k	k	X
ejpam-4441	159	2	=	=	SYM
ejpam-4441	159	3	1	1	NUM
ejpam-4441	159	4	λ	λ	SYM
ejpam-4441	159	5	k	k	PROPN
ejpam-4441	159	6	1	1	NUM
ejpam-4441	159	7	k	k	NOUN
ejpam-4441	159	8	!	!	PUNCT
ejpam-4441	160	1	(	(	PUNCT
ejpam-4441	160	2	eλ	eλ	PROPN
ejpam-4441	160	3	t	t	PROPN
ejpam-4441	160	4	−1	−1	NOUN
ejpam-4441	160	5	)	)	PUNCT
ejpam-4441	160	6	kerte−rt	kerte−rt	X
ejpam-4441	160	7	(	(	PUNCT
ejpam-4441	160	8	25	25	NUM
ejpam-4441	160	9	)	)	PUNCT
ejpam-4441	160	10	=	=	SYM
ejpam-4441	161	1	∞	∞	NUM
ejpam-4441	161	2	∑	∑	PUNCT
ejpam-4441	161	3	l	l	X
ejpam-4441	161	4	=	=	SYM
ejpam-4441	161	5	k	k	X
ejpam-4441	161	6	{	{	PUNCT
ejpam-4441	161	7	l	l	NOUN
ejpam-4441	161	8	+	+	CCONJ
ejpam-4441	161	9	r	r	NOUN
ejpam-4441	161	10	k+	k+	NOUN
ejpam-4441	161	11	r	r	NOUN
ejpam-4441	161	12	}	}	PUNCT
ejpam-4441	161	13	r	r	NOUN
ejpam-4441	161	14	,	,	PUNCT
ejpam-4441	161	15	λ	λ	X
ejpam-4441	161	16	t	t	NOUN
ejpam-4441	161	17	l	l	NOUN
ejpam-4441	161	18	l	l	NOUN
ejpam-4441	161	19	!	!	PUNCT
ejpam-4441	162	1	∞	∞	PROPN
ejpam-4441	162	2	∑	∑	PROPN
ejpam-4441	162	3	m=0	m=0	PROPN
ejpam-4441	162	4	(	(	PUNCT
ejpam-4441	162	5	−r)m	−r)m	NOUN
ejpam-4441	162	6	tm	tm	PROPN
ejpam-4441	162	7	m	m	PROPN
ejpam-4441	162	8	!	!	PUNCT
ejpam-4441	163	1	=	=	SYM
ejpam-4441	163	2	∞	∞	NUM
ejpam-4441	163	3	∑	∑	PUNCT
ejpam-4441	163	4	n	n	PROPN
ejpam-4441	163	5	=	=	SYM
ejpam-4441	163	6	k	k	X
ejpam-4441	163	7	(	(	PUNCT
ejpam-4441	163	8	n	n	CCONJ
ejpam-4441	163	9	∑	∑	PROPN
ejpam-4441	163	10	l	l	X
ejpam-4441	163	11	=	=	X
ejpam-4441	163	12	k	k	X
ejpam-4441	163	13	(	(	PUNCT
ejpam-4441	163	14	n	n	NOUN
ejpam-4441	163	15	l	l	NOUN
ejpam-4441	163	16	)	)	PUNCT
ejpam-4441	163	17	{	{	PUNCT
ejpam-4441	164	1	l	l	NOUN
ejpam-4441	164	2	+	+	CCONJ
ejpam-4441	164	3	r	r	NOUN
ejpam-4441	164	4	k+	k+	NOUN
ejpam-4441	164	5	r	r	NOUN
ejpam-4441	164	6	}	}	PUNCT
ejpam-4441	164	7	r	r	NOUN
ejpam-4441	164	8	,	,	PUNCT
ejpam-4441	164	9	λ	λ	PROPN
ejpam-4441	164	10	(	(	PUNCT
ejpam-4441	164	11	−1)n−lrn−l	−1)n−lrn−l	PROPN
ejpam-4441	164	12	)	)	PUNCT
ejpam-4441	164	13	tn	tn	PROPN
ejpam-4441	164	14	n	n	PROPN
ejpam-4441	164	15	!	!	PUNCT
ejpam-4441	164	16	.	.	PUNCT
ejpam-4441	165	1	therefore	therefore	ADV
ejpam-4441	165	2	,	,	PUNCT
ejpam-4441	165	3	by	by	ADP
ejpam-4441	165	4	comparing	compare	VERB
ejpam-4441	165	5	the	the	DET
ejpam-4441	165	6	coefficients	coefficient	NOUN
ejpam-4441	165	7	on	on	ADP
ejpam-4441	165	8	both	both	DET
ejpam-4441	165	9	sides	side	NOUN
ejpam-4441	165	10	of	of	ADP
ejpam-4441	165	11	(	(	PUNCT
ejpam-4441	165	12	25	25	NUM
ejpam-4441	165	13	)	)	PUNCT
ejpam-4441	165	14	we	we	PRON
ejpam-4441	165	15	obtain	obtain	VERB
ejpam-4441	165	16	the	the	DET
ejpam-4441	165	17	following	follow	VERB
ejpam-4441	165	18	theorem	theorem	VERB
ejpam-4441	165	19	.	.	PUNCT
ejpam-4441	165	20	theorem	theorem	PROPN
ejpam-4441	165	21	6	6	NUM
ejpam-4441	165	22	.	.	PUNCT
ejpam-4441	165	23	for	for	ADP
ejpam-4441	165	24	n	n	PRON
ejpam-4441	165	25	,	,	PUNCT
ejpam-4441	165	26	k	k	X
ejpam-4441	165	27	≥	≥	X
ejpam-4441	165	28	0	0	NUM
ejpam-4441	165	29	with	with	ADP
ejpam-4441	165	30	n	n	PRON
ejpam-4441	165	31	≥	≥	NOUN
ejpam-4441	165	32	k	k	NOUN
ejpam-4441	165	33	,	,	PUNCT
ejpam-4441	165	34	we	we	PRON
ejpam-4441	165	35	have	have	VERB
ejpam-4441	165	36	{	{	PUNCT
ejpam-4441	165	37	n	n	NOUN
ejpam-4441	165	38	k	k	ADJ
ejpam-4441	165	39	}	}	PUNCT
ejpam-4441	165	40	λ	λ	PROPN
ejpam-4441	165	41	=	=	SYM
ejpam-4441	165	42	n	n	CCONJ
ejpam-4441	165	43	∑	∑	PROPN
ejpam-4441	165	44	l	l	X
ejpam-4441	165	45	=	=	X
ejpam-4441	165	46	k	k	X
ejpam-4441	165	47	(	(	PUNCT
ejpam-4441	165	48	n	n	NOUN
ejpam-4441	165	49	l	l	NOUN
ejpam-4441	165	50	)	)	PUNCT
ejpam-4441	165	51	{	{	PUNCT
ejpam-4441	166	1	l	l	NOUN
ejpam-4441	166	2	+	+	CCONJ
ejpam-4441	166	3	r	r	NOUN
ejpam-4441	166	4	k+	k+	NOUN
ejpam-4441	166	5	r	r	NOUN
ejpam-4441	166	6	}	}	PUNCT
ejpam-4441	166	7	r	r	NOUN
ejpam-4441	166	8	,	,	PUNCT
ejpam-4441	166	9	λ	λ	PROPN
ejpam-4441	166	10	(	(	PUNCT
ejpam-4441	166	11	−1)n−lrn−l	−1)n−lrn−l	ADJ
ejpam-4441	166	12	.	.	PUNCT
ejpam-4441	167	1	for	for	ADP
ejpam-4441	167	2	m	m	PROPN
ejpam-4441	167	3	∈	∈	PROPN
ejpam-4441	167	4	n	n	CCONJ
ejpam-4441	167	5	,	,	PUNCT
ejpam-4441	167	6	the	the	DET
ejpam-4441	167	7	higher	high	ADJ
ejpam-4441	167	8	-	-	PUNCT
ejpam-4441	167	9	order	order	NOUN
ejpam-4441	167	10	bernoulli	bernoulli	NOUN
ejpam-4441	167	11	polynomials	polynomial	NOUN
ejpam-4441	167	12	are	be	AUX
ejpam-4441	167	13	defined	define	VERB
ejpam-4441	167	14	by	by	ADP
ejpam-4441	167	15	(	(	PUNCT
ejpam-4441	167	16	t	t	NOUN
ejpam-4441	167	17	et	et	NOUN
ejpam-4441	167	18	−1	−1	NOUN
ejpam-4441	167	19	)	)	PUNCT
ejpam-4441	168	1	m	m	PROPN
ejpam-4441	168	2	ext	ext	NOUN
ejpam-4441	168	3	=	=	SYM
ejpam-4441	168	4	∞	∞	PROPN
ejpam-4441	168	5	∑	∑	PROPN
ejpam-4441	168	6	n=0	n=0	PROPN
ejpam-4441	168	7	b(m	b(m	PROPN
ejpam-4441	168	8	)	)	PUNCT
ejpam-4441	169	1	n	n	CCONJ
ejpam-4441	169	2	(	(	PUNCT
ejpam-4441	169	3	x	x	X
ejpam-4441	169	4	)	)	PUNCT
ejpam-4441	169	5	tn	tn	PROPN
ejpam-4441	169	6	n	n	PROPN
ejpam-4441	169	7	!	!	PROPN
ejpam-4441	169	8	,	,	PUNCT
ejpam-4441	169	9	(	(	PUNCT
ejpam-4441	169	10	see	see	VERB
ejpam-4441	169	11	[	[	X
ejpam-4441	169	12	1,3,7	1,3,7	NUM
ejpam-4441	169	13	]	]	PUNCT
ejpam-4441	169	14	)	)	PUNCT
ejpam-4441	169	15	.	.	PUNCT
ejpam-4441	170	1	(	(	PUNCT
ejpam-4441	170	2	26	26	NUM
ejpam-4441	170	3	)	)	PUNCT
ejpam-4441	170	4	from	from	ADP
ejpam-4441	170	5	(	(	PUNCT
ejpam-4441	170	6	26	26	NUM
ejpam-4441	170	7	)	)	PUNCT
ejpam-4441	170	8	,	,	PUNCT
ejpam-4441	170	9	we	we	PRON
ejpam-4441	170	10	note	note	VERB
ejpam-4441	170	11	that	that	SCONJ
ejpam-4441	170	12	∞	∞	PROPN
ejpam-4441	170	13	∑	∑	PUNCT
ejpam-4441	170	14	n	n	CCONJ
ejpam-4441	170	15	=	=	SYM
ejpam-4441	170	16	k	k	X
ejpam-4441	170	17	{	{	PUNCT
ejpam-4441	170	18	n+	n+	ADP
ejpam-4441	170	19	r	r	NOUN
ejpam-4441	170	20	k+	k+	NOUN
ejpam-4441	170	21	r	r	NOUN
ejpam-4441	170	22	}	}	PUNCT
ejpam-4441	170	23	r	r	NOUN
ejpam-4441	170	24	,	,	PUNCT
ejpam-4441	170	25	λ	λ	PROPN
ejpam-4441	170	26	tn	tn	NOUN
ejpam-4441	170	27	n	n	NOUN
ejpam-4441	170	28	!	!	PUNCT
ejpam-4441	171	1	=	=	SYM
ejpam-4441	171	2	1	1	NUM
ejpam-4441	171	3	λ	λ	SYM
ejpam-4441	171	4	k	k	PROPN
ejpam-4441	171	5	1	1	NUM
ejpam-4441	171	6	k	k	NOUN
ejpam-4441	171	7	!	!	PUNCT
ejpam-4441	172	1	(	(	PUNCT
ejpam-4441	172	2	eλ	eλ	PROPN
ejpam-4441	172	3	t	t	PROPN
ejpam-4441	172	4	−1	−1	NOUN
ejpam-4441	172	5	)	)	PUNCT
ejpam-4441	173	1	kert	kert	PROPN
ejpam-4441	173	2	(	(	PUNCT
ejpam-4441	173	3	27	27	NUM
ejpam-4441	173	4	)	)	PUNCT
ejpam-4441	173	5	=	=	SYM
ejpam-4441	173	6	1	1	NUM
ejpam-4441	173	7	tm	tm	NOUN
ejpam-4441	173	8	1	1	NUM
ejpam-4441	173	9	λ	λ	PROPN
ejpam-4441	173	10	k+m	k+m	PROPN
ejpam-4441	173	11	(	(	PUNCT
ejpam-4441	173	12	k+m	k+m	NUM
ejpam-4441	173	13	)	)	PUNCT
ejpam-4441	173	14	!	!	PUNCT
ejpam-4441	174	1	k	k	X
ejpam-4441	174	2	!	!	PROPN
ejpam-4441	174	3	1	1	NUM
ejpam-4441	174	4	(	(	PUNCT
ejpam-4441	174	5	k+m	k+m	NUM
ejpam-4441	174	6	)	)	PUNCT
ejpam-4441	174	7	!	!	PUNCT
ejpam-4441	175	1	(	(	PUNCT
ejpam-4441	175	2	eλ	eλ	NUM
ejpam-4441	175	3	t	t	X
ejpam-4441	176	1	−1)k+m	−1)k+m	PROPN
ejpam-4441	176	2	(	(	PUNCT
ejpam-4441	176	3	λ	λ	INTJ
ejpam-4441	176	4	t	t	PROPN
ejpam-4441	176	5	eλ	eλ	NOUN
ejpam-4441	176	6	t	t	PROPN
ejpam-4441	176	7	−1	−1	NOUN
ejpam-4441	176	8	)	)	PUNCT
ejpam-4441	176	9	m	m	VERB
ejpam-4441	176	10	ert	ert	NOUN
ejpam-4441	177	1	=	=	X
ejpam-4441	177	2	(	(	PUNCT
ejpam-4441	177	3	k+m	k+m	PROPN
ejpam-4441	177	4	k	k	X
ejpam-4441	177	5	)	)	PUNCT
ejpam-4441	177	6	m	m	PROPN
ejpam-4441	177	7	!	!	PUNCT
ejpam-4441	178	1	tm	tm	PROPN
ejpam-4441	178	2	∞	∞	PROPN
ejpam-4441	178	3	∑	∑	PROPN
ejpam-4441	178	4	l	l	X
ejpam-4441	178	5	=	=	PROPN
ejpam-4441	178	6	k+m	k+m	X
ejpam-4441	178	7	{	{	PUNCT
ejpam-4441	178	8	l	l	NOUN
ejpam-4441	178	9	k+m	k+m	PROPN
ejpam-4441	178	10	}	}	PUNCT
ejpam-4441	178	11	λ	λ	PROPN
ejpam-4441	178	12	t	t	NOUN
ejpam-4441	178	13	l	l	NOUN
ejpam-4441	178	14	l	l	NOUN
ejpam-4441	178	15	!	!	PUNCT
ejpam-4441	179	1	(	(	PUNCT
ejpam-4441	179	2	∞	∞	PROPN
ejpam-4441	179	3	∑	∑	PUNCT
ejpam-4441	179	4	j=0	j=0	PROPN
ejpam-4441	179	5	b(m	b(m	PROPN
ejpam-4441	179	6	)	)	PUNCT
ejpam-4441	179	7	j	j	PROPN
ejpam-4441	179	8	r	r	PROPN
ejpam-4441	179	9	λ	λ	PROPN
ejpam-4441	179	10	)	)	PUNCT
ejpam-4441	180	1	λ	λ	PROPN
ejpam-4441	180	2	jt	jt	PROPN
ejpam-4441	180	3	j	j	PROPN
ejpam-4441	180	4	j	j	PROPN
ejpam-4441	180	5	!	!	PUNCT
ejpam-4441	181	1	=	=	PRON
ejpam-4441	181	2	(	(	PUNCT
ejpam-4441	181	3	k+m	k+m	PROPN
ejpam-4441	181	4	k	k	X
ejpam-4441	181	5	)	)	PUNCT
ejpam-4441	181	6	∞	∞	PROPN
ejpam-4441	181	7	∑	∑	PUNCT
ejpam-4441	181	8	l	l	X
ejpam-4441	181	9	=	=	SYM
ejpam-4441	181	10	k	k	X
ejpam-4441	181	11	{	{	PUNCT
ejpam-4441	181	12	l	l	PROPN
ejpam-4441	181	13	+	+	NOUN
ejpam-4441	181	14	m	m	VERB
ejpam-4441	181	15	k+m	k+m	ADJ
ejpam-4441	181	16	}	}	PUNCT
ejpam-4441	181	17	λ	λ	PROPN
ejpam-4441	181	18	m!l	m!l	PROPN
ejpam-4441	181	19	!	!	PUNCT
ejpam-4441	182	1	(	(	PUNCT
ejpam-4441	182	2	l	l	X
ejpam-4441	182	3	+	+	NOUN
ejpam-4441	182	4	m	m	NOUN
ejpam-4441	182	5	)	)	PUNCT
ejpam-4441	182	6	!	!	PUNCT
ejpam-4441	183	1	t	t	PROPN
ejpam-4441	183	2	l	l	PROPN
ejpam-4441	183	3	l	l	NOUN
ejpam-4441	183	4	!	!	PUNCT
ejpam-4441	184	1	∞	∞	PROPN
ejpam-4441	184	2	∑	∑	PUNCT
ejpam-4441	184	3	j=0	j=0	PROPN
ejpam-4441	184	4	b(m	b(m	PROPN
ejpam-4441	184	5	)	)	PUNCT
ejpam-4441	184	6	j	j	PROPN
ejpam-4441	184	7	(	(	PUNCT
ejpam-4441	184	8	r	r	NOUN
ejpam-4441	184	9	λ	λ	PROPN
ejpam-4441	184	10	)	)	PUNCT
ejpam-4441	185	1	λ	λ	PROPN
ejpam-4441	185	2	jt	jt	PROPN
ejpam-4441	185	3	j	j	PROPN
ejpam-4441	185	4	j	j	PROPN
ejpam-4441	185	5	!	!	PROPN
ejpam-4441	185	6	d.	d.	PROPN
ejpam-4441	185	7	s.	s.	PROPN
ejpam-4441	185	8	kim	kim	PROPN
ejpam-4441	185	9	,	,	PUNCT
ejpam-4441	185	10	h.	h.	PROPN
ejpam-4441	185	11	k.	k.	PROPN
ejpam-4441	185	12	kim	kim	PROPN
ejpam-4441	185	13	,	,	PUNCT
ejpam-4441	185	14	t.	t.	PROPN
ejpam-4441	185	15	kim	kim	PROPN
ejpam-4441	185	16	/	/	SYM
ejpam-4441	185	17	eur	eur	PROPN
ejpam-4441	185	18	.	.	PUNCT
ejpam-4441	186	1	j.	j.	PROPN
ejpam-4441	186	2	pure	pure	PROPN
ejpam-4441	186	3	appl	appl	PROPN
ejpam-4441	186	4	.	.	PROPN
ejpam-4441	186	5	math	math	PROPN
ejpam-4441	186	6	,	,	PUNCT
ejpam-4441	186	7	15	15	NUM
ejpam-4441	186	8	(	(	PUNCT
ejpam-4441	186	9	3	3	NUM
ejpam-4441	186	10	)	)	PUNCT
ejpam-4441	186	11	(	(	PUNCT
ejpam-4441	186	12	2022	2022	NUM
ejpam-4441	186	13	)	)	PUNCT
ejpam-4441	186	14	,	,	PUNCT
ejpam-4441	186	15	1054	1054	NUM
ejpam-4441	186	16	-	-	SYM
ejpam-4441	186	17	1066	1066	NUM
ejpam-4441	186	18	1061	1061	NUM
ejpam-4441	186	19	=	=	SYM
ejpam-4441	186	20	(	(	PUNCT
ejpam-4441	186	21	k+m	k+m	PROPN
ejpam-4441	186	22	k	k	X
ejpam-4441	186	23	)	)	PUNCT
ejpam-4441	186	24	∞	∞	PROPN
ejpam-4441	186	25	∑	∑	PUNCT
ejpam-4441	186	26	n	n	CCONJ
ejpam-4441	186	27	=	=	SYM
ejpam-4441	186	28	k	k	X
ejpam-4441	186	29	(	(	PUNCT
ejpam-4441	186	30	n	n	CCONJ
ejpam-4441	186	31	∑	∑	PROPN
ejpam-4441	186	32	l	l	X
ejpam-4441	186	33	=	=	SYM
ejpam-4441	186	34	k	k	X
ejpam-4441	186	35	(	(	PUNCT
ejpam-4441	186	36	n	n	X
ejpam-4441	186	37	l	l	NOUN
ejpam-4441	186	38	)	)	PUNCT
ejpam-4441	186	39	(	(	PUNCT
ejpam-4441	186	40	l+m	l+m	X
ejpam-4441	186	41	l	l	NOUN
ejpam-4441	186	42	)	)	PUNCT
ejpam-4441	186	43	{	{	PUNCT
ejpam-4441	186	44	l	l	NOUN
ejpam-4441	187	1	+	+	NOUN
ejpam-4441	187	2	m	m	VERB
ejpam-4441	187	3	k+m	k+m	ADJ
ejpam-4441	187	4	}	}	PUNCT
ejpam-4441	187	5	λ	λ	PROPN
ejpam-4441	187	6	λ	λ	NOUN
ejpam-4441	187	7	n−lb(m	n−lb(m	NOUN
ejpam-4441	187	8	)	)	PUNCT
ejpam-4441	187	9	n−l	n−l	NOUN
ejpam-4441	187	10	(	(	PUNCT
ejpam-4441	187	11	r	r	NOUN
ejpam-4441	187	12	λ	λ	PROPN
ejpam-4441	187	13	)	)	PUNCT
ejpam-4441	187	14	)	)	PUNCT
ejpam-4441	187	15	tn	tn	PROPN
ejpam-4441	188	1	n	n	PROPN
ejpam-4441	188	2	!	!	PUNCT
ejpam-4441	188	3	.	.	PUNCT
ejpam-4441	189	1	therefore	therefore	ADV
ejpam-4441	189	2	,	,	PUNCT
ejpam-4441	189	3	by	by	ADP
ejpam-4441	189	4	comparing	compare	VERB
ejpam-4441	189	5	the	the	DET
ejpam-4441	189	6	coefficients	coefficient	NOUN
ejpam-4441	189	7	on	on	ADP
ejpam-4441	189	8	both	both	DET
ejpam-4441	189	9	sides	side	NOUN
ejpam-4441	189	10	of	of	ADP
ejpam-4441	189	11	(	(	PUNCT
ejpam-4441	189	12	27	27	NUM
ejpam-4441	189	13	)	)	PUNCT
ejpam-4441	189	14	,	,	PUNCT
ejpam-4441	189	15	we	we	PRON
ejpam-4441	189	16	obtain	obtain	VERB
ejpam-4441	189	17	the	the	DET
ejpam-4441	189	18	following	follow	VERB
ejpam-4441	189	19	theorem	theorem	VERB
ejpam-4441	189	20	.	.	PUNCT
ejpam-4441	189	21	theorem	theorem	PROPN
ejpam-4441	189	22	7	7	NUM
ejpam-4441	189	23	.	.	NOUN
ejpam-4441	189	24	for	for	ADP
ejpam-4441	189	25	n	n	PRON
ejpam-4441	189	26	,	,	PUNCT
ejpam-4441	189	27	k	k	X
ejpam-4441	189	28	≥	≥	X
ejpam-4441	189	29	0	0	NUM
ejpam-4441	189	30	with	with	ADP
ejpam-4441	189	31	n	n	PRON
ejpam-4441	189	32	≥	≥	NOUN
ejpam-4441	189	33	k	k	NOUN
ejpam-4441	189	34	,	,	PUNCT
ejpam-4441	189	35	we	we	PRON
ejpam-4441	189	36	have{n+r	have{n+r	VERB
ejpam-4441	189	37	k+r	k+r	PROPN
ejpam-4441	189	38	}	}	PUNCT
ejpam-4441	189	39	r	r	NOUN
ejpam-4441	189	40	,	,	PUNCT
ejpam-4441	189	41	λ(k+m	λ(k+m	PROPN
ejpam-4441	189	42	k	k	NOUN
ejpam-4441	189	43	)	)	PUNCT
ejpam-4441	190	1	=	=	PUNCT
ejpam-4441	190	2	n	n	CCONJ
ejpam-4441	190	3	∑	∑	PROPN
ejpam-4441	190	4	l	l	X
ejpam-4441	190	5	=	=	SYM
ejpam-4441	190	6	k	k	X
ejpam-4441	190	7	(	(	PUNCT
ejpam-4441	190	8	n	n	X
ejpam-4441	190	9	l	l	NOUN
ejpam-4441	190	10	)	)	PUNCT
ejpam-4441	190	11	(	(	PUNCT
ejpam-4441	190	12	l+m	l+m	X
ejpam-4441	190	13	l	l	NOUN
ejpam-4441	190	14	)	)	PUNCT
ejpam-4441	190	15	{	{	PUNCT
ejpam-4441	191	1	l	l	NOUN
ejpam-4441	191	2	+	+	NOUN
ejpam-4441	191	3	m	m	PROPN
ejpam-4441	191	4	k+m	k+m	ADJ
ejpam-4441	191	5	}	}	PUNCT
ejpam-4441	191	6	λ	λ	PROPN
ejpam-4441	191	7	b(m	b(m	PROPN
ejpam-4441	191	8	)	)	PUNCT
ejpam-4441	191	9	n−l	n−l	NOUN
ejpam-4441	191	10	(	(	PUNCT
ejpam-4441	191	11	r	r	NOUN
ejpam-4441	191	12	λ	λ	PROPN
ejpam-4441	191	13	)	)	PUNCT
ejpam-4441	191	14	λ	λ	NOUN
ejpam-4441	191	15	n−l	n−l	VERB
ejpam-4441	191	16	.	.	PUNCT
ejpam-4441	192	1	3	3	X
ejpam-4441	192	2	.	.	X
ejpam-4441	192	3	further	further	ADJ
ejpam-4441	192	4	remarks	remark	NOUN
ejpam-4441	192	5	for	for	ADP
ejpam-4441	192	6	m	m	PROPN
ejpam-4441	192	7	,	,	PUNCT
ejpam-4441	192	8	n	n	PRON
ejpam-4441	192	9	≥	≥	NOUN
ejpam-4441	192	10	0	0	NUM
ejpam-4441	192	11	,	,	PUNCT
ejpam-4441	192	12	we	we	PRON
ejpam-4441	192	13	define	define	VERB
ejpam-4441	192	14	λ	λ	ADJ
ejpam-4441	192	15	-analogues	-analogue	NOUN
ejpam-4441	192	16	of	of	ADP
ejpam-4441	192	17	the	the	DET
ejpam-4441	192	18	whitney	whitney	NOUN
ejpam-4441	192	19	-	-	PUNCT
ejpam-4441	192	20	type	type	NOUN
ejpam-4441	192	21	stirling	stirling	NOUN
ejpam-4441	192	22	numbers	number	NOUN
ejpam-4441	192	23	of	of	ADP
ejpam-4441	192	24	the	the	DET
ejpam-4441	192	25	second	second	ADJ
ejpam-4441	192	26	kind	kind	NOUN
ejpam-4441	192	27	as	as	ADP
ejpam-4441	192	28	(	(	PUNCT
ejpam-4441	192	29	mx+1)n	mx+1)n	NOUN
ejpam-4441	192	30	=	=	SYM
ejpam-4441	192	31	n	n	PROPN
ejpam-4441	192	32	∑	∑	ADP
ejpam-4441	192	33	k=0	k=0	PROPN
ejpam-4441	192	34	wm	wm	PROPN
ejpam-4441	192	35	,	,	PUNCT
ejpam-4441	192	36	λ	λ	PROPN
ejpam-4441	192	37	(	(	PUNCT
ejpam-4441	192	38	n	n	X
ejpam-4441	192	39	,	,	PUNCT
ejpam-4441	192	40	k)m	k)m	X
ejpam-4441	193	1	k(x)k	k(x)k	PROPN
ejpam-4441	193	2	,	,	PUNCT
ejpam-4441	193	3	λ	λ	PROPN
ejpam-4441	193	4	,	,	PUNCT
ejpam-4441	193	5	(	(	PUNCT
ejpam-4441	193	6	n	n	CCONJ
ejpam-4441	193	7	≥	≥	NOUN
ejpam-4441	193	8	0	0	NUM
ejpam-4441	193	9	)	)	PUNCT
ejpam-4441	193	10	.	.	PUNCT
ejpam-4441	194	1	(	(	PUNCT
ejpam-4441	194	2	28	28	NUM
ejpam-4441	194	3	)	)	PUNCT
ejpam-4441	194	4	from	from	ADP
ejpam-4441	194	5	(	(	PUNCT
ejpam-4441	194	6	28	28	NUM
ejpam-4441	194	7	)	)	PUNCT
ejpam-4441	194	8	,	,	PUNCT
ejpam-4441	194	9	we	we	PRON
ejpam-4441	194	10	note	note	VERB
ejpam-4441	194	11	that	that	SCONJ
ejpam-4441	194	12	e(mx+1)t	e(mx+1)t	PROPN
ejpam-4441	194	13	=	=	SYM
ejpam-4441	194	14	∞	∞	PROPN
ejpam-4441	194	15	∑	∑	PROPN
ejpam-4441	194	16	m=0	m=0	PROPN
ejpam-4441	194	17	(	(	PUNCT
ejpam-4441	194	18	mx+1)n	mx+1)n	PROPN
ejpam-4441	194	19	tn	tn	PROPN
ejpam-4441	194	20	n	n	CCONJ
ejpam-4441	194	21	!	!	PUNCT
ejpam-4441	195	1	=	=	SYM
ejpam-4441	196	1	∞	∞	NUM
ejpam-4441	196	2	∑	∑	PUNCT
ejpam-4441	196	3	n=0	n=0	PROPN
ejpam-4441	196	4	n	n	CCONJ
ejpam-4441	196	5	∑	∑	ADP
ejpam-4441	196	6	k=0	k=0	PROPN
ejpam-4441	196	7	wm	wm	PROPN
ejpam-4441	196	8	,	,	PUNCT
ejpam-4441	196	9	λ	λ	PROPN
ejpam-4441	196	10	(	(	PUNCT
ejpam-4441	196	11	n	n	X
ejpam-4441	196	12	,	,	PUNCT
ejpam-4441	196	13	k)m	k)m	X
ejpam-4441	197	1	k(x)k	k(x)k	PROPN
ejpam-4441	197	2	,	,	PUNCT
ejpam-4441	197	3	λ	λ	PROPN
ejpam-4441	197	4	tn	tn	NOUN
ejpam-4441	197	5	n	n	ADV
ejpam-4441	197	6	!	!	PUNCT
ejpam-4441	197	7	=	=	SYM
ejpam-4441	198	1	∞	∞	NUM
ejpam-4441	198	2	∑	∑	PUNCT
ejpam-4441	198	3	k=0	k=0	PROPN
ejpam-4441	198	4	∞	∞	PROPN
ejpam-4441	198	5	∑	∑	PUNCT
ejpam-4441	198	6	n	n	PROPN
ejpam-4441	198	7	=	=	PROPN
ejpam-4441	198	8	k	k	PROPN
ejpam-4441	198	9	wm	wm	PROPN
ejpam-4441	198	10	,	,	PUNCT
ejpam-4441	198	11	λ	λ	PROPN
ejpam-4441	198	12	(	(	PUNCT
ejpam-4441	198	13	n	n	X
ejpam-4441	198	14	,	,	PUNCT
ejpam-4441	198	15	k	k	NOUN
ejpam-4441	198	16	)	)	PUNCT
ejpam-4441	198	17	tn	tn	PROPN
ejpam-4441	198	18	n	n	PROPN
ejpam-4441	198	19	!	!	PUNCT
ejpam-4441	199	1	mk(x)k	mk(x)k	NOUN
ejpam-4441	199	2	,	,	PUNCT
ejpam-4441	199	3	λ	λ	INTJ
ejpam-4441	199	4	.	.	PUNCT
ejpam-4441	200	1	(	(	PUNCT
ejpam-4441	200	2	29	29	NUM
ejpam-4441	200	3	)	)	PUNCT
ejpam-4441	200	4	on	on	ADP
ejpam-4441	200	5	the	the	DET
ejpam-4441	200	6	other	other	ADJ
ejpam-4441	200	7	hand	hand	NOUN
ejpam-4441	200	8	,	,	PUNCT
ejpam-4441	200	9	by	by	ADP
ejpam-4441	200	10	(	(	PUNCT
ejpam-4441	200	11	11	11	NUM
ejpam-4441	200	12	)	)	PUNCT
ejpam-4441	200	13	,	,	PUNCT
ejpam-4441	200	14	we	we	PRON
ejpam-4441	200	15	get	get	VERB
ejpam-4441	200	16	e(mx+1)t	e(mx+1)t	NOUN
ejpam-4441	200	17	=	=	PUNCT
ejpam-4441	201	1	et(eλmt	et(eλmt	NOUN
ejpam-4441	201	2	−1	−1	NOUN
ejpam-4441	201	3	+	+	NOUN
ejpam-4441	201	4	1	1	NUM
ejpam-4441	201	5	)	)	PUNCT
ejpam-4441	202	1	x	x	PUNCT
ejpam-4441	202	2	λ	λ	NOUN
ejpam-4441	202	3	=	=	VERB
ejpam-4441	202	4	et	et	NOUN
ejpam-4441	202	5	∞	∞	PROPN
ejpam-4441	202	6	∑	∑	X
ejpam-4441	202	7	k=0	k=0	PROPN
ejpam-4441	202	8	(	(	PUNCT
ejpam-4441	202	9	x	x	PUNCT
ejpam-4441	202	10	λ	λ	X
ejpam-4441	202	11	k	k	PROPN
ejpam-4441	202	12	)	)	PUNCT
ejpam-4441	202	13	(	(	PUNCT
ejpam-4441	202	14	eλmt	eλmt	VERB
ejpam-4441	202	15	−1)k	−1)k	PROPN
ejpam-4441	202	16	=	=	SYM
ejpam-4441	202	17	∞	∞	PROPN
ejpam-4441	202	18	∑	∑	PUNCT
ejpam-4441	202	19	k=0	k=0	X
ejpam-4441	202	20	(	(	PUNCT
ejpam-4441	202	21	1	1	NUM
ejpam-4441	202	22	λ	λ	SYM
ejpam-4441	202	23	k	k	PROPN
ejpam-4441	202	24	1	1	NUM
ejpam-4441	202	25	k	k	NOUN
ejpam-4441	202	26	!	!	PUNCT
ejpam-4441	203	1	(	(	PUNCT
ejpam-4441	203	2	eλmt	eλmt	VERB
ejpam-4441	203	3	−1	−1	NOUN
ejpam-4441	203	4	m	m	VERB
ejpam-4441	203	5	)	)	PUNCT
ejpam-4441	203	6	k	k	PROPN
ejpam-4441	203	7	et	et	PROPN
ejpam-4441	203	8	)	)	PUNCT
ejpam-4441	204	1	mk(x)k	mk(x)k	ADV
ejpam-4441	204	2	,	,	PUNCT
ejpam-4441	204	3	λ	λ	INTJ
ejpam-4441	204	4	.	.	PUNCT
ejpam-4441	205	1	(	(	PUNCT
ejpam-4441	205	2	30	30	NUM
ejpam-4441	205	3	)	)	PUNCT
ejpam-4441	205	4	therefore	therefore	ADV
ejpam-4441	205	5	,	,	PUNCT
ejpam-4441	205	6	by	by	ADP
ejpam-4441	205	7	(	(	PUNCT
ejpam-4441	205	8	29	29	NUM
ejpam-4441	205	9	)	)	PUNCT
ejpam-4441	205	10	and	and	CCONJ
ejpam-4441	205	11	(	(	PUNCT
ejpam-4441	205	12	30	30	NUM
ejpam-4441	205	13	)	)	PUNCT
ejpam-4441	205	14	,	,	PUNCT
ejpam-4441	205	15	we	we	PRON
ejpam-4441	205	16	obtain	obtain	VERB
ejpam-4441	205	17	the	the	DET
ejpam-4441	205	18	generating	generate	VERB
ejpam-4441	205	19	function	function	NOUN
ejpam-4441	205	20	wm	wm	PROPN
ejpam-4441	205	21	,	,	PUNCT
ejpam-4441	205	22	λ	λ	PROPN
ejpam-4441	205	23	(	(	PUNCT
ejpam-4441	205	24	n	n	X
ejpam-4441	205	25	,	,	PUNCT
ejpam-4441	205	26	k	k	NOUN
ejpam-4441	205	27	)	)	PUNCT
ejpam-4441	205	28	,	,	PUNCT
ejpam-4441	205	29	(	(	PUNCT
ejpam-4441	205	30	n	n	CCONJ
ejpam-4441	205	31	,	,	PUNCT
ejpam-4441	205	32	k	k	PROPN
ejpam-4441	205	33	≥	≥	PROPN
ejpam-4441	205	34	0	0	NUM
ejpam-4441	205	35	)	)	PUNCT
ejpam-4441	205	36	.	.	PUNCT
ejpam-4441	206	1	theorem	theorem	ADJ
ejpam-4441	206	2	8	8	NUM
ejpam-4441	206	3	.	.	PUNCT
ejpam-4441	207	1	for	for	ADP
ejpam-4441	207	2	k	k	PROPN
ejpam-4441	207	3	≥	≥	PROPN
ejpam-4441	207	4	0	0	NUM
ejpam-4441	207	5	,	,	PUNCT
ejpam-4441	207	6	we	we	PRON
ejpam-4441	207	7	have	have	VERB
ejpam-4441	207	8	1	1	NUM
ejpam-4441	207	9	k	k	NOUN
ejpam-4441	207	10	!	!	PROPN
ejpam-4441	208	1	1	1	NUM
ejpam-4441	208	2	λ	λ	X
ejpam-4441	208	3	k	k	X
ejpam-4441	208	4	(	(	PUNCT
ejpam-4441	208	5	eλmt	eλmt	VERB
ejpam-4441	208	6	−1	−1	NOUN
ejpam-4441	208	7	m	m	VERB
ejpam-4441	208	8	)	)	PUNCT
ejpam-4441	208	9	k	k	NOUN
ejpam-4441	208	10	et	et	NOUN
ejpam-4441	209	1	=	=	SYM
ejpam-4441	209	2	∞	∞	PROPN
ejpam-4441	209	3	∑	∑	PUNCT
ejpam-4441	209	4	n	n	PROPN
ejpam-4441	209	5	=	=	PROPN
ejpam-4441	209	6	k	k	PROPN
ejpam-4441	209	7	wm	wm	PROPN
ejpam-4441	209	8	,	,	PUNCT
ejpam-4441	209	9	λ	λ	PROPN
ejpam-4441	209	10	(	(	PUNCT
ejpam-4441	209	11	n	n	X
ejpam-4441	209	12	,	,	PUNCT
ejpam-4441	209	13	k	k	NOUN
ejpam-4441	209	14	)	)	PUNCT
ejpam-4441	209	15	tn	tn	PROPN
ejpam-4441	209	16	n	n	PROPN
ejpam-4441	209	17	!	!	PUNCT
ejpam-4441	209	18	.	.	PUNCT
ejpam-4441	210	1	from	from	ADP
ejpam-4441	210	2	theorem	theorem	ADJ
ejpam-4441	210	3	8	8	NUM
ejpam-4441	210	4	,	,	PUNCT
ejpam-4441	210	5	we	we	PRON
ejpam-4441	210	6	note	note	VERB
ejpam-4441	210	7	that	that	SCONJ
ejpam-4441	210	8	∞	∞	PROPN
ejpam-4441	210	9	∑	∑	PUNCT
ejpam-4441	210	10	n	n	CCONJ
ejpam-4441	210	11	=	=	SYM
ejpam-4441	210	12	k	k	X
ejpam-4441	210	13	{	{	PUNCT
ejpam-4441	210	14	n+1	n+1	PROPN
ejpam-4441	210	15	k+1	k+1	X
ejpam-4441	210	16	}	}	PUNCT
ejpam-4441	210	17	λ	λ	PROPN
ejpam-4441	210	18	tn	tn	NOUN
ejpam-4441	210	19	n	n	NOUN
ejpam-4441	210	20	!	!	PUNCT
ejpam-4441	211	1	=	=	PUNCT
ejpam-4441	212	1	d	d	NOUN
ejpam-4441	212	2	dt	dt	X
ejpam-4441	212	3	{	{	PUNCT
ejpam-4441	212	4	∞	∞	PROPN
ejpam-4441	212	5	∑	∑	PUNCT
ejpam-4441	212	6	n	n	CCONJ
ejpam-4441	212	7	=	=	SYM
ejpam-4441	212	8	k	k	X
ejpam-4441	212	9	{	{	PUNCT
ejpam-4441	212	10	n+1	n+1	PROPN
ejpam-4441	212	11	k+1	k+1	X
ejpam-4441	212	12	}	}	PUNCT
ejpam-4441	212	13	λ	λ	SYM
ejpam-4441	212	14	tn+1	tn+1	NUM
ejpam-4441	212	15	(	(	PUNCT
ejpam-4441	212	16	n+1	n+1	NOUN
ejpam-4441	212	17	)	)	PUNCT
ejpam-4441	212	18	!	!	PUNCT
ejpam-4441	212	19	}	}	PUNCT
ejpam-4441	213	1	(	(	PUNCT
ejpam-4441	213	2	31	31	NUM
ejpam-4441	213	3	)	)	PUNCT
ejpam-4441	213	4	d.	d.	PROPN
ejpam-4441	213	5	s.	s.	PROPN
ejpam-4441	213	6	kim	kim	PROPN
ejpam-4441	213	7	,	,	PUNCT
ejpam-4441	213	8	h.	h.	PROPN
ejpam-4441	213	9	k.	k.	PROPN
ejpam-4441	213	10	kim	kim	PROPN
ejpam-4441	213	11	,	,	PUNCT
ejpam-4441	213	12	t.	t.	PROPN
ejpam-4441	213	13	kim	kim	PROPN
ejpam-4441	213	14	/	/	SYM
ejpam-4441	213	15	eur	eur	PROPN
ejpam-4441	213	16	.	.	PUNCT
ejpam-4441	214	1	j.	j.	PROPN
ejpam-4441	214	2	pure	pure	PROPN
ejpam-4441	214	3	appl	appl	PROPN
ejpam-4441	214	4	.	.	PROPN
ejpam-4441	214	5	math	math	PROPN
ejpam-4441	214	6	,	,	PUNCT
ejpam-4441	214	7	15	15	NUM
ejpam-4441	214	8	(	(	PUNCT
ejpam-4441	214	9	3	3	NUM
ejpam-4441	214	10	)	)	PUNCT
ejpam-4441	214	11	(	(	PUNCT
ejpam-4441	214	12	2022	2022	NUM
ejpam-4441	214	13	)	)	PUNCT
ejpam-4441	214	14	,	,	PUNCT
ejpam-4441	214	15	1054	1054	NUM
ejpam-4441	214	16	-	-	SYM
ejpam-4441	214	17	1066	1066	NUM
ejpam-4441	214	18	1062	1062	NUM
ejpam-4441	215	1	=	=	SYM
ejpam-4441	215	2	d	d	NOUN
ejpam-4441	215	3	dt	dt	X
ejpam-4441	215	4	(	(	PUNCT
ejpam-4441	215	5	1	1	NUM
ejpam-4441	215	6	(	(	PUNCT
ejpam-4441	215	7	k+1	k+1	NOUN
ejpam-4441	215	8	)	)	PUNCT
ejpam-4441	215	9	!	!	PUNCT
ejpam-4441	216	1	1	1	NUM
ejpam-4441	216	2	λ	λ	INTJ
ejpam-4441	216	3	k+1	k+1	X
ejpam-4441	216	4	(	(	PUNCT
ejpam-4441	216	5	e	e	X
ejpam-4441	216	6	λ	λ	PROPN
ejpam-4441	216	7	t	t	PROPN
ejpam-4441	216	8	−1)k+1	−1)k+1	VERB
ejpam-4441	216	9	)	)	PUNCT
ejpam-4441	216	10	=	=	SYM
ejpam-4441	216	11	1	1	NUM
ejpam-4441	216	12	k	k	NOUN
ejpam-4441	216	13	!	!	PROPN
ejpam-4441	216	14	1	1	NUM
ejpam-4441	216	15	λ	λ	X
ejpam-4441	216	16	k	k	X
ejpam-4441	216	17	(	(	PUNCT
ejpam-4441	216	18	e	e	X
ejpam-4441	216	19	λ	λ	PROPN
ejpam-4441	216	20	t	t	PROPN
ejpam-4441	216	21	−1)kete(λ−1)t	−1)kete(λ−1)t	PROPN
ejpam-4441	217	1	=	=	SYM
ejpam-4441	217	2	∞	∞	NUM
ejpam-4441	217	3	∑	∑	PUNCT
ejpam-4441	217	4	l	l	X
ejpam-4441	217	5	=	=	PROPN
ejpam-4441	217	6	k	k	X
ejpam-4441	217	7	w1,λ	w1,λ	PROPN
ejpam-4441	217	8	(	(	PUNCT
ejpam-4441	217	9	l	l	NOUN
ejpam-4441	217	10	,	,	PUNCT
ejpam-4441	217	11	k	k	NOUN
ejpam-4441	217	12	)	)	PUNCT
ejpam-4441	217	13	t	t	NOUN
ejpam-4441	217	14	l	l	NOUN
ejpam-4441	217	15	l	l	NOUN
ejpam-4441	217	16	!	!	PUNCT
ejpam-4441	217	17	∞	∞	PROPN
ejpam-4441	217	18	∑	∑	PUNCT
ejpam-4441	217	19	j=0	j=0	PROPN
ejpam-4441	217	20	(	(	PUNCT
ejpam-4441	217	21	λ	λ	NOUN
ejpam-4441	217	22	−1	−1	NOUN
ejpam-4441	217	23	)	)	PUNCT
ejpam-4441	218	1	j	j	PROPN
ejpam-4441	218	2	t	t	PROPN
ejpam-4441	218	3	j	j	PROPN
ejpam-4441	218	4	j	j	PROPN
ejpam-4441	218	5	!	!	PUNCT
ejpam-4441	218	6	=	=	SYM
ejpam-4441	219	1	∞	∞	NUM
ejpam-4441	219	2	∑	∑	PUNCT
ejpam-4441	219	3	n	n	PROPN
ejpam-4441	219	4	=	=	SYM
ejpam-4441	219	5	k	k	X
ejpam-4441	219	6	(	(	PUNCT
ejpam-4441	219	7	n	n	CCONJ
ejpam-4441	219	8	∑	∑	PROPN
ejpam-4441	219	9	l	l	X
ejpam-4441	219	10	=	=	PROPN
ejpam-4441	219	11	k	k	X
ejpam-4441	219	12	w1,λ	w1,λ	PROPN
ejpam-4441	219	13	(	(	PUNCT
ejpam-4441	219	14	l	l	NOUN
ejpam-4441	219	15	,	,	PUNCT
ejpam-4441	219	16	k)(λ	k)(λ	NOUN
ejpam-4441	219	17	−1)n−l	−1)n−l	X
ejpam-4441	219	18	(	(	PUNCT
ejpam-4441	219	19	n	n	X
ejpam-4441	219	20	l	l	NOUN
ejpam-4441	219	21	)	)	PUNCT
ejpam-4441	219	22	)	)	PUNCT
ejpam-4441	219	23	tn	tn	PROPN
ejpam-4441	219	24	n	n	PROPN
ejpam-4441	219	25	!	!	PUNCT
ejpam-4441	219	26	.	.	PUNCT
ejpam-4441	220	1	therefore	therefore	ADV
ejpam-4441	220	2	,	,	PUNCT
ejpam-4441	220	3	by	by	ADP
ejpam-4441	220	4	comparing	compare	VERB
ejpam-4441	220	5	the	the	DET
ejpam-4441	220	6	coefficients	coefficient	NOUN
ejpam-4441	220	7	on	on	ADP
ejpam-4441	220	8	both	both	DET
ejpam-4441	220	9	sides	side	NOUN
ejpam-4441	220	10	of	of	ADP
ejpam-4441	220	11	(	(	PUNCT
ejpam-4441	220	12	31	31	NUM
ejpam-4441	220	13	)	)	PUNCT
ejpam-4441	220	14	,	,	PUNCT
ejpam-4441	220	15	we	we	PRON
ejpam-4441	220	16	obtain	obtain	VERB
ejpam-4441	220	17	the	the	DET
ejpam-4441	220	18	following	follow	VERB
ejpam-4441	220	19	theorem	theorem	VERB
ejpam-4441	220	20	.	.	PUNCT
ejpam-4441	220	21	theorem	theorem	NOUN
ejpam-4441	220	22	9	9	NUM
ejpam-4441	220	23	.	.	PUNCT
ejpam-4441	220	24	for	for	ADP
ejpam-4441	220	25	n	n	PRON
ejpam-4441	220	26	,	,	PUNCT
ejpam-4441	220	27	k	k	X
ejpam-4441	220	28	≥	≥	X
ejpam-4441	220	29	0	0	NUM
ejpam-4441	220	30	with	with	ADP
ejpam-4441	220	31	n	n	PRON
ejpam-4441	220	32	≥	≥	NOUN
ejpam-4441	220	33	k	k	NOUN
ejpam-4441	220	34	,	,	PUNCT
ejpam-4441	220	35	we	we	PRON
ejpam-4441	220	36	have	have	VERB
ejpam-4441	220	37	n	n	NUM
ejpam-4441	220	38	∑	∑	PROPN
ejpam-4441	220	39	l	l	X
ejpam-4441	220	40	=	=	X
ejpam-4441	220	41	k	k	X
ejpam-4441	220	42	(	(	PUNCT
ejpam-4441	220	43	n	n	NOUN
ejpam-4441	220	44	l	l	NOUN
ejpam-4441	220	45	)	)	PUNCT
ejpam-4441	221	1	w1,λ	w1,λ	PROPN
ejpam-4441	221	2	(	(	PUNCT
ejpam-4441	221	3	l	l	NOUN
ejpam-4441	221	4	,	,	PUNCT
ejpam-4441	221	5	k)(λ	k)(λ	NOUN
ejpam-4441	221	6	−1)n−l	−1)n−l	PUNCT
ejpam-4441	221	7	=	=	X
ejpam-4441	221	8	{	{	PUNCT
ejpam-4441	221	9	n+1	n+1	PROPN
ejpam-4441	221	10	k+1	k+1	X
ejpam-4441	221	11	}	}	PUNCT
ejpam-4441	221	12	λ	λ	PROPN
ejpam-4441	221	13	.	.	PUNCT
ejpam-4441	222	1	now	now	ADV
ejpam-4441	222	2	,	,	PUNCT
ejpam-4441	222	3	we	we	PRON
ejpam-4441	222	4	consider	consider	VERB
ejpam-4441	222	5	the	the	DET
ejpam-4441	222	6	λ	λ	NOUN
ejpam-4441	222	7	-analogues	-analogue	NOUN
ejpam-4441	222	8	of	of	ADP
ejpam-4441	222	9	dowling	dowle	VERB
ejpam-4441	222	10	polynomials	polynomial	NOUN
ejpam-4441	222	11	which	which	PRON
ejpam-4441	222	12	are	be	AUX
ejpam-4441	222	13	defined	define	VERB
ejpam-4441	222	14	by	by	ADP
ejpam-4441	222	15	dm	dm	PROPN
ejpam-4441	222	16	,	,	PUNCT
ejpam-4441	222	17	λ	λ	PROPN
ejpam-4441	222	18	(	(	PUNCT
ejpam-4441	222	19	n	n	X
ejpam-4441	222	20	,	,	PUNCT
ejpam-4441	222	21	x	x	NOUN
ejpam-4441	222	22	)	)	PUNCT
ejpam-4441	222	23	=	=	SYM
ejpam-4441	222	24	n	n	PROPN
ejpam-4441	222	25	∑	∑	ADP
ejpam-4441	222	26	k=0	k=0	PROPN
ejpam-4441	222	27	wm	wm	PROPN
ejpam-4441	222	28	,	,	PUNCT
ejpam-4441	222	29	λ	λ	PROPN
ejpam-4441	222	30	(	(	PUNCT
ejpam-4441	222	31	n	n	CCONJ
ejpam-4441	222	32	,	,	PUNCT
ejpam-4441	222	33	k)x	k)x	X
ejpam-4441	222	34	k	k	NOUN
ejpam-4441	222	35	,	,	PUNCT
ejpam-4441	222	36	(	(	PUNCT
ejpam-4441	222	37	n	n	CCONJ
ejpam-4441	222	38	≥	≥	NOUN
ejpam-4441	222	39	0	0	NUM
ejpam-4441	222	40	)	)	PUNCT
ejpam-4441	222	41	.	.	PUNCT
ejpam-4441	223	1	(	(	PUNCT
ejpam-4441	223	2	32	32	NUM
ejpam-4441	223	3	)	)	PUNCT
ejpam-4441	223	4	thus	thus	ADV
ejpam-4441	223	5	,	,	PUNCT
ejpam-4441	223	6	by	by	ADP
ejpam-4441	223	7	(	(	PUNCT
ejpam-4441	223	8	32	32	NUM
ejpam-4441	223	9	)	)	PUNCT
ejpam-4441	223	10	,	,	PUNCT
ejpam-4441	223	11	we	we	PRON
ejpam-4441	223	12	get	get	VERB
ejpam-4441	223	13	∞	∞	PROPN
ejpam-4441	223	14	∑	∑	PROPN
ejpam-4441	223	15	n=0	n=0	PROPN
ejpam-4441	223	16	dm	dm	PROPN
ejpam-4441	223	17	,	,	PUNCT
ejpam-4441	223	18	λ	λ	PROPN
ejpam-4441	223	19	(	(	PUNCT
ejpam-4441	223	20	n	n	X
ejpam-4441	223	21	,	,	PUNCT
ejpam-4441	223	22	x	x	NOUN
ejpam-4441	223	23	)	)	PUNCT
ejpam-4441	223	24	tn	tn	PROPN
ejpam-4441	223	25	n	n	NOUN
ejpam-4441	223	26	!	!	PUNCT
ejpam-4441	224	1	=	=	SYM
ejpam-4441	225	1	∞	∞	NUM
ejpam-4441	225	2	∑	∑	PUNCT
ejpam-4441	225	3	n=0	n=0	PROPN
ejpam-4441	225	4	n	n	CCONJ
ejpam-4441	225	5	∑	∑	ADP
ejpam-4441	225	6	k=0	k=0	PROPN
ejpam-4441	225	7	wm	wm	PROPN
ejpam-4441	225	8	,	,	PUNCT
ejpam-4441	225	9	λ	λ	PROPN
ejpam-4441	225	10	(	(	PUNCT
ejpam-4441	225	11	n	n	CCONJ
ejpam-4441	225	12	,	,	PUNCT
ejpam-4441	225	13	k)x	k)x	X
ejpam-4441	225	14	k	k	PROPN
ejpam-4441	225	15	tn	tn	PROPN
ejpam-4441	225	16	n	n	X
ejpam-4441	225	17	!	!	PUNCT
ejpam-4441	226	1	(	(	PUNCT
ejpam-4441	226	2	33	33	NUM
ejpam-4441	226	3	)	)	PUNCT
ejpam-4441	226	4	=	=	SYM
ejpam-4441	227	1	∞	∞	NUM
ejpam-4441	227	2	∑	∑	PUNCT
ejpam-4441	227	3	k=0	k=0	PROPN
ejpam-4441	227	4	xk	xk	PROPN
ejpam-4441	227	5	∞	∞	PROPN
ejpam-4441	227	6	∑	∑	PUNCT
ejpam-4441	227	7	n	n	PROPN
ejpam-4441	227	8	=	=	PROPN
ejpam-4441	227	9	k	k	PROPN
ejpam-4441	227	10	wm	wm	PROPN
ejpam-4441	227	11	,	,	PUNCT
ejpam-4441	227	12	λ	λ	PROPN
ejpam-4441	227	13	(	(	PUNCT
ejpam-4441	227	14	n	n	X
ejpam-4441	227	15	,	,	PUNCT
ejpam-4441	227	16	k	k	NOUN
ejpam-4441	227	17	)	)	PUNCT
ejpam-4441	227	18	tn	tn	PROPN
ejpam-4441	227	19	n	n	PROPN
ejpam-4441	227	20	!	!	PUNCT
ejpam-4441	228	1	(	(	PUNCT
ejpam-4441	228	2	34	34	NUM
ejpam-4441	228	3	)	)	PUNCT
ejpam-4441	228	4	=	=	SYM
ejpam-4441	228	5	et	et	X
ejpam-4441	228	6	∞	∞	PROPN
ejpam-4441	228	7	∑	∑	PROPN
ejpam-4441	228	8	k=0	k=0	PROPN
ejpam-4441	228	9	xk	xk	PROPN
ejpam-4441	229	1	1	1	NUM
ejpam-4441	229	2	k	k	X
ejpam-4441	229	3	!	!	PROPN
ejpam-4441	230	1	1	1	NUM
ejpam-4441	230	2	λ	λ	X
ejpam-4441	230	3	k	k	X
ejpam-4441	230	4	(	(	PUNCT
ejpam-4441	230	5	eλmt	eλmt	VERB
ejpam-4441	230	6	−1	−1	NOUN
ejpam-4441	230	7	m	m	VERB
ejpam-4441	230	8	)	)	PUNCT
ejpam-4441	230	9	k	k	X
ejpam-4441	230	10	=	=	PUNCT
ejpam-4441	230	11	etex	etex	PROPN
ejpam-4441	230	12	(	(	PUNCT
ejpam-4441	230	13	eλmt−1	eλmt−1	PROPN
ejpam-4441	230	14	λm	λm	ADP
ejpam-4441	230	15	)	)	PUNCT
ejpam-4441	230	16	.	.	PUNCT
ejpam-4441	231	1	theorem	theorem	ADJ
ejpam-4441	231	2	10	10	NUM
ejpam-4441	231	3	.	.	PUNCT
ejpam-4441	232	1	for	for	ADP
ejpam-4441	232	2	m	m	PROPN
ejpam-4441	232	3	∈	∈	PROPN
ejpam-4441	232	4	n	n	CCONJ
ejpam-4441	232	5	,	,	PUNCT
ejpam-4441	232	6	we	we	PRON
ejpam-4441	232	7	have	have	VERB
ejpam-4441	232	8	etex	etex	NOUN
ejpam-4441	232	9	(	(	PUNCT
ejpam-4441	232	10	eλmt−1	eλmt−1	PROPN
ejpam-4441	232	11	λm	λm	NOUN
ejpam-4441	232	12	)	)	PUNCT
ejpam-4441	232	13	=	=	SYM
ejpam-4441	233	1	∞	∞	NUM
ejpam-4441	233	2	∑	∑	PROPN
ejpam-4441	233	3	n=0	n=0	PROPN
ejpam-4441	233	4	dm	dm	PROPN
ejpam-4441	233	5	,	,	PUNCT
ejpam-4441	233	6	λ	λ	PROPN
ejpam-4441	233	7	(	(	PUNCT
ejpam-4441	233	8	n	n	X
ejpam-4441	233	9	,	,	PUNCT
ejpam-4441	233	10	x	x	NOUN
ejpam-4441	233	11	)	)	PUNCT
ejpam-4441	233	12	tn	tn	PROPN
ejpam-4441	233	13	n	n	PROPN
ejpam-4441	233	14	!	!	PUNCT
ejpam-4441	233	15	.	.	PUNCT
ejpam-4441	234	1	when	when	SCONJ
ejpam-4441	234	2	x	x	X
ejpam-4441	234	3	=	=	SYM
ejpam-4441	234	4	1	1	NUM
ejpam-4441	234	5	,	,	PUNCT
ejpam-4441	234	6	dm	dm	NOUN
ejpam-4441	234	7	,	,	PUNCT
ejpam-4441	234	8	λ	λ	PROPN
ejpam-4441	234	9	(	(	PUNCT
ejpam-4441	234	10	n,1	n,1	X
ejpam-4441	234	11	)	)	PUNCT
ejpam-4441	234	12	=	=	SYM
ejpam-4441	234	13	dm	dm	PROPN
ejpam-4441	234	14	,	,	PUNCT
ejpam-4441	234	15	λ	λ	PROPN
ejpam-4441	234	16	(	(	PUNCT
ejpam-4441	234	17	n	n	CCONJ
ejpam-4441	234	18	)	)	PUNCT
ejpam-4441	234	19	are	be	AUX
ejpam-4441	234	20	called	call	VERB
ejpam-4441	234	21	the	the	DET
ejpam-4441	234	22	λ	λ	PROPN
ejpam-4441	234	23	-analogues	-analogue	NOUN
ejpam-4441	234	24	of	of	ADP
ejpam-4441	234	25	dowling	dowle	VERB
ejpam-4441	234	26	numbers	number	NOUN
ejpam-4441	234	27	.	.	PUNCT
ejpam-4441	235	1	we	we	PRON
ejpam-4441	235	2	define	define	VERB
ejpam-4441	235	3	the	the	DET
ejpam-4441	235	4	λ	λ	PROPN
ejpam-4441	235	5	-analogues	-analogue	NOUN
ejpam-4441	235	6	of	of	ADP
ejpam-4441	235	7	bell	bell	NOUN
ejpam-4441	235	8	polynomials	polynomial	NOUN
ejpam-4441	235	9	by	by	ADP
ejpam-4441	235	10	e	e	NOUN
ejpam-4441	235	11	x	x	SYM
ejpam-4441	235	12	λ	λ	PROPN
ejpam-4441	235	13	(	(	PUNCT
ejpam-4441	235	14	eλ	eλ	PROPN
ejpam-4441	235	15	t−1	t−1	PROPN
ejpam-4441	235	16	)	)	PUNCT
ejpam-4441	236	1	=	=	SYM
ejpam-4441	236	2	∞	∞	PROPN
ejpam-4441	236	3	∑	∑	PROPN
ejpam-4441	236	4	n=0	n=0	X
ejpam-4441	236	5	φn	φn	PROPN
ejpam-4441	236	6	,	,	PUNCT
ejpam-4441	236	7	λ	λ	PROPN
ejpam-4441	236	8	(	(	PUNCT
ejpam-4441	236	9	x	x	NOUN
ejpam-4441	236	10	)	)	PUNCT
ejpam-4441	236	11	tn	tn	PROPN
ejpam-4441	236	12	n	n	NUM
ejpam-4441	236	13	!	!	PUNCT
ejpam-4441	236	14	.	.	PUNCT
ejpam-4441	237	1	(	(	PUNCT
ejpam-4441	237	2	35	35	NUM
ejpam-4441	237	3	)	)	PUNCT
ejpam-4441	237	4	thus	thus	ADV
ejpam-4441	237	5	,	,	PUNCT
ejpam-4441	237	6	we	we	PRON
ejpam-4441	237	7	easily	easily	ADV
ejpam-4441	237	8	get	get	VERB
ejpam-4441	237	9	φn	φn	NOUN
ejpam-4441	237	10	,	,	PUNCT
ejpam-4441	237	11	λ	λ	PROPN
ejpam-4441	237	12	(	(	PUNCT
ejpam-4441	237	13	x	x	NOUN
ejpam-4441	237	14	)	)	PUNCT
ejpam-4441	237	15	=	=	SYM
ejpam-4441	238	1	n	n	PROPN
ejpam-4441	238	2	∑	∑	ADP
ejpam-4441	238	3	k=0	k=0	PROPN
ejpam-4441	238	4	{	{	PUNCT
ejpam-4441	238	5	n	n	NOUN
ejpam-4441	238	6	k	k	ADJ
ejpam-4441	238	7	}	}	PUNCT
ejpam-4441	238	8	λ	λ	PROPN
ejpam-4441	238	9	xk	xk	PROPN
ejpam-4441	238	10	,	,	PUNCT
ejpam-4441	238	11	(	(	PUNCT
ejpam-4441	238	12	n	n	CCONJ
ejpam-4441	238	13	≥	≥	NOUN
ejpam-4441	238	14	0	0	NUM
ejpam-4441	238	15	)	)	PUNCT
ejpam-4441	238	16	.	.	PUNCT
ejpam-4441	239	1	when	when	SCONJ
ejpam-4441	239	2	x	x	X
ejpam-4441	239	3	=	=	SYM
ejpam-4441	239	4	1	1	NUM
ejpam-4441	239	5	,	,	PUNCT
ejpam-4441	239	6	φn	φn	INTJ
ejpam-4441	239	7	,	,	PUNCT
ejpam-4441	239	8	λ	λ	PROPN
ejpam-4441	239	9	(	(	PUNCT
ejpam-4441	239	10	1	1	NUM
ejpam-4441	239	11	)	)	PUNCT
ejpam-4441	239	12	=	=	SYM
ejpam-4441	239	13	φn	φn	PROPN
ejpam-4441	239	14	,	,	PUNCT
ejpam-4441	239	15	λ	λ	NOUN
ejpam-4441	239	16	are	be	AUX
ejpam-4441	239	17	called	call	VERB
ejpam-4441	239	18	the	the	DET
ejpam-4441	239	19	λ	λ	PROPN
ejpam-4441	239	20	-analogues	-analogue	NOUN
ejpam-4441	239	21	of	of	ADP
ejpam-4441	239	22	bell	bell	NOUN
ejpam-4441	239	23	numbers	number	NOUN
ejpam-4441	239	24	.	.	PUNCT
ejpam-4441	240	1	d.	d.	PROPN
ejpam-4441	240	2	s.	s.	PROPN
ejpam-4441	240	3	kim	kim	PROPN
ejpam-4441	240	4	,	,	PUNCT
ejpam-4441	240	5	h.	h.	PROPN
ejpam-4441	240	6	k.	k.	PROPN
ejpam-4441	240	7	kim	kim	PROPN
ejpam-4441	240	8	,	,	PUNCT
ejpam-4441	240	9	t.	t.	PROPN
ejpam-4441	240	10	kim	kim	PROPN
ejpam-4441	240	11	/	/	SYM
ejpam-4441	240	12	eur	eur	PROPN
ejpam-4441	240	13	.	.	PUNCT
ejpam-4441	241	1	j.	j.	PROPN
ejpam-4441	241	2	pure	pure	PROPN
ejpam-4441	241	3	appl	appl	PROPN
ejpam-4441	241	4	.	.	PROPN
ejpam-4441	241	5	math	math	PROPN
ejpam-4441	241	6	,	,	PUNCT
ejpam-4441	241	7	15	15	NUM
ejpam-4441	241	8	(	(	PUNCT
ejpam-4441	241	9	3	3	NUM
ejpam-4441	241	10	)	)	PUNCT
ejpam-4441	241	11	(	(	PUNCT
ejpam-4441	241	12	2022	2022	NUM
ejpam-4441	241	13	)	)	PUNCT
ejpam-4441	241	14	,	,	PUNCT
ejpam-4441	241	15	1054	1054	NUM
ejpam-4441	241	16	-	-	SYM
ejpam-4441	241	17	1066	1066	NUM
ejpam-4441	241	18	1063	1063	NUM
ejpam-4441	241	19	from	from	ADP
ejpam-4441	241	20	theorem	theorem	ADJ
ejpam-4441	241	21	10	10	NUM
ejpam-4441	241	22	,	,	PUNCT
ejpam-4441	241	23	we	we	PRON
ejpam-4441	241	24	note	note	VERB
ejpam-4441	241	25	that	that	SCONJ
ejpam-4441	241	26	∞	∞	PROPN
ejpam-4441	241	27	∑	∑	PROPN
ejpam-4441	241	28	n=0	n=0	PROPN
ejpam-4441	241	29	dm	dm	PROPN
ejpam-4441	241	30	,	,	PUNCT
ejpam-4441	241	31	λ	λ	PROPN
ejpam-4441	241	32	(	(	PUNCT
ejpam-4441	241	33	n	n	X
ejpam-4441	241	34	,	,	PUNCT
ejpam-4441	241	35	x	x	NOUN
ejpam-4441	241	36	)	)	PUNCT
ejpam-4441	241	37	tn	tn	PROPN
ejpam-4441	241	38	n	n	NOUN
ejpam-4441	241	39	!	!	PUNCT
ejpam-4441	242	1	=	=	SYM
ejpam-4441	242	2	etex	etex	PROPN
ejpam-4441	242	3	(	(	PUNCT
ejpam-4441	242	4	eλmt−1	eλmt−1	PROPN
ejpam-4441	242	5	λm	λm	NOUN
ejpam-4441	242	6	)	)	PUNCT
ejpam-4441	242	7	=	=	PUNCT
ejpam-4441	243	1	e−	e−	X
ejpam-4441	243	2	x	x	PUNCT
ejpam-4441	244	1	λm	λm	X
ejpam-4441	244	2	etex	etex	PROPN
ejpam-4441	244	3	eλmt	eλmt	NOUN
ejpam-4441	244	4	λm	λm	ADP
ejpam-4441	244	5	(	(	PUNCT
ejpam-4441	244	6	36	36	NUM
ejpam-4441	244	7	)	)	PUNCT
ejpam-4441	244	8	=	=	PUNCT
ejpam-4441	245	1	e−	e−	NOUN
ejpam-4441	245	2	x	x	PUNCT
ejpam-4441	246	1	λm	λm	ADP
ejpam-4441	246	2	∞	∞	NUM
ejpam-4441	246	3	∑	∑	PROPN
ejpam-4441	246	4	k=0	k=0	PROPN
ejpam-4441	246	5	eλmkt+t	eλmkt+t	PROPN
ejpam-4441	246	6	λ	λ	PROPN
ejpam-4441	246	7	kmk	kmk	PROPN
ejpam-4441	246	8	xk	xk	PROPN
ejpam-4441	246	9	k	k	PROPN
ejpam-4441	246	10	!	!	PUNCT
ejpam-4441	246	11	=	=	PUNCT
ejpam-4441	247	1	e−	e−	NOUN
ejpam-4441	247	2	x	x	PUNCT
ejpam-4441	247	3	λm	λm	ADP
ejpam-4441	247	4	∞	∞	NUM
ejpam-4441	247	5	∑	∑	PROPN
ejpam-4441	247	6	k=0	k=0	PROPN
ejpam-4441	247	7	xk	xk	PROPN
ejpam-4441	248	1	k!mkλ	k!mkλ	PROPN
ejpam-4441	248	2	k	k	PROPN
ejpam-4441	249	1	∞	∞	PROPN
ejpam-4441	249	2	∑	∑	PROPN
ejpam-4441	249	3	n=0	n=0	NUM
ejpam-4441	249	4	(	(	PUNCT
ejpam-4441	249	5	λmk+1)n	λmk+1)n	PROPN
ejpam-4441	249	6	tn	tn	PROPN
ejpam-4441	249	7	n	n	ADV
ejpam-4441	249	8	!	!	PUNCT
ejpam-4441	250	1	=	=	SYM
ejpam-4441	251	1	∞	∞	NUM
ejpam-4441	251	2	∑	∑	SYM
ejpam-4441	251	3	n=0	n=0	NUM
ejpam-4441	251	4	(	(	PUNCT
ejpam-4441	251	5	e−	e−	PROPN
ejpam-4441	251	6	x	x	PUNCT
ejpam-4441	251	7	λm	λm	ADP
ejpam-4441	251	8	∞	∞	NUM
ejpam-4441	251	9	∑	∑	PROPN
ejpam-4441	251	10	k=0	k=0	PROPN
ejpam-4441	251	11	xk	xk	PROPN
ejpam-4441	252	1	k!mkλ	k!mkλ	PROPN
ejpam-4441	252	2	k	k	PROPN
ejpam-4441	252	3	(	(	PUNCT
ejpam-4441	252	4	λmk+1)n	λmk+1)n	PROPN
ejpam-4441	252	5	)	)	PUNCT
ejpam-4441	252	6	tn	tn	PROPN
ejpam-4441	252	7	n	n	PROPN
ejpam-4441	252	8	!	!	PUNCT
ejpam-4441	252	9	.	.	PUNCT
ejpam-4441	253	1	therefore	therefore	ADV
ejpam-4441	253	2	,	,	PUNCT
ejpam-4441	253	3	by	by	ADP
ejpam-4441	253	4	comparing	compare	VERB
ejpam-4441	253	5	the	the	DET
ejpam-4441	253	6	coefficients	coefficient	NOUN
ejpam-4441	253	7	on	on	ADP
ejpam-4441	253	8	both	both	DET
ejpam-4441	253	9	sides	side	NOUN
ejpam-4441	253	10	of	of	ADP
ejpam-4441	253	11	(	(	PUNCT
ejpam-4441	253	12	36	36	NUM
ejpam-4441	253	13	)	)	PUNCT
ejpam-4441	253	14	,	,	PUNCT
ejpam-4441	253	15	we	we	PRON
ejpam-4441	253	16	obtain	obtain	VERB
ejpam-4441	253	17	the	the	DET
ejpam-4441	253	18	following	follow	VERB
ejpam-4441	253	19	dobinskilike	dobinskilike	ADJ
ejpam-4441	253	20	formula	formula	NOUN
ejpam-4441	253	21	.	.	PUNCT
ejpam-4441	254	1	theorem	theorem	VERB
ejpam-4441	254	2	11	11	NUM
ejpam-4441	254	3	.	.	PUNCT
ejpam-4441	255	1	for	for	ADP
ejpam-4441	255	2	n	n	PRON
ejpam-4441	255	3	≥	≥	NOUN
ejpam-4441	255	4	0	0	NUM
ejpam-4441	255	5	,	,	PUNCT
ejpam-4441	255	6	we	we	PRON
ejpam-4441	255	7	have	have	VERB
ejpam-4441	255	8	dm	dm	PROPN
ejpam-4441	255	9	,	,	PUNCT
ejpam-4441	255	10	λ	λ	PROPN
ejpam-4441	255	11	(	(	PUNCT
ejpam-4441	255	12	n	n	X
ejpam-4441	255	13	,	,	PUNCT
ejpam-4441	255	14	x	x	NOUN
ejpam-4441	255	15	)	)	PUNCT
ejpam-4441	255	16	=	=	PUNCT
ejpam-4441	256	1	e−	e−	NOUN
ejpam-4441	256	2	x	x	PUNCT
ejpam-4441	256	3	λm	λm	ADP
ejpam-4441	256	4	∞	∞	NUM
ejpam-4441	257	1	∑	∑	PROPN
ejpam-4441	257	2	k=0	k=0	PROPN
ejpam-4441	257	3	xk	xk	PROPN
ejpam-4441	258	1	k!mkλ	k!mkλ	PROPN
ejpam-4441	258	2	k	k	PROPN
ejpam-4441	258	3	(	(	PUNCT
ejpam-4441	258	4	λmk+1)n	λmk+1)n	PROPN
ejpam-4441	258	5	.	.	PUNCT
ejpam-4441	259	1	for	for	ADP
ejpam-4441	259	2	r	r	PROPN
ejpam-4441	259	3	∈	∈	PROPN
ejpam-4441	259	4	n	n	CCONJ
ejpam-4441	259	5	,	,	PUNCT
ejpam-4441	259	6	m	m	PROPN
ejpam-4441	259	7	,	,	PUNCT
ejpam-4441	259	8	n	n	PRON
ejpam-4441	259	9	≥	≥	NOUN
ejpam-4441	259	10	0	0	NUM
ejpam-4441	259	11	,	,	PUNCT
ejpam-4441	259	12	we	we	PRON
ejpam-4441	259	13	consider	consider	VERB
ejpam-4441	259	14	the	the	DET
ejpam-4441	259	15	λ	λ	NOUN
ejpam-4441	259	16	-analogues	-analogue	NOUN
ejpam-4441	259	17	of	of	ADP
ejpam-4441	259	18	the	the	DET
ejpam-4441	259	19	whitneytype	whitneytype	NOUN
ejpam-4441	259	20	r	r	NOUN
ejpam-4441	259	21	-	-	PUNCT
ejpam-4441	259	22	stirling	stirling	NOUN
ejpam-4441	259	23	numbers	number	NOUN
ejpam-4441	259	24	of	of	ADP
ejpam-4441	259	25	the	the	DET
ejpam-4441	259	26	second	second	ADJ
ejpam-4441	259	27	kind	kind	NOUN
ejpam-4441	259	28	defined	define	VERB
ejpam-4441	259	29	by	by	ADP
ejpam-4441	259	30	(	(	PUNCT
ejpam-4441	259	31	mx+	mx+	NOUN
ejpam-4441	259	32	r)n	r)n	NOUN
ejpam-4441	259	33	=	=	SYM
ejpam-4441	259	34	n	n	CCONJ
ejpam-4441	259	35	∑	∑	PUNCT
ejpam-4441	259	36	k=0	k=0	PROPN
ejpam-4441	259	37	w	w	PROPN
ejpam-4441	259	38	(	(	PUNCT
ejpam-4441	259	39	r	r	NOUN
ejpam-4441	259	40	)	)	PUNCT
ejpam-4441	259	41	m	m	PROPN
ejpam-4441	259	42	,	,	PUNCT
ejpam-4441	259	43	λ	λ	X
ejpam-4441	259	44	(	(	PUNCT
ejpam-4441	259	45	n	n	X
ejpam-4441	259	46	,	,	PUNCT
ejpam-4441	259	47	k)m	k)m	X
ejpam-4441	260	1	k(x)k	k(x)k	PROPN
ejpam-4441	260	2	,	,	PUNCT
ejpam-4441	260	3	λ	λ	PROPN
ejpam-4441	260	4	,	,	PUNCT
ejpam-4441	260	5	(	(	PUNCT
ejpam-4441	260	6	n	n	CCONJ
ejpam-4441	260	7	≥	≥	NOUN
ejpam-4441	260	8	0	0	NUM
ejpam-4441	260	9	)	)	PUNCT
ejpam-4441	260	10	.	.	PUNCT
ejpam-4441	261	1	(	(	PUNCT
ejpam-4441	261	2	37	37	NUM
ejpam-4441	261	3	)	)	PUNCT
ejpam-4441	261	4	from	from	ADP
ejpam-4441	261	5	(	(	PUNCT
ejpam-4441	261	6	37	37	NUM
ejpam-4441	261	7	)	)	PUNCT
ejpam-4441	261	8	,	,	PUNCT
ejpam-4441	261	9	we	we	PRON
ejpam-4441	261	10	note	note	VERB
ejpam-4441	261	11	that	that	SCONJ
ejpam-4441	261	12	e(mx+r)t	e(mx+r)t	ADV
ejpam-4441	261	13	=	=	SYM
ejpam-4441	261	14	∞	∞	PROPN
ejpam-4441	261	15	∑	∑	PROPN
ejpam-4441	261	16	n=0	n=0	NUM
ejpam-4441	261	17	(	(	PUNCT
ejpam-4441	261	18	mx+	mx+	NOUN
ejpam-4441	261	19	r)n	r)n	X
ejpam-4441	261	20	tn	tn	NOUN
ejpam-4441	261	21	n	n	X
ejpam-4441	261	22	!	!	PUNCT
ejpam-4441	262	1	=	=	SYM
ejpam-4441	263	1	∞	∞	NUM
ejpam-4441	263	2	∑	∑	SYM
ejpam-4441	263	3	n=0	n=0	NUM
ejpam-4441	263	4	(	(	PUNCT
ejpam-4441	263	5	n	n	CCONJ
ejpam-4441	263	6	∑	∑	ADP
ejpam-4441	263	7	k=0	k=0	PROPN
ejpam-4441	263	8	w	w	PROPN
ejpam-4441	263	9	(	(	PUNCT
ejpam-4441	263	10	r	r	NOUN
ejpam-4441	263	11	)	)	PUNCT
ejpam-4441	263	12	m	m	PROPN
ejpam-4441	263	13	,	,	PUNCT
ejpam-4441	263	14	λ	λ	X
ejpam-4441	263	15	(	(	PUNCT
ejpam-4441	263	16	n	n	X
ejpam-4441	263	17	,	,	PUNCT
ejpam-4441	263	18	k)m	k)m	X
ejpam-4441	263	19	k(x)k	k(x)k	PROPN
ejpam-4441	263	20	)	)	PUNCT
ejpam-4441	263	21	tn	tn	PROPN
ejpam-4441	263	22	n	n	PROPN
ejpam-4441	263	23	!	!	PUNCT
ejpam-4441	264	1	(	(	PUNCT
ejpam-4441	264	2	38	38	NUM
ejpam-4441	264	3	)	)	PUNCT
ejpam-4441	264	4	=	=	SYM
ejpam-4441	265	1	∞	∞	PROPN
ejpam-4441	265	2	∑	∑	PUNCT
ejpam-4441	265	3	k=0	k=0	PROPN
ejpam-4441	265	4	(	(	PUNCT
ejpam-4441	265	5	∞	∞	PROPN
ejpam-4441	265	6	∑	∑	PUNCT
ejpam-4441	265	7	n	n	PROPN
ejpam-4441	265	8	=	=	PROPN
ejpam-4441	265	9	k	k	PROPN
ejpam-4441	265	10	w	w	PROPN
ejpam-4441	265	11	(	(	PUNCT
ejpam-4441	265	12	r	r	NOUN
ejpam-4441	265	13	)	)	PUNCT
ejpam-4441	265	14	m	m	PROPN
ejpam-4441	265	15	,	,	PUNCT
ejpam-4441	265	16	λ	λ	X
ejpam-4441	265	17	(	(	PUNCT
ejpam-4441	265	18	n	n	X
ejpam-4441	265	19	,	,	PUNCT
ejpam-4441	265	20	k	k	NOUN
ejpam-4441	265	21	)	)	PUNCT
ejpam-4441	265	22	tn	tn	PROPN
ejpam-4441	265	23	n	n	PROPN
ejpam-4441	265	24	!	!	PUNCT
ejpam-4441	265	25	)	)	PUNCT
ejpam-4441	266	1	mk(x)k	mk(x)k	X
ejpam-4441	266	2	.	.	PUNCT
ejpam-4441	267	1	on	on	ADP
ejpam-4441	267	2	the	the	DET
ejpam-4441	267	3	other	other	ADJ
ejpam-4441	267	4	hand	hand	NOUN
ejpam-4441	267	5	,	,	PUNCT
ejpam-4441	267	6	by	by	ADP
ejpam-4441	267	7	(	(	PUNCT
ejpam-4441	267	8	1	1	NUM
ejpam-4441	267	9	)	)	PUNCT
ejpam-4441	267	10	,	,	PUNCT
ejpam-4441	267	11	we	we	PRON
ejpam-4441	267	12	get	get	VERB
ejpam-4441	267	13	e(mx+r)t	e(mx+r)t	ADJ
ejpam-4441	267	14	=	=	SYM
ejpam-4441	267	15	ert(emλ	ert(emλ	PROPN
ejpam-4441	267	16	t	t	PROPN
ejpam-4441	267	17	−1	−1	NOUN
ejpam-4441	267	18	+	+	PROPN
ejpam-4441	267	19	1	1	NUM
ejpam-4441	267	20	)	)	PUNCT
ejpam-4441	267	21	x	x	SYM
ejpam-4441	268	1	λ	λ	NOUN
ejpam-4441	268	2	=	=	SYM
ejpam-4441	268	3	∞	∞	PROPN
ejpam-4441	268	4	∑	∑	PUNCT
ejpam-4441	268	5	k=0	k=0	PROPN
ejpam-4441	268	6	(	(	PUNCT
ejpam-4441	268	7	x	x	PUNCT
ejpam-4441	268	8	λ	λ	X
ejpam-4441	268	9	k	k	PROPN
ejpam-4441	268	10	)	)	PUNCT
ejpam-4441	268	11	(	(	PUNCT
ejpam-4441	268	12	emλ	emλ	PROPN
ejpam-4441	268	13	t	t	PROPN
ejpam-4441	268	14	−1)kert	−1)kert	PROPN
ejpam-4441	268	15	(	(	PUNCT
ejpam-4441	268	16	39	39	NUM
ejpam-4441	268	17	)	)	PUNCT
ejpam-4441	268	18	=	=	SYM
ejpam-4441	269	1	∞	∞	NUM
ejpam-4441	269	2	∑	∑	PUNCT
ejpam-4441	269	3	k=0	k=0	PROPN
ejpam-4441	269	4	1	1	NUM
ejpam-4441	269	5	k	k	X
ejpam-4441	269	6	!	!	PROPN
ejpam-4441	269	7	1	1	NUM
ejpam-4441	269	8	λ	λ	X
ejpam-4441	269	9	k	k	X
ejpam-4441	269	10	(	(	PUNCT
ejpam-4441	269	11	e	e	NOUN
ejpam-4441	269	12	mλ	mλ	NOUN
ejpam-4441	269	13	t	t	PROPN
ejpam-4441	269	14	−1)kert(x)k	−1)kert(x)k	PROPN
ejpam-4441	269	15	,	,	PUNCT
ejpam-4441	269	16	λ	λ	X
ejpam-4441	269	17	=	=	SYM
ejpam-4441	269	18	∞	∞	NUM
ejpam-4441	269	19	∑	∑	PUNCT
ejpam-4441	269	20	k=0	k=0	X
ejpam-4441	269	21	(	(	PUNCT
ejpam-4441	269	22	1	1	NUM
ejpam-4441	269	23	k	k	X
ejpam-4441	269	24	!	!	PROPN
ejpam-4441	270	1	1	1	NUM
ejpam-4441	270	2	λ	λ	X
ejpam-4441	270	3	k	k	PROPN
ejpam-4441	270	4	(	(	PUNCT
ejpam-4441	270	5	emλ	emλ	PROPN
ejpam-4441	270	6	t	t	PROPN
ejpam-4441	270	7	−1	−1	NOUN
ejpam-4441	270	8	m	m	VERB
ejpam-4441	270	9	)	)	PUNCT
ejpam-4441	271	1	k	k	PROPN
ejpam-4441	271	2	ert	ert	PROPN
ejpam-4441	271	3	)	)	PUNCT
ejpam-4441	272	1	mk(x)k	mk(x)k	NOUN
ejpam-4441	272	2	,	,	PUNCT
ejpam-4441	272	3	λ	λ	INTJ
ejpam-4441	272	4	.	.	PUNCT
ejpam-4441	273	1	by	by	ADP
ejpam-4441	273	2	(	(	PUNCT
ejpam-4441	273	3	38	38	NUM
ejpam-4441	273	4	)	)	PUNCT
ejpam-4441	273	5	and	and	CCONJ
ejpam-4441	273	6	(	(	PUNCT
ejpam-4441	273	7	39	39	NUM
ejpam-4441	273	8	)	)	PUNCT
ejpam-4441	273	9	,	,	PUNCT
ejpam-4441	273	10	we	we	PRON
ejpam-4441	273	11	get	get	VERB
ejpam-4441	273	12	1	1	NUM
ejpam-4441	273	13	k	k	NOUN
ejpam-4441	273	14	!	!	PROPN
ejpam-4441	274	1	1	1	NUM
ejpam-4441	275	1	λ	λ	X
ejpam-4441	275	2	k	k	X
ejpam-4441	275	3	(	(	PUNCT
ejpam-4441	275	4	eλmt	eλmt	VERB
ejpam-4441	275	5	−1	−1	NOUN
ejpam-4441	275	6	m	m	VERB
ejpam-4441	275	7	)	)	PUNCT
ejpam-4441	276	1	k	k	PROPN
ejpam-4441	277	1	ert	ert	PROPN
ejpam-4441	278	1	=	=	SYM
ejpam-4441	278	2	∞	∞	NUM
ejpam-4441	278	3	∑	∑	PUNCT
ejpam-4441	278	4	n	n	PROPN
ejpam-4441	278	5	=	=	PROPN
ejpam-4441	278	6	k	k	PROPN
ejpam-4441	278	7	w	w	PROPN
ejpam-4441	278	8	(	(	PUNCT
ejpam-4441	278	9	r	r	NOUN
ejpam-4441	278	10	)	)	PUNCT
ejpam-4441	278	11	m	m	PROPN
ejpam-4441	278	12	,	,	PUNCT
ejpam-4441	278	13	λ	λ	X
ejpam-4441	278	14	(	(	PUNCT
ejpam-4441	278	15	n	n	X
ejpam-4441	278	16	,	,	PUNCT
ejpam-4441	278	17	k	k	NOUN
ejpam-4441	278	18	)	)	PUNCT
ejpam-4441	278	19	tn	tn	PROPN
ejpam-4441	278	20	n	n	PROPN
ejpam-4441	278	21	!	!	PROPN
ejpam-4441	278	22	,	,	PUNCT
ejpam-4441	278	23	(	(	PUNCT
ejpam-4441	278	24	40	40	NUM
ejpam-4441	278	25	)	)	PUNCT
ejpam-4441	278	26	d.	d.	PROPN
ejpam-4441	278	27	s.	s.	PROPN
ejpam-4441	278	28	kim	kim	PROPN
ejpam-4441	278	29	,	,	PUNCT
ejpam-4441	278	30	h.	h.	PROPN
ejpam-4441	278	31	k.	k.	PROPN
ejpam-4441	278	32	kim	kim	PROPN
ejpam-4441	278	33	,	,	PUNCT
ejpam-4441	278	34	t.	t.	PROPN
ejpam-4441	278	35	kim	kim	PROPN
ejpam-4441	278	36	/	/	SYM
ejpam-4441	278	37	eur	eur	PROPN
ejpam-4441	278	38	.	.	PUNCT
ejpam-4441	279	1	j.	j.	PROPN
ejpam-4441	279	2	pure	pure	PROPN
ejpam-4441	279	3	appl	appl	PROPN
ejpam-4441	279	4	.	.	PROPN
ejpam-4441	279	5	math	math	PROPN
ejpam-4441	279	6	,	,	PUNCT
ejpam-4441	279	7	15	15	NUM
ejpam-4441	279	8	(	(	PUNCT
ejpam-4441	279	9	3	3	NUM
ejpam-4441	279	10	)	)	PUNCT
ejpam-4441	279	11	(	(	PUNCT
ejpam-4441	279	12	2022	2022	NUM
ejpam-4441	279	13	)	)	PUNCT
ejpam-4441	279	14	,	,	PUNCT
ejpam-4441	279	15	1054	1054	NUM
ejpam-4441	279	16	-	-	SYM
ejpam-4441	279	17	1066	1066	NUM
ejpam-4441	279	18	1064	1064	NUM
ejpam-4441	279	19	where	where	SCONJ
ejpam-4441	279	20	k	k	PROPN
ejpam-4441	279	21	is	be	AUX
ejpam-4441	279	22	a	a	DET
ejpam-4441	279	23	nonnegative	nonnegative	ADJ
ejpam-4441	279	24	integer	integer	NOUN
ejpam-4441	279	25	.	.	PUNCT
ejpam-4441	280	1	therefore	therefore	ADV
ejpam-4441	280	2	,	,	PUNCT
ejpam-4441	280	3	by	by	ADP
ejpam-4441	280	4	(	(	PUNCT
ejpam-4441	280	5	40	40	NUM
ejpam-4441	280	6	)	)	PUNCT
ejpam-4441	280	7	,	,	PUNCT
ejpam-4441	280	8	we	we	PRON
ejpam-4441	280	9	obtain	obtain	VERB
ejpam-4441	280	10	the	the	DET
ejpam-4441	280	11	following	follow	VERB
ejpam-4441	280	12	theorem	theorem	VERB
ejpam-4441	280	13	.	.	PUNCT
ejpam-4441	280	14	theorem	theorem	PROPN
ejpam-4441	280	15	12	12	NUM
ejpam-4441	280	16	.	.	PUNCT
ejpam-4441	281	1	for	for	ADP
ejpam-4441	281	2	k	k	PROPN
ejpam-4441	281	3	≥	≥	PROPN
ejpam-4441	281	4	0	0	NUM
ejpam-4441	281	5	,	,	PUNCT
ejpam-4441	281	6	we	we	PRON
ejpam-4441	281	7	have	have	VERB
ejpam-4441	281	8	1	1	NUM
ejpam-4441	281	9	k	k	NOUN
ejpam-4441	281	10	!	!	PROPN
ejpam-4441	282	1	1	1	NUM
ejpam-4441	282	2	λ	λ	X
ejpam-4441	282	3	k	k	X
ejpam-4441	282	4	(	(	PUNCT
ejpam-4441	282	5	eλmt	eλmt	VERB
ejpam-4441	282	6	−1	−1	NOUN
ejpam-4441	282	7	m	m	VERB
ejpam-4441	282	8	)	)	PUNCT
ejpam-4441	283	1	k	k	PROPN
ejpam-4441	284	1	ert	ert	PROPN
ejpam-4441	285	1	=	=	SYM
ejpam-4441	285	2	∞	∞	NUM
ejpam-4441	285	3	∑	∑	PUNCT
ejpam-4441	285	4	n	n	PROPN
ejpam-4441	285	5	=	=	PROPN
ejpam-4441	285	6	k	k	PROPN
ejpam-4441	285	7	w	w	PROPN
ejpam-4441	285	8	(	(	PUNCT
ejpam-4441	285	9	r	r	NOUN
ejpam-4441	285	10	)	)	PUNCT
ejpam-4441	285	11	m	m	PROPN
ejpam-4441	285	12	,	,	PUNCT
ejpam-4441	285	13	λ	λ	X
ejpam-4441	285	14	(	(	PUNCT
ejpam-4441	285	15	n	n	X
ejpam-4441	285	16	,	,	PUNCT
ejpam-4441	285	17	k	k	NOUN
ejpam-4441	285	18	)	)	PUNCT
ejpam-4441	285	19	tn	tn	PROPN
ejpam-4441	285	20	n	n	PROPN
ejpam-4441	285	21	!	!	PUNCT
ejpam-4441	285	22	.	.	PUNCT
ejpam-4441	286	1	from	from	ADP
ejpam-4441	286	2	(	(	PUNCT
ejpam-4441	286	3	15	15	NUM
ejpam-4441	286	4	)	)	PUNCT
ejpam-4441	286	5	and	and	CCONJ
ejpam-4441	286	6	theorem	theorem	VERB
ejpam-4441	286	7	11	11	NUM
ejpam-4441	286	8	,	,	PUNCT
ejpam-4441	286	9	we	we	PRON
ejpam-4441	286	10	have	have	VERB
ejpam-4441	286	11	w	w	NOUN
ejpam-4441	286	12	(	(	PUNCT
ejpam-4441	286	13	r	r	NOUN
ejpam-4441	286	14	)	)	PUNCT
ejpam-4441	286	15	1,λ	1,λ	NUM
ejpam-4441	286	16	(	(	PUNCT
ejpam-4441	286	17	n	n	X
ejpam-4441	286	18	,	,	PUNCT
ejpam-4441	286	19	k	k	NOUN
ejpam-4441	286	20	)	)	PUNCT
ejpam-4441	287	1	=	=	SYM
ejpam-4441	287	2	{	{	PUNCT
ejpam-4441	287	3	n+	n+	NOUN
ejpam-4441	287	4	r	r	NOUN
ejpam-4441	287	5	k+	k+	NOUN
ejpam-4441	287	6	r	r	NOUN
ejpam-4441	287	7	}	}	PUNCT
ejpam-4441	287	8	r	r	NOUN
ejpam-4441	287	9	,	,	PUNCT
ejpam-4441	287	10	λ	λ	PROPN
ejpam-4441	287	11	,	,	PUNCT
ejpam-4441	287	12	w	w	PROPN
ejpam-4441	287	13	(	(	PUNCT
ejpam-4441	287	14	0	0	NUM
ejpam-4441	287	15	)	)	PUNCT
ejpam-4441	287	16	1,λ	1,λ	NUM
ejpam-4441	287	17	(	(	PUNCT
ejpam-4441	287	18	n	n	X
ejpam-4441	287	19	,	,	PUNCT
ejpam-4441	287	20	k	k	NOUN
ejpam-4441	287	21	)	)	PUNCT
ejpam-4441	287	22	=	=	SYM
ejpam-4441	287	23	{	{	PUNCT
ejpam-4441	287	24	n	n	NOUN
ejpam-4441	287	25	k	k	ADJ
ejpam-4441	287	26	}	}	PUNCT
ejpam-4441	287	27	λ	λ	PROPN
ejpam-4441	287	28	and	and	CCONJ
ejpam-4441	287	29	w	w	PROPN
ejpam-4441	287	30	(	(	PUNCT
ejpam-4441	287	31	1	1	NUM
ejpam-4441	287	32	)	)	PUNCT
ejpam-4441	287	33	m	m	PROPN
ejpam-4441	287	34	,	,	PUNCT
ejpam-4441	287	35	λ	λ	X
ejpam-4441	287	36	(	(	PUNCT
ejpam-4441	287	37	n	n	X
ejpam-4441	287	38	,	,	PUNCT
ejpam-4441	287	39	k	k	NOUN
ejpam-4441	287	40	)	)	PUNCT
ejpam-4441	288	1	=	=	SYM
ejpam-4441	288	2	wm	wm	PROPN
ejpam-4441	288	3	,	,	PUNCT
ejpam-4441	288	4	λ	λ	PROPN
ejpam-4441	288	5	(	(	PUNCT
ejpam-4441	288	6	n	n	X
ejpam-4441	288	7	,	,	PUNCT
ejpam-4441	288	8	k	k	NOUN
ejpam-4441	288	9	)	)	PUNCT
ejpam-4441	288	10	,	,	PUNCT
ejpam-4441	288	11	(	(	PUNCT
ejpam-4441	288	12	n	n	CCONJ
ejpam-4441	288	13	,	,	PUNCT
ejpam-4441	288	14	k	k	PROPN
ejpam-4441	288	15	≥	≥	PROPN
ejpam-4441	288	16	0	0	NUM
ejpam-4441	288	17	)	)	PUNCT
ejpam-4441	288	18	.	.	PUNCT
ejpam-4441	289	1	now	now	ADV
ejpam-4441	289	2	,	,	PUNCT
ejpam-4441	289	3	we	we	PRON
ejpam-4441	289	4	observe	observe	VERB
ejpam-4441	289	5	that	that	SCONJ
ejpam-4441	289	6	∞	∞	PROPN
ejpam-4441	289	7	∑	∑	PUNCT
ejpam-4441	289	8	n	n	PROPN
ejpam-4441	289	9	=	=	PROPN
ejpam-4441	289	10	k	k	PROPN
ejpam-4441	289	11	w	w	PROPN
ejpam-4441	289	12	(	(	PUNCT
ejpam-4441	289	13	r	r	NOUN
ejpam-4441	289	14	)	)	PUNCT
ejpam-4441	289	15	m	m	PROPN
ejpam-4441	289	16	,	,	PUNCT
ejpam-4441	289	17	λ	λ	X
ejpam-4441	289	18	(	(	PUNCT
ejpam-4441	289	19	n	n	X
ejpam-4441	289	20	,	,	PUNCT
ejpam-4441	289	21	k	k	NOUN
ejpam-4441	289	22	)	)	PUNCT
ejpam-4441	289	23	tn	tn	PROPN
ejpam-4441	289	24	n	n	NOUN
ejpam-4441	289	25	!	!	PUNCT
ejpam-4441	290	1	=	=	SYM
ejpam-4441	290	2	1	1	NUM
ejpam-4441	290	3	k	k	NOUN
ejpam-4441	290	4	!	!	PROPN
ejpam-4441	291	1	1	1	NUM
ejpam-4441	291	2	λ	λ	X
ejpam-4441	291	3	k	k	X
ejpam-4441	291	4	(	(	PUNCT
ejpam-4441	291	5	eλmt	eλmt	VERB
ejpam-4441	291	6	−1	−1	NOUN
ejpam-4441	291	7	m	m	VERB
ejpam-4441	291	8	)	)	PUNCT
ejpam-4441	292	1	k	k	PROPN
ejpam-4441	292	2	ert	ert	NOUN
ejpam-4441	292	3	(	(	PUNCT
ejpam-4441	292	4	41	41	NUM
ejpam-4441	292	5	)	)	PUNCT
ejpam-4441	292	6	=	=	SYM
ejpam-4441	293	1	1	1	NUM
ejpam-4441	293	2	k	k	NOUN
ejpam-4441	293	3	!	!	PROPN
ejpam-4441	293	4	1	1	NUM
ejpam-4441	293	5	λ	λ	NOUN
ejpam-4441	293	6	k+α	k+α	PROPN
ejpam-4441	293	7	(	(	PUNCT
ejpam-4441	293	8	eλmt	eλmt	VERB
ejpam-4441	293	9	−1	−1	NOUN
ejpam-4441	293	10	m	m	VERB
ejpam-4441	293	11	)	)	PUNCT
ejpam-4441	293	12	k+α	k+α	VERB
ejpam-4441	293	13	et	et	NOUN
ejpam-4441	293	14	1	1	NUM
ejpam-4441	293	15	tα	tα	PROPN
ejpam-4441	293	16	(	(	PUNCT
ejpam-4441	293	17	λmt	λmt	VERB
ejpam-4441	293	18	eλmt	eλmt	NOUN
ejpam-4441	293	19	−1	−1	NOUN
ejpam-4441	293	20	)	)	PUNCT
ejpam-4441	293	21	α	α	PROPN
ejpam-4441	294	1	e(r−1)t	e(r−1)t	NOUN
ejpam-4441	294	2	=	=	SYM
ejpam-4441	294	3	(	(	PUNCT
ejpam-4441	294	4	k+α	k+α	PROPN
ejpam-4441	294	5	)	)	PUNCT
ejpam-4441	294	6	!	!	PUNCT
ejpam-4441	295	1	k	k	X
ejpam-4441	295	2	!	!	PROPN
ejpam-4441	295	3	1	1	NUM
ejpam-4441	295	4	tα	tα	ADP
ejpam-4441	295	5	1	1	NUM
ejpam-4441	295	6	(	(	PUNCT
ejpam-4441	295	7	k+α	k+α	PROPN
ejpam-4441	295	8	)	)	PUNCT
ejpam-4441	295	9	!	!	PUNCT
ejpam-4441	296	1	1	1	NUM
ejpam-4441	296	2	λ	λ	NOUN
ejpam-4441	296	3	k+α	k+α	PROPN
ejpam-4441	296	4	(	(	PUNCT
ejpam-4441	296	5	eλmt	eλmt	VERB
ejpam-4441	296	6	−1	−1	NOUN
ejpam-4441	296	7	m	m	VERB
ejpam-4441	296	8	)	)	PUNCT
ejpam-4441	296	9	k+α	k+α	VERB
ejpam-4441	296	10	et	et	NOUN
ejpam-4441	296	11	∞	∞	PROPN
ejpam-4441	296	12	∑	∑	PUNCT
ejpam-4441	296	13	j=0	j=0	PROPN
ejpam-4441	296	14	b(α	b(α	PROPN
ejpam-4441	296	15	)	)	PUNCT
ejpam-4441	296	16	j	j	PROPN
ejpam-4441	296	17	(	(	PUNCT
ejpam-4441	296	18	r−1	r−1	PROPN
ejpam-4441	296	19	mλ	mλ	NOUN
ejpam-4441	296	20	)	)	PUNCT
ejpam-4441	297	1	λ	λ	PROPN
ejpam-4441	297	2	jm	jm	PROPN
ejpam-4441	297	3	j	j	PROPN
ejpam-4441	297	4	t	t	PROPN
ejpam-4441	297	5	j	j	PROPN
ejpam-4441	297	6	j	j	PROPN
ejpam-4441	297	7	!	!	PUNCT
ejpam-4441	297	8	=	=	SYM
ejpam-4441	298	1	α	α	X
ejpam-4441	298	2	!	!	PUNCT
ejpam-4441	298	3	tα	tα	PROPN
ejpam-4441	298	4	(	(	PUNCT
ejpam-4441	298	5	k+α	k+α	PROPN
ejpam-4441	298	6	k	k	PROPN
ejpam-4441	298	7	)	)	PUNCT
ejpam-4441	299	1	∞	∞	PROPN
ejpam-4441	299	2	∑	∑	PUNCT
ejpam-4441	299	3	l	l	X
ejpam-4441	299	4	=	=	PROPN
ejpam-4441	299	5	k+α	k+α	PROPN
ejpam-4441	299	6	wm	wm	PROPN
ejpam-4441	299	7	,	,	PUNCT
ejpam-4441	299	8	λ	λ	PROPN
ejpam-4441	299	9	(	(	PUNCT
ejpam-4441	299	10	l	l	NOUN
ejpam-4441	299	11	,	,	PUNCT
ejpam-4441	299	12	k+α	k+α	PROPN
ejpam-4441	299	13	)	)	PUNCT
ejpam-4441	299	14	t	t	NOUN
ejpam-4441	299	15	l	l	NOUN
ejpam-4441	299	16	l	l	NOUN
ejpam-4441	299	17	!	!	PUNCT
ejpam-4441	300	1	∞	∞	PROPN
ejpam-4441	300	2	∑	∑	PUNCT
ejpam-4441	300	3	j=0	j=0	PROPN
ejpam-4441	300	4	b(α	b(α	PROPN
ejpam-4441	300	5	)	)	PUNCT
ejpam-4441	300	6	j	j	PROPN
ejpam-4441	300	7	(	(	PUNCT
ejpam-4441	300	8	r−	r−	PROPN
ejpam-4441	300	9	j	j	PROPN
ejpam-4441	300	10	mλ	mλ	PROPN
ejpam-4441	300	11	)	)	PUNCT
ejpam-4441	301	1	λ	λ	PROPN
ejpam-4441	301	2	jm	jm	PROPN
ejpam-4441	301	3	j	j	PROPN
ejpam-4441	301	4	t	t	PROPN
ejpam-4441	301	5	j	j	PROPN
ejpam-4441	301	6	j	j	PROPN
ejpam-4441	301	7	!	!	PUNCT
ejpam-4441	302	1	=	=	PUNCT
ejpam-4441	303	1	(	(	PUNCT
ejpam-4441	303	2	k+α	k+α	PROPN
ejpam-4441	303	3	k	k	X
ejpam-4441	303	4	)	)	PUNCT
ejpam-4441	303	5	(	(	PUNCT
ejpam-4441	303	6	∞	∞	NUM
ejpam-4441	303	7	∑	∑	PROPN
ejpam-4441	303	8	l	l	X
ejpam-4441	303	9	=	=	PROPN
ejpam-4441	303	10	k	k	X
ejpam-4441	303	11	wm	wm	PROPN
ejpam-4441	303	12	,	,	PUNCT
ejpam-4441	303	13	λ	λ	PROPN
ejpam-4441	303	14	(	(	PUNCT
ejpam-4441	303	15	l	l	X
ejpam-4441	303	16	+	+	NOUN
ejpam-4441	303	17	α	α	NOUN
ejpam-4441	303	18	,	,	PUNCT
ejpam-4441	303	19	k+α)(l+α	k+α)(l+α	NOUN
ejpam-4441	303	20	l	l	NOUN
ejpam-4441	303	21	)	)	PUNCT
ejpam-4441	303	22	t	t	NOUN
ejpam-4441	303	23	l	l	NOUN
ejpam-4441	303	24	l	l	NOUN
ejpam-4441	303	25	!	!	PUNCT
ejpam-4441	303	26	)	)	PUNCT
ejpam-4441	304	1	∞	∞	NUM
ejpam-4441	304	2	∑	∑	PUNCT
ejpam-4441	304	3	j=0	j=0	PROPN
ejpam-4441	304	4	b(α	b(α	PROPN
ejpam-4441	304	5	)	)	PUNCT
ejpam-4441	304	6	j	j	PROPN
ejpam-4441	304	7	(	(	PUNCT
ejpam-4441	304	8	r−	r−	PROPN
ejpam-4441	304	9	j	j	PROPN
ejpam-4441	304	10	mλ	mλ	PROPN
ejpam-4441	304	11	)	)	PUNCT
ejpam-4441	305	1	λ	λ	PROPN
ejpam-4441	305	2	jm	jm	PROPN
ejpam-4441	305	3	j	j	PROPN
ejpam-4441	305	4	t	t	PROPN
ejpam-4441	305	5	j	j	PROPN
ejpam-4441	305	6	j	j	PROPN
ejpam-4441	305	7	!	!	PUNCT
ejpam-4441	306	1	=	=	PUNCT
ejpam-4441	307	1	(	(	PUNCT
ejpam-4441	307	2	k+α	k+α	PROPN
ejpam-4441	307	3	k	k	PROPN
ejpam-4441	307	4	)	)	PUNCT
ejpam-4441	307	5	∞	∞	PROPN
ejpam-4441	307	6	∑	∑	PUNCT
ejpam-4441	307	7	n	n	CCONJ
ejpam-4441	307	8	=	=	SYM
ejpam-4441	307	9	k	k	X
ejpam-4441	307	10	(	(	PUNCT
ejpam-4441	307	11	n	n	CCONJ
ejpam-4441	307	12	∑	∑	PROPN
ejpam-4441	307	13	l	l	X
ejpam-4441	307	14	=	=	SYM
ejpam-4441	307	15	k	k	X
ejpam-4441	307	16	(	(	PUNCT
ejpam-4441	307	17	n	n	X
ejpam-4441	307	18	l	l	NOUN
ejpam-4441	307	19	)	)	PUNCT
ejpam-4441	307	20	(	(	PUNCT
ejpam-4441	307	21	l+α	l+α	NOUN
ejpam-4441	307	22	l	l	NOUN
ejpam-4441	307	23	)	)	PUNCT
ejpam-4441	307	24	wm	wm	PROPN
ejpam-4441	307	25	,	,	PUNCT
ejpam-4441	307	26	λ	λ	PROPN
ejpam-4441	307	27	(	(	PUNCT
ejpam-4441	307	28	l	l	X
ejpam-4441	307	29	+	+	NOUN
ejpam-4441	307	30	α	α	NOUN
ejpam-4441	307	31	,	,	PUNCT
ejpam-4441	307	32	k+α)b(α	k+α)b(α	PROPN
ejpam-4441	307	33	)	)	PUNCT
ejpam-4441	307	34	n−l	n−l	NOUN
ejpam-4441	307	35	(	(	PUNCT
ejpam-4441	307	36	r−n+	r−n+	ADJ
ejpam-4441	307	37	l	l	NOUN
ejpam-4441	307	38	mλ	mλ	NOUN
ejpam-4441	307	39	)	)	PUNCT
ejpam-4441	308	1	λ	λ	INTJ
ejpam-4441	308	2	n−lmn−l	n−lmn−l	PROPN
ejpam-4441	308	3	)	)	PUNCT
ejpam-4441	308	4	tn	tn	PROPN
ejpam-4441	308	5	n	n	PROPN
ejpam-4441	308	6	!	!	PROPN
ejpam-4441	308	7	,	,	PUNCT
ejpam-4441	308	8	where	where	SCONJ
ejpam-4441	308	9	α	α	NOUN
ejpam-4441	308	10	is	be	AUX
ejpam-4441	308	11	a	a	DET
ejpam-4441	308	12	positive	positive	ADJ
ejpam-4441	308	13	integer	integer	NOUN
ejpam-4441	308	14	.	.	PUNCT
ejpam-4441	309	1	comparing	compare	VERB
ejpam-4441	309	2	the	the	DET
ejpam-4441	309	3	coefficients	coefficient	NOUN
ejpam-4441	309	4	on	on	ADP
ejpam-4441	309	5	both	both	DET
ejpam-4441	309	6	sides	side	NOUN
ejpam-4441	309	7	of	of	ADP
ejpam-4441	309	8	(	(	PUNCT
ejpam-4441	309	9	41	41	NUM
ejpam-4441	309	10	)	)	PUNCT
ejpam-4441	309	11	,	,	PUNCT
ejpam-4441	309	12	we	we	PRON
ejpam-4441	309	13	have	have	VERB
ejpam-4441	309	14	the	the	DET
ejpam-4441	309	15	following	follow	VERB
ejpam-4441	309	16	theorem	theorem	VERB
ejpam-4441	309	17	.	.	PUNCT
ejpam-4441	309	18	theorem	theorem	PROPN
ejpam-4441	309	19	13	13	NUM
ejpam-4441	309	20	.	.	PUNCT
ejpam-4441	310	1	for	for	ADP
ejpam-4441	310	2	n	n	PRON
ejpam-4441	310	3	,	,	PUNCT
ejpam-4441	310	4	k	k	PROPN
ejpam-4441	310	5	∈	∈	PROPN
ejpam-4441	310	6	n∪{0	n∪{0	NOUN
ejpam-4441	310	7	}	}	PUNCT
ejpam-4441	310	8	and	and	CCONJ
ejpam-4441	310	9	α	α	PRON
ejpam-4441	310	10	∈	∈	PROPN
ejpam-4441	310	11	n	n	CCONJ
ejpam-4441	310	12	,	,	PUNCT
ejpam-4441	310	13	we	we	PRON
ejpam-4441	310	14	have	have	VERB
ejpam-4441	310	15	(	(	PUNCT
ejpam-4441	310	16	k+α	k+α	PROPN
ejpam-4441	310	17	k	k	X
ejpam-4441	310	18	)	)	PUNCT
ejpam-4441	310	19	−1	−1	NOUN
ejpam-4441	311	1	w	w	NOUN
ejpam-4441	311	2	(	(	PUNCT
ejpam-4441	311	3	r	r	NOUN
ejpam-4441	311	4	)	)	PUNCT
ejpam-4441	311	5	m	m	PROPN
ejpam-4441	311	6	,	,	PUNCT
ejpam-4441	311	7	λ	λ	X
ejpam-4441	311	8	(	(	PUNCT
ejpam-4441	311	9	n	n	X
ejpam-4441	311	10	,	,	PUNCT
ejpam-4441	311	11	k	k	NOUN
ejpam-4441	311	12	)	)	PUNCT
ejpam-4441	311	13	=	=	SYM
ejpam-4441	311	14	n	n	CCONJ
ejpam-4441	311	15	∑	∑	PROPN
ejpam-4441	311	16	l	l	X
ejpam-4441	311	17	=	=	SYM
ejpam-4441	311	18	k	k	X
ejpam-4441	311	19	(	(	PUNCT
ejpam-4441	311	20	n	n	X
ejpam-4441	311	21	l	l	NOUN
ejpam-4441	311	22	)	)	PUNCT
ejpam-4441	311	23	(	(	PUNCT
ejpam-4441	311	24	l+α	l+α	NOUN
ejpam-4441	311	25	l	l	NOUN
ejpam-4441	311	26	)	)	PUNCT
ejpam-4441	311	27	wm	wm	PROPN
ejpam-4441	311	28	,	,	PUNCT
ejpam-4441	311	29	λ	λ	PROPN
ejpam-4441	311	30	(	(	PUNCT
ejpam-4441	311	31	l	l	X
ejpam-4441	311	32	+	+	NOUN
ejpam-4441	311	33	α	α	NOUN
ejpam-4441	311	34	,	,	PUNCT
ejpam-4441	311	35	k+α)b(α	k+α)b(α	PROPN
ejpam-4441	311	36	)	)	PUNCT
ejpam-4441	311	37	n−l	n−l	NOUN
ejpam-4441	311	38	(	(	PUNCT
ejpam-4441	311	39	r−n+	r−n+	ADJ
ejpam-4441	311	40	l	l	NOUN
ejpam-4441	311	41	mλ	mλ	NOUN
ejpam-4441	311	42	)	)	PUNCT
ejpam-4441	311	43	λ	λ	INTJ
ejpam-4441	311	44	n−lmn−l	n−lmn−l	ADJ
ejpam-4441	311	45	.	.	PROPN
ejpam-4441	312	1	4	4	NUM
ejpam-4441	312	2	.	.	X
ejpam-4441	312	3	conclusion	conclusion	NOUN
ejpam-4441	312	4	in	in	ADP
ejpam-4441	312	5	this	this	DET
ejpam-4441	312	6	paper	paper	NOUN
ejpam-4441	312	7	,	,	PUNCT
ejpam-4441	312	8	we	we	PRON
ejpam-4441	312	9	introduced	introduce	VERB
ejpam-4441	312	10	the	the	DET
ejpam-4441	312	11	λ	λ	PROPN
ejpam-4441	312	12	-analogues	-analogue	NOUN
ejpam-4441	312	13	of	of	ADP
ejpam-4441	312	14	r	r	NOUN
ejpam-4441	312	15	-	-	PUNCT
ejpam-4441	312	16	stirling	stirling	NOUN
ejpam-4441	312	17	numbers	number	NOUN
ejpam-4441	312	18	of	of	ADP
ejpam-4441	312	19	the	the	DET
ejpam-4441	312	20	second	second	ADJ
ejpam-4441	312	21	which	which	PRON
ejpam-4441	312	22	appear	appear	VERB
ejpam-4441	312	23	as	as	ADP
ejpam-4441	312	24	the	the	DET
ejpam-4441	312	25	coefficients	coefficient	NOUN
ejpam-4441	312	26	when	when	SCONJ
ejpam-4441	312	27	powers	power	NOUN
ejpam-4441	312	28	of	of	ADP
ejpam-4441	312	29	x+	x+	X
ejpam-4441	312	30	r	r	NOUN
ejpam-4441	312	31	are	be	AUX
ejpam-4441	312	32	expressed	express	VERB
ejpam-4441	312	33	in	in	ADP
ejpam-4441	312	34	terms	term	NOUN
ejpam-4441	312	35	of	of	ADP
ejpam-4441	312	36	the	the	DET
ejpam-4441	312	37	degenerate	degenerate	ADJ
ejpam-4441	312	38	falling	fall	VERB
ejpam-4441	312	39	factorial	factorial	ADJ
ejpam-4441	312	40	references	reference	NOUN
ejpam-4441	312	41	1065	1065	NUM
ejpam-4441	312	42	sequence	sequence	NOUN
ejpam-4441	312	43	.	.	PUNCT
ejpam-4441	313	1	we	we	PRON
ejpam-4441	313	2	obtained	obtain	VERB
ejpam-4441	313	3	some	some	DET
ejpam-4441	313	4	properties	property	NOUN
ejpam-4441	313	5	,	,	PUNCT
ejpam-4441	313	6	recurrence	recurrence	NOUN
ejpam-4441	313	7	relations	relation	NOUN
ejpam-4441	313	8	and	and	CCONJ
ejpam-4441	313	9	certain	certain	ADJ
ejpam-4441	313	10	identities	identity	NOUN
ejpam-4441	313	11	on	on	ADP
ejpam-4441	313	12	such	such	ADJ
ejpam-4441	313	13	numbers	number	NOUN
ejpam-4441	313	14	.	.	PUNCT
ejpam-4441	314	1	we	we	PRON
ejpam-4441	314	2	also	also	ADV
ejpam-4441	314	3	introduced	introduce	VERB
ejpam-4441	314	4	the	the	DET
ejpam-4441	314	5	λ	λ	PROPN
ejpam-4441	314	6	-analogues	-analogue	NOUN
ejpam-4441	314	7	of	of	ADP
ejpam-4441	314	8	whitney	whitney	NOUN
ejpam-4441	314	9	-	-	PUNCT
ejpam-4441	314	10	type	type	NOUN
ejpam-4441	314	11	r	r	NOUN
ejpam-4441	314	12	-	-	PUNCT
ejpam-4441	314	13	stirling	stirling	NOUN
ejpam-4441	314	14	numbers	number	NOUN
ejpam-4441	314	15	of	of	ADP
ejpam-4441	314	16	the	the	DET
ejpam-4441	314	17	second	second	ADJ
ejpam-4441	314	18	and	and	CCONJ
ejpam-4441	314	19	derived	derive	VERB
ejpam-4441	314	20	similar	similar	ADJ
ejpam-4441	314	21	results	result	NOUN
ejpam-4441	314	22	to	to	ADP
ejpam-4441	314	23	the	the	DET
ejpam-4441	314	24	case	case	NOUN
ejpam-4441	314	25	of	of	ADP
ejpam-4441	314	26	the	the	DET
ejpam-4441	314	27	λ	λ	PROPN
ejpam-4441	314	28	-analogues	-analogue	NOUN
ejpam-4441	314	29	of	of	ADP
ejpam-4441	314	30	r	r	NOUN
ejpam-4441	314	31	-	-	PUNCT
ejpam-4441	314	32	stirling	stirling	NOUN
ejpam-4441	314	33	numbers	number	NOUN
ejpam-4441	314	34	of	of	ADP
ejpam-4441	314	35	the	the	DET
ejpam-4441	314	36	second	second	NOUN
ejpam-4441	314	37	.	.	PUNCT
ejpam-4441	315	1	furthermore	furthermore	ADV
ejpam-4441	315	2	,	,	PUNCT
ejpam-4441	315	3	the	the	DET
ejpam-4441	315	4	λ	λ	PROPN
ejpam-4441	315	5	-analogues	-analogue	NOUN
ejpam-4441	315	6	of	of	ADP
ejpam-4441	315	7	dowling	dowle	VERB
ejpam-4441	315	8	polynomials	polynomial	NOUN
ejpam-4441	315	9	were	be	AUX
ejpam-4441	315	10	introduced	introduce	VERB
ejpam-4441	315	11	as	as	ADP
ejpam-4441	315	12	a	a	DET
ejpam-4441	315	13	natural	natural	ADJ
ejpam-4441	315	14	extension	extension	NOUN
ejpam-4441	315	15	of	of	ADP
ejpam-4441	315	16	the	the	DET
ejpam-4441	315	17	analogues	analogue	NOUN
ejpam-4441	315	18	of	of	ADP
ejpam-4441	315	19	whitney	whitney	NOUN
ejpam-4441	315	20	-	-	PUNCT
ejpam-4441	315	21	type	type	NOUN
ejpam-4441	315	22	stirling	stirling	NOUN
ejpam-4441	315	23	numbers	number	NOUN
ejpam-4441	315	24	of	of	ADP
ejpam-4441	315	25	the	the	DET
ejpam-4441	315	26	second	second	ADJ
ejpam-4441	315	27	kind	kind	NOUN
ejpam-4441	315	28	and	and	CCONJ
ejpam-4441	315	29	a	a	DET
ejpam-4441	315	30	dobinski	dobinski	ADJ
ejpam-4441	315	31	-	-	PUNCT
ejpam-4441	315	32	like	like	ADJ
ejpam-4441	315	33	formula	formula	NOUN
ejpam-4441	315	34	for	for	ADP
ejpam-4441	315	35	them	they	PRON
ejpam-4441	315	36	was	be	AUX
ejpam-4441	315	37	deduced	deduce	VERB
ejpam-4441	315	38	.	.	PUNCT
ejpam-4441	316	1	it	it	PRON
ejpam-4441	316	2	is	be	AUX
ejpam-4441	316	3	one	one	NUM
ejpam-4441	316	4	of	of	ADP
ejpam-4441	316	5	our	our	PRON
ejpam-4441	316	6	future	future	ADJ
ejpam-4441	316	7	projects	project	NOUN
ejpam-4441	316	8	to	to	PART
ejpam-4441	316	9	continue	continue	VERB
ejpam-4441	316	10	to	to	PART
ejpam-4441	316	11	study	study	VERB
ejpam-4441	316	12	analogues	analogue	NOUN
ejpam-4441	316	13	of	of	ADP
ejpam-4441	316	14	some	some	DET
ejpam-4441	316	15	special	special	ADJ
ejpam-4441	316	16	numbers	number	NOUN
ejpam-4441	316	17	and	and	CCONJ
ejpam-4441	316	18	polynomials	polynomial	NOUN
ejpam-4441	316	19	and	and	CCONJ
ejpam-4441	316	20	to	to	PART
ejpam-4441	316	21	find	find	VERB
ejpam-4441	316	22	their	their	PRON
ejpam-4441	316	23	applications	application	NOUN
ejpam-4441	316	24	in	in	ADP
ejpam-4441	316	25	physics	physics	NOUN
ejpam-4441	316	26	,	,	PUNCT
ejpam-4441	316	27	science	science	NOUN
ejpam-4441	316	28	and	and	CCONJ
ejpam-4441	316	29	engineering	engineering	NOUN
ejpam-4441	316	30	.	.	PUNCT
ejpam-4441	317	1	funding	funding	NOUN
ejpam-4441	317	2	this	this	DET
ejpam-4441	317	3	work	work	NOUN
ejpam-4441	317	4	was	be	AUX
ejpam-4441	317	5	supported	support	VERB
ejpam-4441	317	6	by	by	ADP
ejpam-4441	317	7	the	the	DET
ejpam-4441	317	8	basic	basic	ADJ
ejpam-4441	317	9	science	science	NOUN
ejpam-4441	317	10	research	research	NOUN
ejpam-4441	317	11	program	program	NOUN
ejpam-4441	317	12	,	,	PUNCT
ejpam-4441	317	13	the	the	DET
ejpam-4441	317	14	national	national	PROPN
ejpam-4441	317	15	research	research	PROPN
ejpam-4441	317	16	foundation	foundation	PROPN
ejpam-4441	317	17	of	of	ADP
ejpam-4441	317	18	korea	korea	PROPN
ejpam-4441	317	19	,	,	PUNCT
ejpam-4441	317	20	(	(	PUNCT
ejpam-4441	317	21	nrf-2021r1f1a1050151	nrf-2021r1f1a1050151	PROPN
ejpam-4441	317	22	)	)	PUNCT
ejpam-4441	317	23	.	.	PUNCT
ejpam-4441	318	1	references	reference	NOUN
ejpam-4441	318	2	[	[	X
ejpam-4441	318	3	1	1	X
ejpam-4441	318	4	]	]	PUNCT
ejpam-4441	318	5	s.	s.	PROPN
ejpam-4441	318	6	araci	araci	PROPN
ejpam-4441	318	7	.	.	PUNCT
ejpam-4441	319	1	a	a	DET
ejpam-4441	319	2	new	new	ADJ
ejpam-4441	319	3	class	class	NOUN
ejpam-4441	319	4	of	of	ADP
ejpam-4441	319	5	bernoulli	bernoulli	NOUN
ejpam-4441	319	6	polynomials	polynomial	NOUN
ejpam-4441	319	7	attached	attach	VERB
ejpam-4441	319	8	to	to	ADP
ejpam-4441	319	9	polyexponential	polyexponential	ADJ
ejpam-4441	319	10	functions	function	NOUN
ejpam-4441	319	11	and	and	CCONJ
ejpam-4441	319	12	related	related	ADJ
ejpam-4441	319	13	identities	identity	NOUN
ejpam-4441	319	14	.	.	PUNCT
ejpam-4441	320	1	advanced	advanced	ADJ
ejpam-4441	320	2	studies	study	NOUN
ejpam-4441	320	3	in	in	ADP
ejpam-4441	320	4	contemporary	contemporary	ADJ
ejpam-4441	320	5	mathematics	mathematic	NOUN
ejpam-4441	320	6	.	.	PUNCT
ejpam-4441	320	7	,	,	PUNCT
ejpam-4441	320	8	31(2):195–204	31(2):195–204	PROPN
ejpam-4441	320	9	,	,	PUNCT
ejpam-4441	320	10	2021	2021	NUM
ejpam-4441	320	11	.	.	PUNCT
ejpam-4441	321	1	[	[	X
ejpam-4441	321	2	2	2	NUM
ejpam-4441	321	3	]	]	PUNCT
ejpam-4441	321	4	m.	m.	NOUN
ejpam-4441	321	5	s.	s.	PROPN
ejpam-4441	321	6	aydin	aydin	PROPN
ejpam-4441	321	7	,	,	PUNCT
ejpam-4441	321	8	m.	m.	NOUN
ejpam-4441	321	9	acikgoz	acikgoz	ADJ
ejpam-4441	321	10	,	,	PUNCT
ejpam-4441	321	11	and	and	CCONJ
ejpam-4441	321	12	s.	s.	PROPN
ejpam-4441	321	13	araci	araci	PROPN
ejpam-4441	321	14	.	.	PUNCT
ejpam-4441	322	1	a	a	DET
ejpam-4441	322	2	new	new	ADJ
ejpam-4441	322	3	construction	construction	NOUN
ejpam-4441	322	4	on	on	ADP
ejpam-4441	322	5	the	the	DET
ejpam-4441	322	6	degenerate	degenerate	ADJ
ejpam-4441	322	7	hurwitz	hurwitz	PROPN
ejpam-4441	322	8	-	-	PUNCT
ejpam-4441	322	9	zeta	zeta	PROPN
ejpam-4441	322	10	function	function	NOUN
ejpam-4441	322	11	associated	associate	VERB
ejpam-4441	322	12	with	with	ADP
ejpam-4441	322	13	certain	certain	ADJ
ejpam-4441	322	14	applications	application	NOUN
ejpam-4441	322	15	.	.	PUNCT
ejpam-4441	323	1	proceedings	proceeding	NOUN
ejpam-4441	323	2	of	of	ADP
ejpam-4441	323	3	the	the	DET
ejpam-4441	323	4	jangjeon	jangjeon	PROPN
ejpam-4441	323	5	mathematical	mathematical	PROPN
ejpam-4441	323	6	society	society	NOUN
ejpam-4441	323	7	,	,	PUNCT
ejpam-4441	323	8	25(2):195–203	25(2):195–203	NOUN
ejpam-4441	323	9	,	,	PUNCT
ejpam-4441	323	10	2022	2022	NUM
ejpam-4441	323	11	.	.	PUNCT
ejpam-4441	324	1	[	[	X
ejpam-4441	324	2	3	3	X
ejpam-4441	324	3	]	]	X
ejpam-4441	324	4	l.	l.	PROPN
ejpam-4441	324	5	carlitz	carlitz	PROPN
ejpam-4441	324	6	.	.	PUNCT
ejpam-4441	324	7	degenerate	degenerate	ADJ
ejpam-4441	324	8	stirling	stirling	PROPN
ejpam-4441	324	9	,	,	PUNCT
ejpam-4441	324	10	bernoulli	bernoulli	PROPN
ejpam-4441	324	11	and	and	CCONJ
ejpam-4441	324	12	eulerian	eulerian	ADJ
ejpam-4441	324	13	numbers	number	NOUN
ejpam-4441	324	14	.	.	PUNCT
ejpam-4441	325	1	utilitas	utilitas	PROPN
ejpam-4441	325	2	mathematica	mathematica	PROPN
ejpam-4441	325	3	.	.	PROPN
ejpam-4441	325	4	,	,	PUNCT
ejpam-4441	325	5	15:51–88	15:51–88	NUM
ejpam-4441	325	6	,	,	PUNCT
ejpam-4441	325	7	1979	1979	NUM
ejpam-4441	325	8	.	.	PUNCT
ejpam-4441	326	1	[	[	X
ejpam-4441	326	2	4	4	NUM
ejpam-4441	326	3	]	]	PUNCT
ejpam-4441	326	4	l.	l.	PROPN
ejpam-4441	326	5	comtet	comtet	PROPN
ejpam-4441	326	6	.	.	PUNCT
ejpam-4441	327	1	advanced	advanced	ADJ
ejpam-4441	327	2	combinatorics	combinatoric	NOUN
ejpam-4441	327	3	.	.	PUNCT
ejpam-4441	328	1	the	the	DET
ejpam-4441	328	2	art	art	NOUN
ejpam-4441	328	3	of	of	ADP
ejpam-4441	328	4	finite	finite	NOUN
ejpam-4441	328	5	and	and	CCONJ
ejpam-4441	328	6	infinite	infinite	ADJ
ejpam-4441	328	7	expansions	expansion	NOUN
ejpam-4441	328	8	.	.	PUNCT
ejpam-4441	328	9	,	,	PUNCT
ejpam-4441	328	10	volume	volume	NOUN
ejpam-4441	328	11	isbn	isbn	NOUN
ejpam-4441	328	12	:	:	PUNCT
ejpam-4441	328	13	90	90	NUM
ejpam-4441	328	14	-	-	PUNCT
ejpam-4441	328	15	277	277	NUM
ejpam-4441	328	16	-	-	PUNCT
ejpam-4441	328	17	0441	0441	NUM
ejpam-4441	328	18	-	-	PUNCT
ejpam-4441	328	19	4	4	NUM
ejpam-4441	328	20	.	.	NUM
ejpam-4441	328	21	1974	1974	NUM
ejpam-4441	328	22	.	.	PUNCT
ejpam-4441	329	1	[	[	X
ejpam-4441	329	2	5	5	X
ejpam-4441	329	3	]	]	PUNCT
ejpam-4441	329	4	w.	w.	PROPN
ejpam-4441	329	5	a.	a.	PROPN
ejpam-4441	329	6	khan	khan	PROPN
ejpam-4441	329	7	,	,	PUNCT
ejpam-4441	329	8	m.	m.	NOUN
ejpam-4441	329	9	ghayasuddin	ghayasuddin	NOUN
ejpam-4441	329	10	,	,	PUNCT
ejpam-4441	329	11	and	and	CCONJ
ejpam-4441	329	12	d.	d.	PROPN
ejpam-4441	329	13	srivastava	srivastava	PROPN
ejpam-4441	329	14	.	.	PUNCT
ejpam-4441	330	1	a	a	DET
ejpam-4441	330	2	new	new	ADJ
ejpam-4441	330	3	class	class	NOUN
ejpam-4441	330	4	of	of	ADP
ejpam-4441	330	5	partially	partially	ADV
ejpam-4441	330	6	degenerate	degenerate	ADJ
ejpam-4441	330	7	laguerre	laguerre	NOUN
ejpam-4441	330	8	-	-	PUNCT
ejpam-4441	330	9	based	base	VERB
ejpam-4441	330	10	hermite	hermite	PROPN
ejpam-4441	330	11	-	-	PUNCT
ejpam-4441	330	12	genocchi	genocchi	PROPN
ejpam-4441	330	13	polynomials	polynomial	NOUN
ejpam-4441	330	14	.	.	PUNCT
ejpam-4441	331	1	advanced	advanced	ADJ
ejpam-4441	331	2	studies	study	NOUN
ejpam-4441	331	3	in	in	ADP
ejpam-4441	331	4	contemporary	contemporary	ADJ
ejpam-4441	331	5	mathematics	mathematics	PROPN
ejpam-4441	331	6	(	(	PUNCT
ejpam-4441	331	7	kyungshang	kyungshang	PROPN
ejpam-4441	331	8	)	)	PUNCT
ejpam-4441	331	9	.	.	PUNCT
ejpam-4441	331	10	,	,	PUNCT
ejpam-4441	331	11	32(1):71–83	32(1):71–83	NUM
ejpam-4441	331	12	,	,	PUNCT
ejpam-4441	331	13	2022	2022	NUM
ejpam-4441	331	14	.	.	PUNCT
ejpam-4441	332	1	[	[	X
ejpam-4441	332	2	6	6	NUM
ejpam-4441	332	3	]	]	PUNCT
ejpam-4441	332	4	d.	d.	PROPN
ejpam-4441	332	5	s.	s.	PROPN
ejpam-4441	332	6	kim	kim	PROPN
ejpam-4441	332	7	and	and	CCONJ
ejpam-4441	332	8	t.	t.	PROPN
ejpam-4441	332	9	kim.a	kim.a	PROPN
ejpam-4441	332	10	.	.	PUNCT
ejpam-4441	332	11	note	note	NOUN
ejpam-4441	332	12	on	on	ADP
ejpam-4441	332	13	a	a	DET
ejpam-4441	332	14	new	new	ADJ
ejpam-4441	332	15	type	type	NOUN
ejpam-4441	332	16	of	of	ADP
ejpam-4441	332	17	degenerate	degenerate	ADJ
ejpam-4441	332	18	bernoulli	bernoulli	NOUN
ejpam-4441	332	19	numbers	number	NOUN
ejpam-4441	332	20	.	.	PUNCT
ejpam-4441	333	1	russian	russian	ADJ
ejpam-4441	333	2	journal	journal	PROPN
ejpam-4441	333	3	of	of	ADP
ejpam-4441	333	4	mathematical	mathematical	ADJ
ejpam-4441	333	5	physics	physics	NOUN
ejpam-4441	333	6	.	.	PUNCT
ejpam-4441	333	7	,	,	PUNCT
ejpam-4441	333	8	27(2):227–235	27(2):227–235	NUM
ejpam-4441	333	9	,	,	PUNCT
ejpam-4441	333	10	2020	2020	NUM
ejpam-4441	333	11	.	.	PUNCT
ejpam-4441	334	1	[	[	X
ejpam-4441	334	2	7	7	X
ejpam-4441	334	3	]	]	PUNCT
ejpam-4441	334	4	h.	h.	PROPN
ejpam-4441	334	5	k.	k.	PROPN
ejpam-4441	334	6	kim	kim	PROPN
ejpam-4441	334	7	.	.	PUNCT
ejpam-4441	335	1	central	central	ADJ
ejpam-4441	335	2	lah	lah	PROPN
ejpam-4441	335	3	numbers	number	NOUN
ejpam-4441	335	4	and	and	CCONJ
ejpam-4441	335	5	central	central	ADJ
ejpam-4441	335	6	lah	lah	PROPN
ejpam-4441	335	7	-	-	PUNCT
ejpam-4441	335	8	bell	bell	NOUN
ejpam-4441	335	9	numbers	number	NOUN
ejpam-4441	335	10	.	.	PUNCT
ejpam-4441	336	1	advanced	advanced	ADJ
ejpam-4441	336	2	studies	study	NOUN
ejpam-4441	336	3	in	in	ADP
ejpam-4441	336	4	contemporary	contemporary	ADJ
ejpam-4441	336	5	mathematics	mathematic	NOUN
ejpam-4441	336	6	.	.	PUNCT
ejpam-4441	336	7	,	,	PUNCT
ejpam-4441	336	8	32(1):103–111	32(1):103–111	PROPN
ejpam-4441	336	9	,	,	PUNCT
ejpam-4441	336	10	2022	2022	NUM
ejpam-4441	336	11	.	.	PUNCT
ejpam-4441	337	1	[	[	X
ejpam-4441	337	2	8	8	NUM
ejpam-4441	337	3	]	]	PUNCT
ejpam-4441	337	4	t.	t.	PROPN
ejpam-4441	337	5	kim	kim	PROPN
ejpam-4441	337	6	and	and	CCONJ
ejpam-4441	337	7	d.	d.	PROPN
ejpam-4441	337	8	s.	s.	PROPN
ejpam-4441	337	9	kim	kim	PROPN
ejpam-4441	337	10	.	.	PUNCT
ejpam-4441	338	1	some	some	DET
ejpam-4441	338	2	identities	identity	NOUN
ejpam-4441	338	3	on	on	ADP
ejpam-4441	338	4	λ	λ	PROPN
ejpam-4441	338	5	-analogues	-analogue	NOUN
ejpam-4441	338	6	of	of	ADP
ejpam-4441	338	7	r	r	NOUN
ejpam-4441	338	8	-	-	PUNCT
ejpam-4441	338	9	stirling	stirling	NOUN
ejpam-4441	338	10	numbers	number	NOUN
ejpam-4441	338	11	of	of	ADP
ejpam-4441	338	12	the	the	DET
ejpam-4441	338	13	first	first	ADJ
ejpam-4441	338	14	kind	kind	NOUN
ejpam-4441	338	15	.	.	PUNCT
ejpam-4441	339	1	filomat	filomat	PROPN
ejpam-4441	339	2	.	.	PROPN
ejpam-4441	339	3	,	,	PUNCT
ejpam-4441	339	4	34(2):451–460	34(2):451–460	PROPN
ejpam-4441	339	5	,	,	PUNCT
ejpam-4441	339	6	2020	2020	NUM
ejpam-4441	339	7	.	.	PUNCT
ejpam-4441	340	1	[	[	X
ejpam-4441	340	2	9	9	NUM
ejpam-4441	340	3	]	]	PUNCT
ejpam-4441	340	4	t.	t.	PROPN
ejpam-4441	340	5	kim	kim	PROPN
ejpam-4441	340	6	and	and	CCONJ
ejpam-4441	340	7	d.	d.	PROPN
ejpam-4441	340	8	s.	s.	PROPN
ejpam-4441	340	9	kim	kim	PROPN
ejpam-4441	340	10	.	.	PUNCT
ejpam-4441	341	1	on	on	ADP
ejpam-4441	341	2	some	some	DET
ejpam-4441	341	3	degenerate	degenerate	ADJ
ejpam-4441	341	4	differential	differential	NOUN
ejpam-4441	341	5	and	and	CCONJ
ejpam-4441	341	6	degenerate	degenerate	ADJ
ejpam-4441	341	7	difference	difference	NOUN
ejpam-4441	341	8	operators	operator	NOUN
ejpam-4441	341	9	.	.	PUNCT
ejpam-4441	342	1	russian	russian	ADJ
ejpam-4441	342	2	journal	journal	PROPN
ejpam-4441	342	3	of	of	ADP
ejpam-4441	342	4	mathematical	mathematical	ADJ
ejpam-4441	342	5	physics	physics	NOUN
ejpam-4441	342	6	.	.	PUNCT
ejpam-4441	342	7	,	,	PUNCT
ejpam-4441	342	8	29(1):37–46	29(1):37–46	NUM
ejpam-4441	342	9	,	,	PUNCT
ejpam-4441	342	10	2022	2022	NUM
ejpam-4441	342	11	.	.	PUNCT
ejpam-4441	343	1	references	reference	NOUN
ejpam-4441	343	2	1066	1066	NUM
ejpam-4441	344	1	[	[	X
ejpam-4441	344	2	10	10	NUM
ejpam-4441	344	3	]	]	PUNCT
ejpam-4441	344	4	t.	t.	PROPN
ejpam-4441	344	5	kim	kim	PROPN
ejpam-4441	344	6	,	,	PUNCT
ejpam-4441	344	7	d.	d.	PROPN
ejpam-4441	344	8	s.	s.	PROPN
ejpam-4441	344	9	kim	kim	PROPN
ejpam-4441	344	10	,	,	PUNCT
ejpam-4441	344	11	l.-c	l.-c	PROPN
ejpam-4441	344	12	.	.	PUNCT
ejpam-4441	345	1	jang	jang	PROPN
ejpam-4441	345	2	,	,	PUNCT
ejpam-4441	345	3	h	h	PROPN
ejpam-4441	345	4	.lee	.lee	NOUN
ejpam-4441	345	5	,	,	PUNCT
ejpam-4441	345	6	and	and	CCONJ
ejpam-4441	345	7	h.	h.	PROPN
ejpam-4441	345	8	kim	kim	PROPN
ejpam-4441	345	9	.	.	PUNCT
ejpam-4441	346	1	representations	representation	NOUN
ejpam-4441	346	2	of	of	ADP
ejpam-4441	346	3	degenerate	degenerate	ADJ
ejpam-4441	346	4	hermite	hermite	ADJ
ejpam-4441	346	5	polynomials	polynomial	NOUN
ejpam-4441	346	6	.	.	PUNCT
ejpam-4441	347	1	advances	advance	NOUN
ejpam-4441	347	2	in	in	ADP
ejpam-4441	347	3	applied	applied	ADJ
ejpam-4441	347	4	mathematics	mathematic	NOUN
ejpam-4441	347	5	.	.	PUNCT
ejpam-4441	347	6	,	,	PUNCT
ejpam-4441	347	7	139(102359	139(102359	NUM
ejpam-4441	347	8	)	)	PUNCT
ejpam-4441	347	9	,	,	PUNCT
ejpam-4441	347	10	2022	2022	NUM
ejpam-4441	347	11	.	.	PUNCT
ejpam-4441	348	1	[	[	X
ejpam-4441	348	2	11	11	NUM
ejpam-4441	348	3	]	]	PUNCT
ejpam-4441	348	4	t.	t.	PROPN
ejpam-4441	348	5	kim	kim	PROPN
ejpam-4441	348	6	,	,	PUNCT
ejpam-4441	348	7	d.	d.	PROPN
ejpam-4441	348	8	s.	s.	PROPN
ejpam-4441	348	9	kim	kim	PROPN
ejpam-4441	348	10	,	,	PUNCT
ejpam-4441	348	11	h.	h.	PROPN
ejpam-4441	348	12	lee	lee	PROPN
ejpam-4441	348	13	,	,	PUNCT
ejpam-4441	348	14	and	and	CCONJ
ejpam-4441	348	15	j.-w	j.-w	PROPN
ejpam-4441	348	16	.	.	PUNCT
ejpam-4441	349	1	park	park	NOUN
ejpam-4441	349	2	.	.	PUNCT
ejpam-4441	350	1	a	a	DET
ejpam-4441	350	2	note	note	NOUN
ejpam-4441	350	3	on	on	ADP
ejpam-4441	350	4	degenerate	degenerate	ADJ
ejpam-4441	350	5	r	r	NOUN
ejpam-4441	350	6	-	-	PUNCT
ejpam-4441	350	7	stirling	stirling	NOUN
ejpam-4441	350	8	numbers	number	NOUN
ejpam-4441	350	9	.	.	PUNCT
ejpam-4441	351	1	journal	journal	PROPN
ejpam-4441	351	2	of	of	ADP
ejpam-4441	351	3	inequalities	inequality	NOUN
ejpam-4441	351	4	and	and	CCONJ
ejpam-4441	351	5	applications	application	NOUN
ejpam-4441	351	6	.	.	PUNCT
ejpam-4441	352	1	,	,	PUNCT
ejpam-4441	352	2	2020:225:12	2020:225:12	NUM
ejpam-4441	352	3	pp	pp	ADJ
ejpam-4441	352	4	,	,	PUNCT
ejpam-4441	352	5	2020	2020	NUM
ejpam-4441	352	6	.	.	PUNCT
ejpam-4441	353	1	[	[	X
ejpam-4441	353	2	12	12	NUM
ejpam-4441	353	3	]	]	X
ejpam-4441	353	4	s.	s.	PROPN
ejpam-4441	353	5	roman	roman	PROPN
ejpam-4441	353	6	.	.	PUNCT
ejpam-4441	354	1	the	the	DET
ejpam-4441	354	2	umbral	umbral	ADJ
ejpam-4441	354	3	calculus	calculus	NOUN
ejpam-4441	354	4	.	.	PUNCT
ejpam-4441	354	5	,	,	PUNCT
ejpam-4441	354	6	volume	volume	NOUN
ejpam-4441	354	7	isbn	isbn	NOUN
ejpam-4441	354	8	:	:	PUNCT
ejpam-4441	354	9	0	0	NUM
ejpam-4441	354	10	-	-	SYM
ejpam-4441	354	11	12	12	NUM
ejpam-4441	354	12	-	-	PUNCT
ejpam-4441	354	13	594380	594380	NUM
ejpam-4441	354	14	-	-	PUNCT
ejpam-4441	354	15	6	6	NUM
ejpam-4441	354	16	.	.	NOUN
ejpam-4441	354	17	1984	1984	NUM
ejpam-4441	354	18	.	.	PUNCT
ejpam-4441	355	1	[	[	X
ejpam-4441	355	2	13	13	NUM
ejpam-4441	355	3	]	]	X
ejpam-4441	355	4	y.	y.	NOUN
ejpam-4441	355	5	simsek	simsek	PROPN
ejpam-4441	355	6	.	.	PUNCT
ejpam-4441	356	1	identities	identity	NOUN
ejpam-4441	356	2	and	and	CCONJ
ejpam-4441	356	3	relations	relation	NOUN
ejpam-4441	356	4	related	relate	VERB
ejpam-4441	356	5	to	to	ADP
ejpam-4441	356	6	combinatorial	combinatorial	ADJ
ejpam-4441	356	7	numbers	number	NOUN
ejpam-4441	356	8	and	and	CCONJ
ejpam-4441	356	9	polynomials	polynomial	NOUN
ejpam-4441	356	10	.	.	PUNCT
ejpam-4441	357	1	proceedings	proceeding	NOUN
ejpam-4441	357	2	of	of	ADP
ejpam-4441	357	3	the	the	DET
ejpam-4441	357	4	jangjeon	jangjeon	PROPN
ejpam-4441	357	5	mathematical	mathematical	PROPN
ejpam-4441	357	6	society	society	NOUN
ejpam-4441	357	7	.	.	PUNCT
ejpam-4441	357	8	,	,	PUNCT
ejpam-4441	357	9	20(1):127–135	20(1):127–135	PROPN
ejpam-4441	357	10	,	,	PUNCT
ejpam-4441	357	11	2017	2017	NUM
ejpam-4441	357	12	.	.	PUNCT
ejpam-4441	358	1	[	[	X
ejpam-4441	358	2	14	14	NUM
ejpam-4441	358	3	]	]	X
ejpam-4441	358	4	y.	y.	NOUN
ejpam-4441	358	5	simsek	simsek	PROPN
ejpam-4441	358	6	.	.	PUNCT
ejpam-4441	359	1	construction	construction	NOUN
ejpam-4441	359	2	of	of	ADP
ejpam-4441	359	3	generalized	generalized	ADJ
ejpam-4441	359	4	leibnitz	leibnitz	NOUN
ejpam-4441	359	5	type	type	NOUN
ejpam-4441	359	6	numbers	number	NOUN
ejpam-4441	359	7	and	and	CCONJ
ejpam-4441	359	8	their	their	PRON
ejpam-4441	359	9	properties	property	NOUN
ejpam-4441	359	10	.	.	PUNCT
ejpam-4441	360	1	advanced	advanced	ADJ
ejpam-4441	360	2	studies	study	NOUN
ejpam-4441	360	3	in	in	ADP
ejpam-4441	360	4	contemporary	contemporary	ADJ
ejpam-4441	360	5	mathematics	mathematics	PROPN
ejpam-4441	360	6	(	(	PUNCT
ejpam-4441	360	7	kyungshang	kyungshang	PROPN
ejpam-4441	360	8	)	)	PUNCT
ejpam-4441	360	9	.	.	PUNCT
ejpam-4441	360	10	,	,	PUNCT
ejpam-4441	360	11	31(3):311–323	31(3):311–323	PROPN
ejpam-4441	360	12	,	,	PUNCT
ejpam-4441	360	13	2021	2021	NUM
ejpam-4441	360	14	.	.	PUNCT