id	sid	eid	entity	type
ejpam-6743	1	1	european journal	ORG
ejpam-6743	1	2	2025	DATE
ejpam-6743	1	3	18	CARDINAL
ejpam-6743	1	4	4	CARDINAL
ejpam-6743	1	5	6743	CARDINAL
ejpam-6743	1	6	1307-5543	DATE
ejpam-6743	1	7	new york	GPE
ejpam-6743	1	8	tanny-dowling	ORG
ejpam-6743	1	9	mahid m. mangontarum1,2,∗	PERSON
ejpam-6743	1	10	norlailah m. madid1	PERSON
ejpam-6743	2	1	mindanao state university	ORG
ejpam-6743	2	2	marawi city 9700	GPE
ejpam-6743	2	3	2	CARDINAL
ejpam-6743	2	4	mindanao state university	ORG
ejpam-6743	2	5	marawi city 9700	GPE
ejpam-6743	2	6	philippines	GPE
ejpam-6743	5	1	2020	DATE
ejpam-6743	5	2	11b83	CARDINAL
ejpam-6743	5	3	11b73	CARDINAL
ejpam-6743	5	4	dowling polynomial 1	PERSON
ejpam-6743	6	1	second	ORDINAL
ejpam-6743	6	2	1	CARDINAL
ejpam-6743	7	1	47	CARDINAL
ejpam-6743	7	2	2	CARDINAL
ejpam-6743	8	1	n∑ k=0	PERSON
ejpam-6743	8	2	1	CARDINAL
ejpam-6743	9	1	x)k	TIME
ejpam-6743	9	2	1)(x− 2	DATE
ejpam-6743	9	3	3	CARDINAL
ejpam-6743	11	1	second	ORDINAL
ejpam-6743	14	1	mangontarum.mahid@msumain.edu.ph	PERSON
ejpam-6743	14	2	m. m. mangontarum	PERSON
ejpam-6743	14	3	n. m. madid	PERSON
ejpam-6743	14	4	campong.aa82@s.msumain.edu.ph	CARDINAL
ejpam-6743	14	5	a. a. campong	PERSON
ejpam-6743	15	1	1	CARDINAL
ejpam-6743	15	2	2025	CARDINAL
ejpam-6743	16	1	m. m. mangontarum et al	PERSON
ejpam-6743	17	1	j. pure	PERSON
ejpam-6743	17	2	18	CARDINAL
ejpam-6743	17	3	4	CARDINAL
ejpam-6743	17	4	2025	CARDINAL
ejpam-6743	17	5	6743 2	DATE
ejpam-6743	17	6	8	CARDINAL
ejpam-6743	17	7	4	CARDINAL
ejpam-6743	18	1	n∑ k=0	PERSON
ejpam-6743	20	1	2	CARDINAL
ejpam-6743	20	2	5	CARDINAL
ejpam-6743	21	1	3.14	CARDINAL
ejpam-6743	22	1	∞∑ n=0	PERSON
ejpam-6743	23	1	1 1− x(ez	TIME
ejpam-6743	23	2	1	CARDINAL
ejpam-6743	24	1	3	CARDINAL
ejpam-6743	25	1	1	CARDINAL
ejpam-6743	25	2	n∑ k=0	PERSON
ejpam-6743	26	1	4	CARDINAL
ejpam-6743	28	1	1	CARDINAL
ejpam-6743	28	2	3	CARDINAL
ejpam-6743	29	1	n=0 wn(1	GPE
ejpam-6743	32	1	1 2−	CARDINAL
ejpam-6743	33	1	5	CARDINAL
ejpam-6743	34	1	kellner	PERSON
ejpam-6743	35	1	6	CARDINAL
ejpam-6743	36	1	−1	DATE
ejpam-6743	37	1	6	CARDINAL
ejpam-6743	37	2	nth bernoulli	ORG
ejpam-6743	40	1	− 1	EVENT
ejpam-6743	41	1	7	CARDINAL
ejpam-6743	41	2	6	CARDINAL
ejpam-6743	42	1	7	CARDINAL
ejpam-6743	42	2	215	CARDINAL
ejpam-6743	42	3	36	CARDINAL
ejpam-6743	42	4	n∑ k=0	PERSON
ejpam-6743	42	5	j=0	GPE
ejpam-6743	45	1	n∑ k=1	PERSON
ejpam-6743	48	1	9	CARDINAL
ejpam-6743	48	2	m. m. mangontarum et al	PERSON
ejpam-6743	49	1	j. pure	PERSON
ejpam-6743	49	2	18	CARDINAL
ejpam-6743	49	3	4	CARDINAL
ejpam-6743	49	4	2025	CARDINAL
ejpam-6743	49	5	6743 3	DATE
ejpam-6743	49	6	8	CARDINAL
ejpam-6743	50	1	5	CARDINAL
ejpam-6743	51	1	n∑ k=0	PERSON
ejpam-6743	51	2	10	CARDINAL
ejpam-6743	51	3	5	CARDINAL
ejpam-6743	53	1	11	CARDINAL
ejpam-6743	53	2	5	CARDINAL
ejpam-6743	54	1	3.13	CARDINAL
ejpam-6743	58	1	n=0	PERSON
ejpam-6743	59	1	12	CARDINAL
ejpam-6743	59	2	8	CARDINAL
ejpam-6743	60	1	9	CARDINAL
ejpam-6743	61	1	10	CARDINAL
ejpam-6743	62	1	11	CARDINAL
ejpam-6743	63	1	12	CARDINAL
ejpam-6743	64	1	2016	DATE
ejpam-6743	65	1	13	CARDINAL
ejpam-6743	65	2	tanny-dowling	ORG
ejpam-6743	65	3	a(n;x	PERSON
ejpam-6743	65	4	a(n;x	PERSON
ejpam-6743	65	5	n∑ k=0	PERSON
ejpam-6743	65	6	k!w̃m	GPE
ejpam-6743	65	7	a(n, k)x k	GPE
ejpam-6743	65	8	13	CARDINAL
ejpam-6743	67	1	me−az m−	PERSON
ejpam-6743	68	1	1	CARDINAL
ejpam-6743	68	2	14	CARDINAL
ejpam-6743	68	3	a(n, k	ORG
ejpam-6743	68	4	second	ORDINAL
ejpam-6743	69	1	f̃1,0(n;x	ORG
ejpam-6743	70	1	14	CARDINAL
ejpam-6743	70	2	a(n;x	PERSON
ejpam-6743	72	1	8	CARDINAL
ejpam-6743	73	1	tanny-dowling	ORG
ejpam-6743	74	1	kellner	PERSON
ejpam-6743	74	2	6	CARDINAL
ejpam-6743	74	3	tanny-dowling	ORG
ejpam-6743	75	1	second	ORDINAL
ejpam-6743	76	1	5	CARDINAL
ejpam-6743	76	2	tanny-dowling	ORG
ejpam-6743	77	1	m. m. mangontarum et al	PERSON
ejpam-6743	78	1	j. pure	PERSON
ejpam-6743	78	2	18	CARDINAL
ejpam-6743	78	3	4	CARDINAL
ejpam-6743	78	4	2025	CARDINAL
ejpam-6743	78	5	6743 4	DATE
ejpam-6743	78	6	first	ORDINAL
ejpam-6743	78	7	tanny-dowling	ORG
ejpam-6743	78	8	kellner	PERSON
ejpam-6743	78	9	6	CARDINAL
ejpam-6743	78	10	6	CARDINAL
ejpam-6743	79	1	1	CARDINAL
ejpam-6743	80	1	−1	DATE
ejpam-6743	80	2	0	CARDINAL
ejpam-6743	80	3	a(n;mx)dx = mnbn	GPE
ejpam-6743	81	1	15	CARDINAL
ejpam-6743	82	1	14	CARDINAL
ejpam-6743	83	1	1−	CARDINAL
ejpam-6743	85	1	16	CARDINAL
ejpam-6743	85	2	7	CARDINAL
ejpam-6743	86	1	|1− xemz	PERSON
ejpam-6743	86	2	1	CARDINAL
ejpam-6743	86	3	n=0 mnbn	GPE
ejpam-6743	88	1	1	CARDINAL
ejpam-6743	89	1	f̃1,0(n;x	ORG
ejpam-6743	89	2	1	CARDINAL
ejpam-6743	89	3	0	CARDINAL
ejpam-6743	89	4	1	CARDINAL
ejpam-6743	89	5	0	CARDINAL
ejpam-6743	89	6	kellner	PERSON
ejpam-6743	89	7	6	CARDINAL
ejpam-6743	89	8	6	CARDINAL
ejpam-6743	90	1	13	CARDINAL
ejpam-6743	92	1	n∑ k=0 mkk!w̃m	PERSON
ejpam-6743	92	2	a(n, k)x k	PERSON
ejpam-6743	93	1	n∑ k=0 mkk!w̃m	PERSON
ejpam-6743	93	2	a(n, k	ORG
ejpam-6743	93	3	xkdx m. m. mangontarum et al	PERSON
ejpam-6743	94	1	j. pure	PERSON
ejpam-6743	94	2	18	CARDINAL
ejpam-6743	94	3	4	CARDINAL
ejpam-6743	94	4	2025	CARDINAL
ejpam-6743	94	5	6743 5	DATE
ejpam-6743	94	6	8	CARDINAL
ejpam-6743	94	7	n∑ k=0 mkk!w̃m	PERSON
ejpam-6743	94	8	a(n, k	ORG
ejpam-6743	94	9	−1)k k	PERSON
ejpam-6743	96	1	1	CARDINAL
ejpam-6743	97	1	bernoulli polynomial bn (	ORG
ejpam-6743	98	1	n∑ k=0	PERSON
ejpam-6743	98	2	k!w̃m	GPE
ejpam-6743	98	3	a(n, k	ORG
ejpam-6743	99	1	17	CARDINAL
ejpam-6743	99	2	2	CARDINAL
ejpam-6743	100	1	k	PERSON
ejpam-6743	100	2	0	CARDINAL
ejpam-6743	100	3	1	CARDINAL
ejpam-6743	100	4	9	CARDINAL
ejpam-6743	101	1	a(n, k	ORG
ejpam-6743	102	1	13	CARDINAL
ejpam-6743	103	1	38	CARDINAL
ejpam-6743	103	2	a(n, k	ORG
ejpam-6743	103	3	mkk	PERSON
ejpam-6743	104	1	j=0	GPE
ejpam-6743	104	2	17	CARDINAL
ejpam-6743	105	1	n∑ k=0	PERSON
ejpam-6743	105	2	j=0	GPE
ejpam-6743	105	3	−1)j	ORG
ejpam-6743	106	1	18	CARDINAL
ejpam-6743	106	2	7	CARDINAL
ejpam-6743	106	3	8)	CARDINAL
ejpam-6743	109	1	19	CARDINAL
ejpam-6743	109	2	dowling	PERSON
ejpam-6743	109	3	13	CARDINAL
ejpam-6743	110	1	89	CARDINAL
ejpam-6743	110	2	a(n;x	PERSON
ejpam-6743	111	1	n∑ k=0	PERSON
ejpam-6743	111	2	a(n, k)x k	ORG
ejpam-6743	111	3	13	CARDINAL
ejpam-6743	112	1	91	CARDINAL
ejpam-6743	113	1	∞∑ n=0	PERSON
ejpam-6743	113	2	a(n;x	PERSON
ejpam-6743	115	1	20	CARDINAL
ejpam-6743	115	2	tanny-dowling	ORG
ejpam-6743	115	3	dowling	PERSON
ejpam-6743	116	1	5	CARDINAL
ejpam-6743	116	2	11	CARDINAL
ejpam-6743	117	1	m. m. mangontarum et al	PERSON
ejpam-6743	118	1	j. pure	PERSON
ejpam-6743	118	2	18	CARDINAL
ejpam-6743	118	3	4	CARDINAL
ejpam-6743	118	4	2025	CARDINAL
ejpam-6743	118	5	6743 6	DATE
ejpam-6743	118	6	8	CARDINAL
ejpam-6743	118	7	2	CARDINAL
ejpam-6743	119	1	tanny-dowling	ORG
ejpam-6743	119	2	a(n;x	PERSON
ejpam-6743	122	1	21	CARDINAL
ejpam-6743	123	1	definition,∫	ORG
ejpam-6743	127	1	n∑ k=0	PERSON
ejpam-6743	127	2	a(n, k)x	GPE
ejpam-6743	128	1	n∑ k=0	PERSON
ejpam-6743	128	2	a(n, k)x k	ORG
ejpam-6743	131	1	19	CARDINAL
ejpam-6743	131	2	13	CARDINAL
ejpam-6743	131	3	∞ 0	PERSON
ejpam-6743	133	1	n∑ k=0	PERSON
ejpam-6743	133	2	k!w̃m	GPE
ejpam-6743	133	3	a(n, k)x	GPE
ejpam-6743	133	4	a(n;x	PERSON
ejpam-6743	134	1	3	CARDINAL
ejpam-6743	135	1	f̃1,0(n;x	ORG
ejpam-6743	135	2	22	CARDINAL
ejpam-6743	135	3	5	CARDINAL
ejpam-6743	135	4	11	CARDINAL
ejpam-6743	136	1	a(n;x	PERSON
ejpam-6743	137	1	3	CARDINAL
ejpam-6743	138	1	tanny-dowling	ORG
ejpam-6743	138	2	∞∑ n=0	PERSON
ejpam-6743	140	1	1− x m	QUANTITY
ejpam-6743	142	1	23	CARDINAL
ejpam-6743	143	1	21	CARDINAL
ejpam-6743	143	2	∞∑ n=0	PERSON
ejpam-6743	146	1	a(n;xλ	GPE
ejpam-6743	148	1	20	CARDINAL
ejpam-6743	148	2	∞∑ n=0	PERSON
ejpam-6743	151	1	m. m. mangontarum et al	PERSON
ejpam-6743	152	1	j. pure	PERSON
ejpam-6743	152	2	18	CARDINAL
ejpam-6743	152	3	4	CARDINAL
ejpam-6743	152	4	2025	CARDINAL
ejpam-6743	152	5	6743 7	DATE
ejpam-6743	152	6	4	CARDINAL
ejpam-6743	154	1	1	CARDINAL
ejpam-6743	155	1	n=0 f̃1,0(n;x	PERSON
ejpam-6743	155	2	24	CARDINAL
ejpam-6743	155	3	5	CARDINAL
ejpam-6743	155	4	12	CARDINAL
ejpam-6743	156	1	3	CARDINAL
ejpam-6743	157	1	12	CARDINAL
ejpam-6743	157	2	apostol-euler	PERSON
ejpam-6743	158	1	15	CARDINAL
ejpam-6743	160	1	philippines	GPE
ejpam-6743	160	2	2022	CARDINAL
ejpam-6743	160	3	msp	ORG
ejpam-6743	160	4	624-op	QUANTITY
ejpam-6743	160	5	s. 2022	ORG
ejpam-6743	161	1	1	CARDINAL
ejpam-6743	161	2	j. stirling	PERSON
ejpam-6743	162	1	differentialis sive tractatus de	LOC
ejpam-6743	163	1	london	GPE
ejpam-6743	163	2	1730	CARDINAL
ejpam-6743	164	1	2	CARDINAL
ejpam-6743	164	2	c. chen	PERSON
ejpam-6743	164	3	k. kho	PERSON
ejpam-6743	166	1	world scientific publishing co.	ORG
ejpam-6743	166	2	1992	DATE
ejpam-6743	167	1	3	CARDINAL
ejpam-6743	169	1	d. reidel publishing co.	ORG
ejpam-6743	169	2	1974	DATE
ejpam-6743	170	1	4	CARDINAL
ejpam-6743	170	2	s. m. tanny	PERSON
ejpam-6743	172	1	canadian	NORP
ejpam-6743	172	2	17:733–738	CARDINAL
ejpam-6743	172	3	1975	DATE
ejpam-6743	173	1	5	CARDINAL
ejpam-6743	173	2	k. n. boyadzhiev	PERSON
ejpam-6743	175	1	23:3849–3866, 2005	DATE
ejpam-6743	176	1	6	CARDINAL
ejpam-6743	176	2	b. c. kellner	PERSON
ejpam-6743	177	1	stirling	GPE
ejpam-6743	178	1	14	CARDINAL
ejpam-6743	178	2	a54, 2014	DATE
ejpam-6743	179	1	7	CARDINAL
ejpam-6743	179	2	j. worpitzky	PERSON
ejpam-6743	180	1	studien über	PERSON
ejpam-6743	181	1	journal für	ORG
ejpam-6743	181	2	und angewandte mathematik	PERSON
ejpam-6743	181	3	94:203–232	CARDINAL
ejpam-6743	181	4	1883	DATE
ejpam-6743	182	1	8	CARDINAL
ejpam-6743	182	2	l. kargın	PERSON
ejpam-6743	184	1	integer sequences	ORG
ejpam-6743	184	2	20	CARDINAL
ejpam-6743	184	3	article 17.4.4,	LAW
ejpam-6743	184	4	2017	DATE
ejpam-6743	185	1	m. m. mangontarum et al	PERSON
ejpam-6743	186	1	j. pure	PERSON
ejpam-6743	186	2	18	CARDINAL
ejpam-6743	186	3	4	CARDINAL
ejpam-6743	186	4	2025	CARDINAL
ejpam-6743	186	5	6743 8	DATE
ejpam-6743	187	1	9	CARDINAL
ejpam-6743	187	2	a. dil	PERSON
ejpam-6743	187	3	v. kurt	PERSON
ejpam-6743	189	1	integer sequences	ORG
ejpam-6743	189	2	14	CARDINAL
ejpam-6743	189	3	article 11.4.6, 2011	LAW
ejpam-6743	190	1	10	CARDINAL
ejpam-6743	190	2	k. n. boyadzhiev	PERSON
ejpam-6743	190	3	a. dil	PERSON
ejpam-6743	192	1	mathematica	PERSON
ejpam-6743	192	2	42:203–224	CARDINAL
ejpam-6743	192	3	2016	DATE
ejpam-6743	193	1	11	CARDINAL
ejpam-6743	193	2	l. kargın	PERSON
ejpam-6743	193	3	b. çekim	PERSON
ejpam-6743	195	1	turkish	NORP
ejpam-6743	195	2	42:887–903	CARDINAL
ejpam-6743	195	3	2018	DATE
ejpam-6743	196	1	12	CARDINAL
ejpam-6743	196	2	w. ramı́rez	PERSON
ejpam-6743	196	3	c. cesarano	PERSON
ejpam-6743	197	1	generalized apostolbernoulli	PERSON
ejpam-6743	197	2	apostol-euler	PERSON
ejpam-6743	198	1	carpathian	NORP
ejpam-6743	198	2	14:354–363	CARDINAL
ejpam-6743	198	3	2022	CARDINAL
ejpam-6743	199	1	13	CARDINAL
ejpam-6743	199	2	m. m. mangontarum	PERSON
ejpam-6743	199	3	o. i. cauntongan	PERSON
ejpam-6743	199	4	a. p. macodi	PERSON
ejpam-6743	201	1	article id 6206207	LAW
ejpam-6743	201	2	16	CARDINAL
ejpam-6743	201	3	2016	DATE
ejpam-6743	202	1	14	CARDINAL
ejpam-6743	202	2	m. m. mangontarum	PERSON
ejpam-6743	202	3	n. m. madid	PERSON
ejpam-6743	203	1	noncentral tanny-dowling	PERSON
ejpam-6743	204	1	integer sequences	ORG
ejpam-6743	204	2	24	CARDINAL
ejpam-6743	204	3	article 21.2.4,	LAW
ejpam-6743	204	4	2021	CARDINAL
ejpam-6743	205	1	15	CARDINAL
ejpam-6743	205	2	m. m. mangontarum	PERSON
ejpam-6743	206	1	two	CARDINAL
ejpam-6743	206	2	generalized spivey’s	PERSON
ejpam-6743	207	1	indian	NORP
ejpam-6743	207	2	54:703–712	CARDINAL
ejpam-6743	207	3	2023	CARDINAL