id	sid	eid	entity	type
ejpam-4498	1	1	european journal	ORG
ejpam-4498	2	1	15	CARDINAL
ejpam-4498	2	2	3	CARDINAL
ejpam-4498	2	3	2022	CARDINAL
ejpam-4498	2	4	1237-1253	DATE
ejpam-4498	2	5	1307-5543	DATE
ejpam-4498	2	6	new york	GPE
ejpam-4498	2	7	yukio kobayashi department	ORG
ejpam-4498	2	8	1-236 tangi-machi	QUANTITY
ejpam-4498	2	9	hachioji-shi	PERSON
ejpam-4498	2	10	tokyo	GPE
ejpam-4498	2	11	japan	GPE
ejpam-4498	6	1	two	CARDINAL
ejpam-4498	16	1	2020	DATE
ejpam-4498	16	2	97h20	CARDINAL
ejpam-4498	16	3	combinatorics	ORG
ejpam-4498	16	4	y. kobayashi	PERSON
ejpam-4498	16	5	1237	CARDINAL
ejpam-4498	17	1	2022	CARDINAL
ejpam-4498	18	1	yukio kobayashi	PERSON
ejpam-4498	19	1	j. pure	PERSON
ejpam-4498	19	2	15	CARDINAL
ejpam-4498	19	3	3	CARDINAL
ejpam-4498	19	4	2022	CARDINAL
ejpam-4498	19	5	1237-1253 1238 1	CARDINAL
ejpam-4498	24	1	6	CARDINAL
ejpam-4498	26	1	1	CARDINAL
ejpam-4498	31	1	10	CARDINAL
ejpam-4498	32	1	2	CARDINAL
ejpam-4498	33	1	four	CARDINAL
ejpam-4498	33	2	7	CARDINAL
ejpam-4498	33	3	9	CARDINAL
ejpam-4498	34	1	1 2	CARDINAL
ejpam-4498	34	2	1	CARDINAL
ejpam-4498	34	3	2 + 2	DATE
ejpam-4498	34	4	3 + 3	DATE
ejpam-4498	34	5	4 + ·	DATE
ejpam-4498	35	1	1	CARDINAL
ejpam-4498	36	1	k + ·	PERSON
ejpam-4498	36	2	1	CARDINAL
ejpam-4498	36	3	1	CARDINAL
ejpam-4498	37	1	1	CARDINAL
ejpam-4498	37	2	+ 3c2 + 4c2 +	DATE
ejpam-4498	38	1	2	CARDINAL
ejpam-4498	38	2	1 +	DATE
ejpam-4498	38	3	1 + 2 + 3	DATE
ejpam-4498	38	4	1 + 2 + 3 + ·	DATE
ejpam-4498	38	5	3	CARDINAL
ejpam-4498	38	6	1	CARDINAL
ejpam-4498	38	7	2	CARDINAL
ejpam-4498	38	8	1	CARDINAL
ejpam-4498	38	9	1	CARDINAL
ejpam-4498	38	10	4	CARDINAL
ejpam-4498	38	11	four	CARDINAL
ejpam-4498	40	1	yukio kobayashi	PERSON
ejpam-4498	41	1	j. pure	PERSON
ejpam-4498	41	2	15	CARDINAL
ejpam-4498	41	3	3	CARDINAL
ejpam-4498	41	4	2022	CARDINAL
ejpam-4498	41	5	1237-1253 1239	TIME
ejpam-4498	42	1	first	ORDINAL
ejpam-4498	42	2	1	CARDINAL
ejpam-4498	42	3	2	CARDINAL
ejpam-4498	43	1	2	CARDINAL
ejpam-4498	43	2	2	CARDINAL
ejpam-4498	43	3	1	CARDINAL
ejpam-4498	46	1	7	CARDINAL
ejpam-4498	46	2	9	DATE
ejpam-4498	46	3	11	CARDINAL
ejpam-4498	47	1	second	ORDINAL
ejpam-4498	47	2	2	CARDINAL
ejpam-4498	47	3	3	CARDINAL
ejpam-4498	48	1	1 + 2 + ·	DATE
ejpam-4498	49	1	+ k.	PERSON
ejpam-4498	49	2	1	CARDINAL
ejpam-4498	49	3	3	CARDINAL
ejpam-4498	49	4	1	CARDINAL
ejpam-4498	49	5	1(1 + 1	DATE
ejpam-4498	51	1	1	CARDINAL
ejpam-4498	51	2	2	CARDINAL
ejpam-4498	52	1	5) third	CARDINAL
ejpam-4498	52	2	4	CARDINAL
ejpam-4498	52	3	3	CARDINAL
ejpam-4498	52	4	1 + 2 + 3	DATE
ejpam-4498	54	1	1 + 2 + 3 +	CARDINAL
ejpam-4498	54	2	1	CARDINAL
ejpam-4498	55	1	1 + 2 + 3 +	QUANTITY
ejpam-4498	55	2	1	CARDINAL
ejpam-4498	55	3	1 + 1 +	DATE
ejpam-4498	55	4	+ 1)︸	DATE
ejpam-4498	55	5	2 + 2 + ·	DATE
ejpam-4498	55	6	+ 2)︸	CARDINAL
ejpam-4498	56	1	1	CARDINAL
ejpam-4498	56	2	two	CARDINAL
ejpam-4498	56	3	one	CARDINAL
ejpam-4498	57	1	6	CARDINAL
ejpam-4498	57	2	1	CARDINAL
ejpam-4498	57	3	2	CARDINAL
ejpam-4498	57	4	3	CARDINAL
ejpam-4498	57	5	4	CARDINAL
ejpam-4498	57	6	1	CARDINAL
ejpam-4498	59	1	3	CARDINAL
ejpam-4498	59	2	first	ORDINAL
ejpam-4498	61	1	2	CARDINAL
ejpam-4498	61	2	section 2	LAW
ejpam-4498	61	3	five	CARDINAL
ejpam-4498	61	4	2	CARDINAL
ejpam-4498	62	1	2	CARDINAL
ejpam-4498	62	2	3	CARDINAL
ejpam-4498	63	1	3	CARDINAL
ejpam-4498	64	1	1 + 2 + 3 + 4 + 5	DATE
ejpam-4498	64	2	5	CARDINAL
ejpam-4498	64	3	1	CARDINAL
ejpam-4498	64	4	5 + 2	DATE
ejpam-4498	64	5	4 + 3	DATE
ejpam-4498	65	1	2 + 5	DATE
ejpam-4498	65	2	1	CARDINAL
ejpam-4498	66	1	2	CARDINAL
ejpam-4498	66	2	1 + 3	DATE
ejpam-4498	66	3	2 + 4	DATE
ejpam-4498	67	1	4	CARDINAL
ejpam-4498	68	1	7	CARDINAL
ejpam-4498	68	2	yukio kobayashi	PERSON
ejpam-4498	69	1	j. pure	PERSON
ejpam-4498	69	2	15	CARDINAL
ejpam-4498	69	3	3	CARDINAL
ejpam-4498	69	4	2022	CARDINAL
ejpam-4498	69	5	1237-1253	DATE
ejpam-4498	71	1	2c2	CARDINAL
ejpam-4498	71	2	1	CARDINAL
ejpam-4498	71	3	1	CARDINAL
ejpam-4498	71	4	2	CARDINAL
ejpam-4498	71	5	3	CARDINAL
ejpam-4498	71	6	4	CARDINAL
ejpam-4498	73	1	1	CARDINAL
ejpam-4498	74	1	2	CARDINAL
ejpam-4498	74	2	five	CARDINAL
ejpam-4498	74	3	1 to 5	CARDINAL
ejpam-4498	75	1	first	ORDINAL
ejpam-4498	75	2	5+2	DATE
ejpam-4498	75	3	4+3	DATE
ejpam-4498	75	4	3+4	DATE
ejpam-4498	75	5	2+5	DATE
ejpam-4498	75	6	1	DATE
ejpam-4498	75	7	second	ORDINAL
ejpam-4498	75	8	2	CARDINAL
ejpam-4498	75	9	1+3	DATE
ejpam-4498	75	10	2+4	DATE
ejpam-4498	75	11	3+5	DATE
ejpam-4498	75	12	4	DATE
ejpam-4498	75	13	3	CARDINAL
ejpam-4498	76	1	4	CARDINAL
ejpam-4498	77	1	1 + 2 + 3 + 4 + 5	DATE
ejpam-4498	78	1	5−	DATE
ejpam-4498	78	2	1 + 2 + 3 + 4 + 5	DATE
ejpam-4498	78	3	1	CARDINAL
ejpam-4498	78	4	4 + 2	DATE
ejpam-4498	78	5	3 + 3	DATE
ejpam-4498	78	6	2 + 4	DATE
ejpam-4498	78	7	1	CARDINAL
ejpam-4498	78	8	2	CARDINAL
ejpam-4498	78	9	1 + 3	DATE
ejpam-4498	78	10	2 + 4	DATE
ejpam-4498	78	11	3 + 5	DATE
ejpam-4498	78	12	4	CARDINAL
ejpam-4498	79	1	7	CARDINAL
ejpam-4498	81	1	1	CARDINAL
ejpam-4498	81	2	2	CARDINAL
ejpam-4498	81	3	1	CARDINAL
ejpam-4498	81	4	2	CARDINAL
ejpam-4498	82	1	2 + ·	DATE
ejpam-4498	83	1	1	CARDINAL
ejpam-4498	83	2	9	CARDINAL
ejpam-4498	83	3	1	CARDINAL
ejpam-4498	83	4	yukio kobayashi	PERSON
ejpam-4498	84	1	j. pure	PERSON
ejpam-4498	84	2	15	CARDINAL
ejpam-4498	84	3	3	CARDINAL
ejpam-4498	84	4	2022	CARDINAL
ejpam-4498	84	5	1237-1253 1241	CARDINAL
ejpam-4498	85	1	3	CARDINAL
ejpam-4498	87	1	4	CARDINAL
ejpam-4498	89	1	1 ·	CARDINAL
ejpam-4498	89	2	1	CARDINAL
ejpam-4498	89	3	2	CARDINAL
ejpam-4498	89	4	1	CARDINAL
ejpam-4498	89	5	1	CARDINAL
ejpam-4498	89	6	2	CARDINAL
ejpam-4498	90	1	2 + ·	DATE
ejpam-4498	91	1	1	CARDINAL
ejpam-4498	92	1	10	CARDINAL
ejpam-4498	92	2	4	CARDINAL
ejpam-4498	92	3	9	CARDINAL
ejpam-4498	92	4	10	CARDINAL
ejpam-4498	93	1	1	CARDINAL
ejpam-4498	93	2	9	CARDINAL
ejpam-4498	94	1	1	CARDINAL
ejpam-4498	94	2	1	CARDINAL
ejpam-4498	94	3	2	CARDINAL
ejpam-4498	94	4	1	CARDINAL
ejpam-4498	94	5	1	CARDINAL
ejpam-4498	94	6	1 2	CARDINAL
ejpam-4498	94	7	1	CARDINAL
ejpam-4498	94	8	2 + 2	DATE
ejpam-4498	94	9	3 + 3	DATE
ejpam-4498	94	10	4 + ·	DATE
ejpam-4498	94	11	1	CARDINAL
ejpam-4498	94	12	1	CARDINAL
ejpam-4498	95	1	11	CARDINAL
ejpam-4498	95	2	9	CARDINAL
ejpam-4498	96	1	3 2	CARDINAL
ejpam-4498	96	2	1	CARDINAL
ejpam-4498	97	1	3 + 3	DATE
ejpam-4498	97	2	4 + ·	DATE
ejpam-4498	98	1	1	CARDINAL
ejpam-4498	98	2	1	CARDINAL
ejpam-4498	99	1	12	CARDINAL
ejpam-4498	99	2	1	CARDINAL
ejpam-4498	99	3	2 + 2	DATE
ejpam-4498	99	4	3 + 3	DATE
ejpam-4498	99	5	4 + ·	DATE
ejpam-4498	100	1	1	CARDINAL
ejpam-4498	101	1	1 3	CARDINAL
ejpam-4498	101	2	1)n(n+ 1	DATE
ejpam-4498	101	3	13	CARDINAL
ejpam-4498	101	4	yukio kobayashi	PERSON
ejpam-4498	102	1	j. pure	PERSON
ejpam-4498	102	2	15	CARDINAL
ejpam-4498	102	3	3	CARDINAL
ejpam-4498	102	4	2022	CARDINAL
ejpam-4498	102	5	1237-1253 1242	CARDINAL
ejpam-4498	102	6	1	CARDINAL
ejpam-4498	103	1	+ n = n	QUANTITY
ejpam-4498	103	2	11	CARDINAL
ejpam-4498	103	3	1	CARDINAL
ejpam-4498	103	4	2 + 2	DATE
ejpam-4498	103	5	3 + 3	DATE
ejpam-4498	103	6	4 + ·	DATE
ejpam-4498	103	7	1	CARDINAL
ejpam-4498	103	8	2	CARDINAL
ejpam-4498	103	9	1	CARDINAL
ejpam-4498	103	10	2	CARDINAL
ejpam-4498	103	11	1	CARDINAL
ejpam-4498	103	12	+ n	PERSON
ejpam-4498	103	13	1]− n	QUANTITY
ejpam-4498	103	14	1	CARDINAL
ejpam-4498	104	1	14	CARDINAL
ejpam-4498	104	2	9	CARDINAL
ejpam-4498	105	1	3	CARDINAL
ejpam-4498	105	2	1	CARDINAL
ejpam-4498	105	3	2	CARDINAL
ejpam-4498	105	4	1	CARDINAL
ejpam-4498	105	5	+ n	PERSON
ejpam-4498	105	6	1]− n	QUANTITY
ejpam-4498	105	7	1	CARDINAL
ejpam-4498	106	1	15	CARDINAL
ejpam-4498	106	2	1	CARDINAL
ejpam-4498	106	3	2	CARDINAL
ejpam-4498	106	4	1	CARDINAL
ejpam-4498	106	5	1	CARDINAL
ejpam-4498	107	1	16	CARDINAL
ejpam-4498	107	2	13	CARDINAL
ejpam-4498	107	3	16	CARDINAL
ejpam-4498	107	4	10	CARDINAL
ejpam-4498	107	5	9	CARDINAL
ejpam-4498	108	1	16	CARDINAL
ejpam-4498	108	2	two	CARDINAL
ejpam-4498	109	1	1	CARDINAL
ejpam-4498	109	2	2	CARDINAL
ejpam-4498	109	3	1	CARDINAL
ejpam-4498	110	1	1	CARDINAL
ejpam-4498	110	2	1 3	DATE
ejpam-4498	110	3	2	CARDINAL
ejpam-4498	110	4	1 2 n(n+ 1	QUANTITY
ejpam-4498	110	5	1 3	CARDINAL
ejpam-4498	110	6	2	CARDINAL
ejpam-4498	110	7	n∑ k=1	PERSON
ejpam-4498	111	1	17	CARDINAL
ejpam-4498	111	2	1	CARDINAL
ejpam-4498	111	3	2	CARDINAL
ejpam-4498	111	4	1	CARDINAL
ejpam-4498	111	5	1	CARDINAL
ejpam-4498	111	6	1 3 n · 1 2	QUANTITY
ejpam-4498	111	7	2	CARDINAL
ejpam-4498	111	8	1 3 n n+1∑ k=1 k.	QUANTITY
ejpam-4498	112	1	18	CARDINAL
ejpam-4498	112	2	17	CARDINAL
ejpam-4498	112	3	18	CARDINAL
ejpam-4498	112	4	section 6.	LAW
ejpam-4498	112	5	4	CARDINAL
ejpam-4498	112	6	2	CARDINAL
ejpam-4498	113	1	2 yukio kobayashi	QUANTITY
ejpam-4498	114	1	j. pure	PERSON
ejpam-4498	114	2	15	CARDINAL
ejpam-4498	114	3	3	CARDINAL
ejpam-4498	114	4	2022	CARDINAL
ejpam-4498	114	5	1237-1253 1243	DATE
ejpam-4498	114	6	3	CARDINAL
ejpam-4498	114	7	5	CARDINAL
ejpam-4498	116	1	5	CARDINAL
ejpam-4498	116	2	1	CARDINAL
ejpam-4498	116	3	5 + 2	DATE
ejpam-4498	116	4	4 + 3	DATE
ejpam-4498	116	5	3 + 4	DATE
ejpam-4498	116	6	2 + 5	DATE
ejpam-4498	116	7	1	CARDINAL
ejpam-4498	116	8	1	CARDINAL
ejpam-4498	116	9	1 + 2	QUANTITY
ejpam-4498	116	10	2 + 3	DATE
ejpam-4498	116	11	3 + 4	DATE
ejpam-4498	116	12	4 + 5	DATE
ejpam-4498	116	13	5	CARDINAL
ejpam-4498	117	1	19	CARDINAL
ejpam-4498	117	2	1	CARDINAL
ejpam-4498	117	3	5 + 2	DATE
ejpam-4498	118	1	3 + 4	DATE
ejpam-4498	119	1	1	CARDINAL
ejpam-4498	119	2	1 + 2 + 3 + 4 + 5	DATE
ejpam-4498	120	1	6	CARDINAL
ejpam-4498	121	1	20	CARDINAL
ejpam-4498	121	2	20	CARDINAL
ejpam-4498	123	1	5	CARDINAL
ejpam-4498	124	1	20	CARDINAL
ejpam-4498	124	2	17	CARDINAL
ejpam-4498	125	1	20	CARDINAL
ejpam-4498	125	2	12 + 22 + ·	DATE
ejpam-4498	125	3	1 + 2 + ·	DATE
ejpam-4498	125	4	1	CARDINAL
ejpam-4498	125	5	2	CARDINAL
ejpam-4498	125	6	1	CARDINAL
ejpam-4498	127	1	1 2 n(n+	QUANTITY
ejpam-4498	127	2	1 3	CARDINAL
ejpam-4498	127	3	2	CARDINAL
ejpam-4498	127	4	1 2 n(n+ 1	QUANTITY
ejpam-4498	127	5	1 6 n(n+ 1)(2n+ 1	QUANTITY
ejpam-4498	128	1	21	CARDINAL
ejpam-4498	128	2	21	CARDINAL
ejpam-4498	130	1	1 3	DATE
ejpam-4498	131	1	k=1 k.	PERSON
ejpam-4498	132	1	22	CARDINAL
ejpam-4498	132	2	yukio kobayashi	PERSON
ejpam-4498	133	1	j. pure	PERSON
ejpam-4498	133	2	15	CARDINAL
ejpam-4498	133	3	3	CARDINAL
ejpam-4498	133	4	2022	CARDINAL
ejpam-4498	133	5	1237-1253 1244 5	CARDINAL
ejpam-4498	134	1	section 3	DATE
ejpam-4498	135	1	n∑ k=1	PERSON
ejpam-4498	136	1	− k	PERSON
ejpam-4498	138	1	n∑ k=1	PERSON
ejpam-4498	139	1	1−	QUANTITY
ejpam-4498	140	1	n∑ k=1	PERSON
ejpam-4498	143	1	23	CARDINAL
ejpam-4498	143	2	21	CARDINAL
ejpam-4498	143	3	22	CARDINAL
ejpam-4498	143	4	23	CARDINAL
ejpam-4498	145	1	n∑ k=1	PERSON
ejpam-4498	146	1	1−	QUANTITY
ejpam-4498	147	1	21	CARDINAL
ejpam-4498	147	2	22	CARDINAL
ejpam-4498	147	3	5	CARDINAL
ejpam-4498	148	1	n∑ k=1	PERSON
ejpam-4498	151	1	24	CARDINAL
ejpam-4498	151	2	n∑ k=1	PERSON
ejpam-4498	152	1	2	CARDINAL
ejpam-4498	152	2	n∑ k=1 ∫	PERSON
ejpam-4498	154	1	25	CARDINAL
ejpam-4498	154	2	24	CARDINAL
ejpam-4498	154	3	25	CARDINAL
ejpam-4498	154	4	n∑ k=1 k(n+	PERSON
ejpam-4498	154	5	1− k	TIME
ejpam-4498	155	1	n∑ k=1	PERSON
ejpam-4498	157	1	1− 2x)dx	TIME
ejpam-4498	157	2	1− 2x)dx+	CARDINAL
ejpam-4498	157	3	1	CARDINAL
ejpam-4498	157	4	2 1	DATE
ejpam-4498	157	5	1− 2x)dx+	CARDINAL
ejpam-4498	158	1	n−	ORG
ejpam-4498	159	1	k k−1	PERSON
ejpam-4498	159	2	1− 2x)dx+	CARDINAL
ejpam-4498	159	3	1− 2x)dx	TIME
ejpam-4498	159	4	n∑ k=1	PERSON
ejpam-4498	159	5	1− k	PRODUCT
ejpam-4498	160	1	k k−1	PERSON
ejpam-4498	160	2	1− 2x)dx	TIME
ejpam-4498	161	1	n∑ k=1	PERSON
ejpam-4498	161	2	1− k	PRODUCT
ejpam-4498	162	1	k k−1 yukio kobayashi	ORG
ejpam-4498	163	1	j. pure	PERSON
ejpam-4498	163	2	15	CARDINAL
ejpam-4498	163	3	3	CARDINAL
ejpam-4498	163	4	2022	CARDINAL
ejpam-4498	163	5	1237-1253 1245	DATE
ejpam-4498	164	1	n∑ k=1	PERSON
ejpam-4498	164	2	1−	CARDINAL
ejpam-4498	164	3	1)k	CARDINAL
ejpam-4498	164	4	1)(k	CARDINAL
ejpam-4498	164	5	1	CARDINAL
ejpam-4498	165	1	n∑ k=1	PERSON
ejpam-4498	166	1	1− k)(n−	PRODUCT
ejpam-4498	166	2	2	CARDINAL
ejpam-4498	166	3	n∑ k=1	PERSON
ejpam-4498	167	1	1− k)− 2	PRODUCT
ejpam-4498	168	1	n∑ k=1 k(n+	PERSON
ejpam-4498	168	2	1− k	TIME
ejpam-4498	168	3	26	CARDINAL
ejpam-4498	168	4	3 n∑ k=1 k(n+	QUANTITY
ejpam-4498	168	5	1− k	TIME
ejpam-4498	168	6	2	CARDINAL
ejpam-4498	168	7	n∑ k=1	PERSON
ejpam-4498	169	1	1− k	PRODUCT
ejpam-4498	171	1	2	CARDINAL
ejpam-4498	171	2	n∑ k=1	PERSON
ejpam-4498	172	1	2	CARDINAL
ejpam-4498	172	2	1 2	CARDINAL
ejpam-4498	172	3	1 2 n(n+ 1)(n+ 2	QUANTITY
ejpam-4498	173	1	27	CARDINAL
ejpam-4498	174	1	n∑ k=1 k(n+	PERSON
ejpam-4498	175	1	1− k	TIME
ejpam-4498	176	1	28	CARDINAL
ejpam-4498	179	1	n∑ k=1	PERSON
ejpam-4498	180	1	5	CARDINAL
ejpam-4498	181	1	6	CARDINAL
ejpam-4498	181	2	6.1	CARDINAL
ejpam-4498	182	1	17	CARDINAL
ejpam-4498	182	2	18	CARDINAL
ejpam-4498	186	1	yukio kobayashi	PERSON
ejpam-4498	187	1	j. pure	PERSON
ejpam-4498	187	2	15	CARDINAL
ejpam-4498	187	3	3	CARDINAL
ejpam-4498	187	4	2022	CARDINAL
ejpam-4498	187	5	1237-1253 1246	DATE
ejpam-4498	187	6	2︷ ︸︸	ORG
ejpam-4498	188	1	n+2b0 +	DATE
ejpam-4498	189	1	29	CARDINAL
ejpam-4498	189	2	three	CARDINAL
ejpam-4498	189	3	29	CARDINAL
ejpam-4498	190	1	1 2 3	CARDINAL
ejpam-4498	190	2	3 4	CARDINAL
ejpam-4498	190	3	2	CARDINAL
ejpam-4498	190	4	1	CARDINAL
ejpam-4498	190	5	2	CARDINAL
ejpam-4498	191	1	2	CARDINAL
ejpam-4498	191	2	4 5	CARDINAL
ejpam-4498	191	3	2	CARDINAL
ejpam-4498	191	4	1	CARDINAL
ejpam-4498	192	1	2	CARDINAL
ejpam-4498	193	1	1	CARDINAL
ejpam-4498	194	1	1	CARDINAL
ejpam-4498	194	2	1	CARDINAL
ejpam-4498	194	3	6	CARDINAL
ejpam-4498	195	1	29	CARDINAL
ejpam-4498	196	1	four	CARDINAL
ejpam-4498	196	2	1	CARDINAL
ejpam-4498	196	3	2	CARDINAL
ejpam-4498	196	4	3	CARDINAL
ejpam-4498	196	5	4	CARDINAL
ejpam-4498	196	6	3	CARDINAL
ejpam-4498	197	1	6	CARDINAL
ejpam-4498	197	2	3	CARDINAL
ejpam-4498	199	1	2	CARDINAL
ejpam-4498	199	2	3	CARDINAL
ejpam-4498	201	1	30	CARDINAL
ejpam-4498	201	2	1	CARDINAL
ejpam-4498	201	3	yukio kobayashi	PERSON
ejpam-4498	202	1	j. pure	PERSON
ejpam-4498	202	2	15	CARDINAL
ejpam-4498	202	3	3	CARDINAL
ejpam-4498	202	4	2022	CARDINAL
ejpam-4498	202	5	1237-1253 1247	CARDINAL
ejpam-4498	204	1	k=1 k	PERSON
ejpam-4498	205	1	 1 3	DATE
ejpam-4498	205	2	1	CARDINAL
ejpam-4498	205	3	2	CARDINAL
ejpam-4498	205	4	1	CARDINAL
ejpam-4498	205	5	2	CARDINAL
ejpam-4498	205	6	+ k	PERSON
ejpam-4498	206	1	n−	ORG
ejpam-4498	206	2	n∑ k=1 k(n+	PERSON
ejpam-4498	206	3	1− k	TIME
ejpam-4498	206	4	1	CARDINAL
ejpam-4498	206	5	n∑ k=1	PERSON
ejpam-4498	208	1	− n∑ k=1 k2	PERSON
ejpam-4498	208	2	1)n+1c2	CARDINAL
ejpam-4498	208	3	n∑ k=1 k+1c2	PERSON
ejpam-4498	210	1	6.2	CARDINAL
ejpam-4498	211	1	20	CARDINAL
ejpam-4498	211	2	combinatorics	ORG
ejpam-4498	211	3	1	CARDINAL
ejpam-4498	211	4	7	CARDINAL
ejpam-4498	212	1	1 1 1 1 2 2 1 2 1 1 2 3 2 1 2 3 3 1 2 3	QUANTITY
ejpam-4498	213	1	3	CARDINAL
ejpam-4498	213	2	7	CARDINAL
ejpam-4498	214	1	two	CARDINAL
ejpam-4498	215	1	two	CARDINAL
ejpam-4498	216	1	yukio kobayashi	PERSON
ejpam-4498	217	1	j. pure	PERSON
ejpam-4498	217	2	15	CARDINAL
ejpam-4498	217	3	3	CARDINAL
ejpam-4498	217	4	2022	CARDINAL
ejpam-4498	217	5	1237-1253 1248	CARDINAL
ejpam-4498	217	6	7	CARDINAL
ejpam-4498	218	1	31	CARDINAL
ejpam-4498	218	2	two	CARDINAL
ejpam-4498	219	1	12	CARDINAL
ejpam-4498	219	2	1	CARDINAL
ejpam-4498	219	3	22	CARDINAL
ejpam-4498	219	4	1 +	DATE
ejpam-4498	220	1	32	CARDINAL
ejpam-4498	220	2	1 + 2	DATE
ejpam-4498	220	3	1 + 2 + 3	DATE
ejpam-4498	221	1		GPE
ejpam-4498	221	2	7	CARDINAL
ejpam-4498	221	3	8	CARDINAL
ejpam-4498	221	4	1 1 + 2 1 1 + 2 1 + 2 + 3	QUANTITY
ejpam-4498	221	5	8	CARDINAL
ejpam-4498	222	1	12 + 22	DATE
ejpam-4498	223	1	2	CARDINAL
ejpam-4498	224	1	1 +	CARDINAL
ejpam-4498	225	1	32	CARDINAL
ejpam-4498	225	2	12 + 22 + ·	DATE
ejpam-4498	225	3	2	CARDINAL
ejpam-4498	225	4	1 +	DATE
ejpam-4498	227	1	1 + 2 + ·	DATE
ejpam-4498	227	2	1	CARDINAL
ejpam-4498	227	3	2n+2c3	CARDINAL
ejpam-4498	228	1	33	CARDINAL
ejpam-4498	228	2	section 6.1	LAW
ejpam-4498	228	3	33	CARDINAL
ejpam-4498	228	4	1 6 n(n+ 1)(2n+ 1	QUANTITY
ejpam-4498	229	1	1	CARDINAL
ejpam-4498	230	1	1	CARDINAL
ejpam-4498	232	1	1	CARDINAL
ejpam-4498	233	1	2	CARDINAL
ejpam-4498	233	2	1	CARDINAL
ejpam-4498	233	3	1	CARDINAL
ejpam-4498	234	1	12	CARDINAL
ejpam-4498	235	1	2 n+1c3 +	DATE
ejpam-4498	236	1	yukio kobayashi	PERSON
ejpam-4498	237	1	j. pure	PERSON
ejpam-4498	237	2	15	CARDINAL
ejpam-4498	237	3	3	CARDINAL
ejpam-4498	237	4	2022	CARDINAL
ejpam-4498	237	5	1237-1253 1249 7	CARDINAL
ejpam-4498	238	1	2	CARDINAL
ejpam-4498	240	1	2	CARDINAL
ejpam-4498	240	2	6.1	CARDINAL
ejpam-4498	240	3	nc2s	LANGUAGE
ejpam-4498	240	4	nc3s	ORG
ejpam-4498	241	1	2	CARDINAL
ejpam-4498	242	1	nc4	ORG
ejpam-4498	242	2	6c4	CARDINAL
ejpam-4498	242	3	1 + 4 + 10	DATE
ejpam-4498	242	4	1 +	DATE
ejpam-4498	242	5	1 + 3	DATE
ejpam-4498	242	6	1 + 3 + 6	DATE
ejpam-4498	243	1	1 +	DATE
ejpam-4498	244	1	1 +	DATE
ejpam-4498	244	2	1 + 2 + 3	DATE
ejpam-4498	244	3	3c3 + 4c3	DATE
ejpam-4498	245	1	+ 5c3	DATE
ejpam-4498	245	2	34	CARDINAL
ejpam-4498	246	1	1 + 5 + 15 + 35	DATE
ejpam-4498	246	2	1 + (	DATE
ejpam-4498	246	3	1 + 4	DATE
ejpam-4498	246	4	1 + 4 + 10	DATE
ejpam-4498	246	5	1 + 4 + 10 + 20	DATE
ejpam-4498	247	1	1 +	DATE
ejpam-4498	247	2	1 + 3	DATE
ejpam-4498	248	1	1 +	DATE
ejpam-4498	248	2	1 + 3	DATE
ejpam-4498	248	3	1 + 3 + 6	DATE
ejpam-4498	249	1	1 +	DATE
ejpam-4498	249	2	1 + 3	DATE
ejpam-4498	249	3	1 + 3 + 6	DATE
ejpam-4498	249	4	1 + 3 + 6 + 10	DATE
ejpam-4498	251	1	3c3	CARDINAL
ejpam-4498	252	1	3c3 + 4c3	DATE
ejpam-4498	253	1	3c3 + 4c3 + 5c3	DATE
ejpam-4498	254	1	3c3 + 4c3	DATE
ejpam-4498	255	1	35	CARDINAL
ejpam-4498	256	1	30	CARDINAL
ejpam-4498	258	1	36	CARDINAL
ejpam-4498	258	2	yukio kobayashi	PERSON
ejpam-4498	259	1	j. pure	PERSON
ejpam-4498	259	2	15	CARDINAL
ejpam-4498	259	3	3	CARDINAL
ejpam-4498	259	4	2022	CARDINAL
ejpam-4498	259	5	1237-1253 1250	CARDINAL
ejpam-4498	259	6	2	CARDINAL
ejpam-4498	261	1	2c2	CARDINAL
ejpam-4498	262	1	1	CARDINAL
ejpam-4498	263	1	1 + 2	DATE
ejpam-4498	264	1	5c2	CARDINAL
ejpam-4498	265	1	1 + 2 + 3 + 4	DATE
ejpam-4498	265	2	3c3	CARDINAL
ejpam-4498	265	3	1	CARDINAL
ejpam-4498	265	4	4c3	CARDINAL
ejpam-4498	266	1	1 + 3	DATE
ejpam-4498	266	2	5c3	CARDINAL
ejpam-4498	266	3	1 + 3 + 6	DATE
ejpam-4498	266	4	6c3	CARDINAL
ejpam-4498	266	5	1 + 3 + 6 + 10	DATE
ejpam-4498	267	1	4c4	CARDINAL
ejpam-4498	268	1	1	CARDINAL
ejpam-4498	268	2	5c4	CARDINAL
ejpam-4498	269	1	1 + 4	DATE
ejpam-4498	269	2	6c4	CARDINAL
ejpam-4498	269	3	1 + 4 + 10	DATE
ejpam-4498	270	1	1 + 4 + 10 + 20	DATE
ejpam-4498	271	1	5c5	CARDINAL
ejpam-4498	271	2	1	CARDINAL
ejpam-4498	272	1	6c5	CARDINAL
ejpam-4498	272	2	1 + 5	DATE
ejpam-4498	272	3	1 + 5 + 15	DATE
ejpam-4498	275	1	1	CARDINAL
ejpam-4498	278	1	6c4	CARDINAL
ejpam-4498	278	2	5c4	CARDINAL
ejpam-4498	278	3	9	CARDINAL
ejpam-4498	279	1	4c3	CARDINAL
ejpam-4498	279	2	3c3	CARDINAL
ejpam-4498	279	3	four	CARDINAL
ejpam-4498	279	4	two	CARDINAL
ejpam-4498	279	5	three	CARDINAL
ejpam-4498	279	6	four	CARDINAL
ejpam-4498	279	7	five	CARDINAL
ejpam-4498	279	8	six	CARDINAL
ejpam-4498	279	9	one	CARDINAL
ejpam-4498	279	10	4c3	CARDINAL
ejpam-4498	280	1	5c4	CARDINAL
ejpam-4498	280	2	8	CARDINAL
ejpam-4498	280	3	8	CARDINAL
ejpam-4498	281	1	yukio kobayashi	PERSON
ejpam-4498	282	1	j. pure	PERSON
ejpam-4498	282	2	15	CARDINAL
ejpam-4498	282	3	3	CARDINAL
ejpam-4498	282	4	2022	CARDINAL
ejpam-4498	282	5	1237-1253	DATE
ejpam-4498	283	1	1 + 2 + 3 3	DATE
ejpam-4498	283	2	1 + 2 1 3	CARDINAL
ejpam-4498	283	3	1 + 2 1 1 5c3	QUANTITY
ejpam-4498	283	4	10 4c3	CARDINAL
ejpam-4498	283	5	4 3c3	CARDINAL
ejpam-4498	283	6	1	CARDINAL
ejpam-4498	284	1	three	CARDINAL
ejpam-4498	284	2	2	CARDINAL
ejpam-4498	284	3	3	DATE
ejpam-4498	284	4	4	DATE
ejpam-4498	284	5	5	DATE
ejpam-4498	284	6	6	CARDINAL
ejpam-4498	284	7	1	CARDINAL
ejpam-4498	285	1	three	CARDINAL
ejpam-4498	285	2	3	CARDINAL
ejpam-4498	285	3	4	DATE
ejpam-4498	285	4	5	DATE
ejpam-4498	285	5	6	CARDINAL
ejpam-4498	285	6	1	CARDINAL
ejpam-4498	285	7	2	CARDINAL
ejpam-4498	286	1	three	CARDINAL
ejpam-4498	286	2	4	CARDINAL
ejpam-4498	286	3	5	DATE
ejpam-4498	286	4	6	DATE
ejpam-4498	286	5	1	CARDINAL
ejpam-4498	286	6	2	CARDINAL
ejpam-4498	286	7	3	CARDINAL
ejpam-4498	286	8	9	CARDINAL
ejpam-4498	286	9	6c4	CARDINAL
ejpam-4498	288	1	four	CARDINAL
ejpam-4498	288	2	two	CARDINAL
ejpam-4498	289	1	5c4s	CARDINAL
ejpam-4498	290	1	↓	CARDINAL
ejpam-4498	290	2	↓	ORG
ejpam-4498	290	3	1	CARDINAL
ejpam-4498	290	4	2	CARDINAL
ejpam-4498	290	5	3	CARDINAL
ejpam-4498	290	6	4	CARDINAL
ejpam-4498	292	1	24	CARDINAL
ejpam-4498	292	2	25	CARDINAL
ejpam-4498	293	1	34	CARDINAL
ejpam-4498	293	2	35	CARDINAL
ejpam-4498	295	1	1	CARDINAL
ejpam-4498	295	2	2	CARDINAL
ejpam-4498	295	3	3	CARDINAL
ejpam-4498	295	4	4	CARDINAL
ejpam-4498	295	5	1252	CARDINAL
ejpam-4498	295	6	1	CARDINAL
ejpam-4498	297	1	2	CARDINAL
ejpam-4498	297	2	37	CARDINAL
ejpam-4498	300	1	slater	PERSON
ejpam-4498	301	1	12	CARDINAL
ejpam-4498	302	1	slater	PERSON
ejpam-4498	302	2	frank	PERSON
ejpam-4498	303	1	english	LANGUAGE
ejpam-4498	304	1	1	CARDINAL
ejpam-4498	304	2	c. alsina	PERSON
ejpam-4498	304	3	r. b. nelsen	PERSON
ejpam-4498	306	1	european journal	ORG
ejpam-4498	306	2	3:118–127	CARDINAL
ejpam-4498	306	3	2010	DATE
ejpam-4498	307	1	2	CARDINAL
ejpam-4498	309	1	benjamin	PERSON
ejpam-4498	309	2	1972	DATE
ejpam-4498	310	1	3	CARDINAL
ejpam-4498	310	2	y. kobayashi	PERSON
ejpam-4498	311	1	n∑ k=1 k2	PERSON
ejpam-4498	313	1	j. math	PERSON
ejpam-4498	314	1	sci. tech.	ORG
ejpam-4498	314	2	42:235–239, 2011	DATE
ejpam-4498	315	1	4	CARDINAL
ejpam-4498	315	2	y. kobayashi	PERSON
ejpam-4498	316	1	n∑ k=1	PERSON
ejpam-4498	317	1	n∑ k=1 k2	PERSON
ejpam-4498	317	2	n∑ k=1	PERSON
ejpam-4498	320	1	j. math	PERSON
ejpam-4498	321	1	sci. tech.	ORG
ejpam-4498	321	2	42:657–664,	DATE
ejpam-4498	321	3	2011	DATE
ejpam-4498	322	1	42 (2011	DATE
ejpam-4498	322	2	1123	CARDINAL
ejpam-4498	323	1	5	CARDINAL
ejpam-4498	323	2	y. kobayashi	PERSON
ejpam-4498	324	1	1ℓ+2ℓ+	CARDINAL
ejpam-4498	325	1	+nℓ	DATE
ejpam-4498	327	1	j. math	PERSON
ejpam-4498	328	1	sci. tech.	ORG
ejpam-4498	328	2	44:132–142	CARDINAL
ejpam-4498	328	3	2013	DATE
ejpam-4498	329	1	6	CARDINAL
ejpam-4498	329	2	y. kobayashi	PERSON
ejpam-4498	332	1	j. math	PERSON
ejpam-4498	333	1	sci. tech.	ORG
ejpam-4498	333	2	46:469–476	CARDINAL
ejpam-4498	333	3	2015	DATE
ejpam-4498	334	1	46	DATE
ejpam-4498	334	2	2015	CARDINAL
ejpam-4498	334	3	795	CARDINAL
ejpam-4498	335	1	1253	CARDINAL
ejpam-4498	335	2	7	CARDINAL
ejpam-4498	335	3	y. kobayashi	PERSON
ejpam-4498	338	1	19:57–58, 2019	DATE
ejpam-4498	339	1	8	CARDINAL
ejpam-4498	339	2	y. kobayashi	PERSON
ejpam-4498	342	1	21:83–91	CARDINAL
ejpam-4498	342	2	2021	DATE
ejpam-4498	343	1	9	CARDINAL
ejpam-4498	343	2	l. c. larson	PERSON
ejpam-4498	344	1	1 + 2 +	QUANTITY
ejpam-4498	345	1	j.	PERSON
ejpam-4498	345	2	16:369–382, 1985	DATE
ejpam-4498	346	1	10	CARDINAL
ejpam-4498	346	2	guo liu	PERSON
ejpam-4498	347	1	ramanujan	GPE
ejpam-4498	348	1	the ramanujan journal.	ORG
ejpam-4498	348	2	7:407–434	CARDINAL
ejpam-4498	348	3	2003	DATE
ejpam-4498	349	1	11	CARDINAL
ejpam-4498	349	2	r. b. nelsen	PERSON
ejpam-4498	351	1	the mathematical association of america	ORG
ejpam-4498	351	2	2000	DATE
ejpam-4498	352	1	12	CARDINAL
ejpam-4498	352	2	j. c. slater	PERSON
ejpam-4498	352	3	n. h. frank	PERSON
ejpam-4498	354	1	mcgrawhill, 1933	ORG