A077042 - cp's OEIS frontend

A077042 Square array read by falling antidiagonals of central polynomial coefficients: largest coefficient in expansion of (1 + x + x^2 + ... + x^(n-1))^k = ((1-x^n)/(1-x))^k, i.e., the coefficient of x^floor(k(n-1)/2) and of x^ceiling(k(n-1)/2); also number of compositions of floor(k*(n+1)/2) into exactly k positive integers each no more than n.

n	a(n)
0	1
1	0
2	1
3	0
4	1
5	1
6	0
7	1
8	1
9	1
10	0
11	1
12	2
13	1
14	1
15	0
16	1
17	3
18	3
19	1
20	1
21	0
22	1
23	6
24	7
25	4
26	1
27	1
28	0
29	1
30	10
31	19
32	12
33	5
34	1
35	1
36	0
37	1
38	20
39	51
40	44
41	19
42	6
43	1
44	1
45	0
46	1
47	35
48	141
49	155
50	85
51	27
52	7
53	1
54	1
55	0
56	1
57	70
58	393
59	580
60	381
61	146
62	37
63	8
64	1
65	1
66	0
67	1
68	126
69	1107
70	2128
71	1751
72	780
73	231
74	48
75	9
76	1
77	1
78	0
79	1
80	252
81	3139

[1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 3, 3, 1, 1, 0, 1, 6, 7, 4, 1, 1, 0, 1, 10, 19, 12, 5, 1, 1, 0, 1, 20, 51, 44, 19, 6, 1, 1, 0, 1, 35, 141, 155, 85, 27, 7, 1, 1, 0, 1, 70, 393, 580, 381, 146, 37, 8, 1, 1, 0, 1, 126, 1107, 2128, 1751, 780, 231, 48, 9, 1, 1, 0, 1, 252, 3139]

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