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A309010 Square array A(n, k) = Sum_{j=0..n} binomial(n,j)^k, n >= 0, k >= 0, read by antidiagonals.

Table of values

n a(n)
0 1
1 1
2 2
3 1
4 2
5 3
6 1
7 2
8 4
9 4
10 1
11 2
12 6
13 8
14 5
15 1
16 2
17 10
18 20
19 16
20 6
21 1
22 2
23 18
24 56
25 70
26 32
27 7
28 1
29 2
30 34
31 164
32 346
33 252
34 64
35 8
36 1
37 2
38 66
39 488
40 1810
41 2252
42 924
43 128
44 9
45 1
46 2
47 130
48 1460
49 9826
50 21252
51 15184
52 3432
53 256
54 10
55 1
56 2
57 258
58 4376
59 54850
60 206252
61 263844
62 104960
63 12870
64 512
65 11

List of values

[1, 1, 2, 1, 2, 3, 1, 2, 4, 4, 1, 2, 6, 8, 5, 1, 2, 10, 20, 16, 6, 1, 2, 18, 56, 70, 32, 7, 1, 2, 34, 164, 346, 252, 64, 8, 1, 2, 66, 488, 1810, 2252, 924, 128, 9, 1, 2, 130, 1460, 9826, 21252, 15184, 3432, 256, 10, 1, 2, 258, 4376, 54850, 206252, 263844, 104960, 12870, 512, 11]