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%I #39 Nov 29 2020 02:11:56
%S 1,1,1,1,1,2,1,1,2,2,1,1,2,3,3,1,1,2,5,5,3,1,1,2,9,11,8,4,1,1,2,17,29,
%T 26,13,4,1,1,2,33,83,92,63,21,5,1,1,2,65,245,338,343,153,34,5,1,1,2,
%U 129,731,1268,1923,1281,376,55,6
%N A(n,k) = Sum_{j=0..floor(n/2)} binomial(n-j,j)^k, square array A(n,k) read by antidiagonals, for n >= 0, k >= 0.
%H Seiichi Manyama, <a href="/A323767/b323767.txt">Antidiagonals n = 0..139, flattened</a>
%e Square array begins:
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 1, 1, 1, 1, 1, 1, 1, ...
%e 2, 2, 2, 2, 2, 2, 2, ...
%e 2, 3, 5, 9, 17, 33, 65, ...
%e 3, 5, 11, 29, 83, 245, 731, ...
%e 3, 8, 26, 92, 338, 1268, 4826, ...
%e 4, 13, 63, 343, 1923, 10903, 62283, ...
%e 4, 21, 153, 1281, 11553, 108801, 1050753, ...
%t f := Sum[Power[Binomial[#1 - i, i], #2], {i, 0, #1/2}] &;a = Flatten[Reverse[DeleteCases[Table[Table[f[m - n, n], {n, 0, 20}], {m, 0, 20}], 0, Infinity], 2]] (* _Elijah Beregovsky_, Nov 24 2020 *)
%Y Columns 0-5 give A004526(n+2), A000045(n+1), A051286, A181545, A181546, A181547.
%Y Rows 0-5 give A000012, A000012, A007395, A000051, A168607, A074506.
%Y Main diagonal gives A323769.
%Y Cf. A011973,
%K nonn,tabl
%O 0,6
%A _Seiichi Manyama_, Jan 27 2019
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