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A306846 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-1))/((1-x)^k-x^k).

%I A306846 #31 Jun 21 2021 03:01:37
%S A306846 1,1,2,1,1,4,1,1,2,8,1,1,1,4,16,1,1,1,2,8,32,1,1,1,1,5,16,64,1,1,1,1,
%T A306846 2,11,32,128,1,1,1,1,1,6,22,64,256,1,1,1,1,1,2,16,43,128,512,1,1,1,1,
%U A306846 1,1,7,36,85,256,1024,1,1,1,1,1,1,2,22,72,170,512,2048
%N A306846 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-1))/((1-x)^k-x^k).
%H A306846 Seiichi Manyama, <a href="/A306846/b306846.txt">Antidiagonals n = 0..139, flattened</a>
%F A306846 A(n,k) = Sum_{j=0..floor(n/k)} binomial(n,k*j).
%e A306846 Square array begins:
%e A306846      1,   1,  1,  1,  1,  1, 1, 1, 1, ...
%e A306846      2,   1,  1,  1,  1,  1, 1, 1, 1, ...
%e A306846      4,   2,  1,  1,  1,  1, 1, 1, 1, ...
%e A306846      8,   4,  2,  1,  1,  1, 1, 1, 1, ...
%e A306846     16,   8,  5,  2,  1,  1, 1, 1, 1, ...
%e A306846     32,  16, 11,  6,  2,  1, 1, 1, 1, ...
%e A306846     64,  32, 22, 16,  7,  2, 1, 1, 1, ...
%e A306846    128,  64, 43, 36, 22,  8, 2, 1, 1, ...
%e A306846    256, 128, 85, 72, 57, 29, 9, 2, 1, ...
%t A306846 T[n_, k_] := Sum[Binomial[n, k*j], {j, 0, Floor[n/k]}]; Table[T[k, n - k + 1], {n, 0, 11}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Jun 21 2021 *)
%Y A306846 Columns 1-9 give A000079, A011782, A024493, A038503, A139398, A306847, A306852, A306859, A306860.
%Y A306846 Cf. A306680.
%K A306846 nonn,tabl
%O A306846 0,3
%A A306846 _Seiichi Manyama_, Mar 13 2019