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A294756 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1-j^(k*j)*x^j)^j(k*j) in powers of x.

%I A294756 #15 Dec 21 2020 17:29:32
%S A294756 1,1,1,1,1,2,1,1,17,3,1,1,257,746,5,1,1,4097,531698,66442,7,1,1,65537,
%T A294756 387424586,4295533810,9843731,11,1,1,1048577,282429602018,
%U A294756 281475372654922,95371863223331,2187951485,15,1,1,16777217,205891133143226,18446744358295025890,931322857677725493491,4738477951108288824,680615166718,22
%N A294756 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1-j^(k*j)*x^j)^j(k*j) in powers of x.
%H A294756 Seiichi Manyama, <a href="/A294756/b294756.txt">Antidiagonals n = 0..38, flattened</a>
%F A294756 A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(1+k*(d+j))) * A(n-j,k) for n > 0.
%e A294756 Square array begins:
%e A294756    1,     1,          1,               1, ...
%e A294756    1,     1,          1,               1, ...
%e A294756    2,    17,        257,            4097, ...
%e A294756    3,   746,     531698,       387424586, ...
%e A294756    5, 66442, 4295533810, 281475372654922, ...
%Y A294756 Columns k=0..1 give A000041, A294757.
%Y A294756 Rows n=0-1 give A000012.
%Y A294756 Cf. A294699.
%K A294756 nonn,tabl
%O A294756 0,6
%A A294756 _Seiichi Manyama_, Nov 08 2017