cp's OEIS Frontend

A294585 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*x^j)^(j^k).

%I A294585 #17 Nov 04 2017 10:56:08
%S A294585 1,1,1,1,1,2,1,1,5,3,1,1,17,14,5,1,1,65,98,42,7,1,1,257,794,514,103,
%T A294585 11,1,1,1025,6818,7194,2435,289,15,1,1,4097,60074,107170,69475,12752,
%U A294585 690,22,1,1,16385,535538,1649322,2177411,715277,58849,1771,30
%N A294585 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*x^j)^(j^k).
%H A294585 Seiichi Manyama, <a href="/A294585/b294585.txt">Antidiagonals n = 0..113, flattened</a>
%F A294585 A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k+1+k*j/d)) * A(n-j,k) for n > 0.
%e A294585 Square array begins:
%e A294585    1,  1,   1,    1,      1, ...
%e A294585    1,  1,   1,    1,      1, ...
%e A294585    2,  5,  17,   65,    257, ...
%e A294585    3, 14,  98,  794,   6818, ...
%e A294585    5, 42, 514, 7194, 107170, ...
%Y A294585 Columns k=0..2 give A000041, A266941, A294586.
%Y A294585 Rows n=0-1 give A000012.
%K A294585 nonn,tabl
%O A294585 0,6
%A A294585 _Seiichi Manyama_, Nov 03 2017