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A294950 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 in powers of x.

%I A294950 #19 Nov 18 2017 04:21:46
%S A294950 1,1,1,1,1,3,1,1,9,6,1,1,33,90,13,1,1,129,2220,1162,24,1,1,513,59178,
%T A294950 265132,17435,48,1,1,2049,1594836,67180330,49163241,310193,86,1,1,
%U A294950 8193,43048770,17181660628,152662629227,13121450895,6286826,160
%N A294950 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 in powers of x.
%H A294950 Seiichi Manyama, <a href="/A294950/b294950.txt">Antidiagonals n = 0..52, flattened</a>
%F A294950 A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(2+k*j)) * A(n-j,k) for n > 0.
%e A294950 Square array begins:
%e A294950     1,     1,        1,            1,               1, ...
%e A294950     1,     1,        1,            1,               1, ...
%e A294950     3,     9,       33,          129,             513, ...
%e A294950     6,    90,     2220,        59178,         1594836, ...
%e A294950    13,  1162,   265132,     67180330,     17181660628, ...
%e A294950    24, 17435, 49163241, 152662629227, 476855156157129, ...
%Y A294950 Columns k=0..2 give A000219, A294813, A294954.
%Y A294950 Rows n=0+1, 2 give A000012, A087289.
%Y A294950 Cf. A294609, A294758, A294808.
%K A294950 nonn,tabl
%O A294950 0,6
%A A294950 _Seiichi Manyama_, Nov 12 2017