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A294609 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*x^j)^(j^(k*j)) in powers of x.

%I A294609 #15 Nov 07 2017 08:30:51
%S A294609 1,1,1,1,1,3,1,1,9,6,1,1,33,90,14,1,1,129,2220,1154,25,1,1,513,59178,
%T A294609 264908,17427,56,1,1,2049,1594836,67176362,49163017,309117,97,1,1,
%U A294609 8193,43048770,17181595604,152662625259,13120646934,6285102,198
%N A294609 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*x^j)^(j^(k*j)) in powers of x.
%H A294609 Seiichi Manyama, <a href="/A294609/b294609.txt">Antidiagonals n = 0..52, flattened</a>
%F A294609 A(0,k) = 1 and A(n,k) = (1/n) * Sum_{j=1..n} (Sum_{d|j} d^(k*d+1+j/d)) * A(n-j,k) for n > 0.
%e A294609 Square array begins:
%e A294609     1,    1,      1,        1,           1, ...
%e A294609     1,    1,      1,        1,           1, ...
%e A294609     3,    9,     33,      129,         513, ...
%e A294609     6,   90,   2220,    59178,     1594836, ...
%e A294609    14, 1154, 264908, 67176362, 17181595604, ...
%Y A294609 Columns k=0..2 give A006906, A294610, A294611.
%Y A294609 Rows n=0-1 give A000012.
%Y A294609 Cf. A294605.
%K A294609 nonn,tabl
%O A294609 0,6
%A A294609 _Seiichi Manyama_, Nov 04 2017