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A294605 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-j*x^j)^(j^(k*j)) in powers of x.

%I A294605 #17 Nov 07 2017 11:09:18
%S A294605 1,1,-1,1,-1,-2,1,-1,-8,-1,1,-1,-32,-73,-1,1,-1,-128,-2155,-919,5,1,
%T A294605 -1,-512,-58921,-259477,-13977,1,1,-1,-2048,-1593811,-67041751,
%U A294605 -48496477,-253640,13,1,-1,-8192,-43044673,-17178144301,-152513231553,-13001163543,-5290184,4
%N A294605 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1-j*x^j)^(j^(k*j)) in powers of x.
%H A294605 Seiichi Manyama, <a href="/A294605/b294605.txt">Antidiagonals n = 0..52, flattened</a>
%F A294605 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 A294605 Square array begins:
%e A294605     1,    1,       1,         1,            1, ...
%e A294605    -1,   -1,      -1,        -1,           -1, ...
%e A294605    -2,   -8,     -32,      -128,         -512, ...
%e A294605    -1,  -73,   -2155,    -58921,     -1593811, ...
%e A294605    -1, -919, -259477, -67041751, -17178144301, ...
%Y A294605 Columns k=0..2 give A022661, A294606, A294607.
%Y A294605 Rows n=0..1 give A000012, (-1)*A000012.
%Y A294605 Cf. A283675, A294609.
%K A294605 sign,tabl
%O A294605 0,6
%A A294605 _Seiichi Manyama_, Nov 04 2017