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