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%I #30 Nov 03 2017 19:18:43
%S 1,1,-1,1,-1,-2,1,-1,-4,-1,1,-1,-8,-5,0,1,-1,-16,-19,-3,4,1,-1,-32,
%T -65,-21,23,4,1,-1,-64,-211,-111,139,44,7,1,-1,-128,-665,-525,863,448,
%U 104,3,1,-1,-256,-2059,-2343,5419,4316,1414,70,-2,1,-1,-512,-6305,-10101,34103,40024,18164,1206,-93,-9
%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^k*x^j)^j.
%H Seiichi Manyama, <a href="/A294580/b294580.txt">Antidiagonals n = 0..139, flattened</a>
%F A(0,k) = 1 and A(n,k) = -(1/n) * Sum_{j=1..n} (Sum_{d|j} d^(2+k*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, -4, -8, -16, -32, ...
%e -1, -5, -19, -65, -211, ...
%e 0, -3, -21, -111, -525, ...
%Y Columns k=0..2 give A073592, A266964, A294581.
%Y Rows n=0..3 give A000012, (-1)*A000012, (-1)*A000079(n+1), (-1)*A001047(n+1).
%Y Cf. A292166, A294582.
%K sign,tabl,look
%O 0,6
%A _Seiichi Manyama_, Nov 02 2017
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