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%I #49 Oct 08 2017 17:38:30
%S 1,1,0,1,2,0,1,2,5,0,1,2,1,10,0,1,2,1,-2,20,0,1,2,1,4,-4,36,0,1,2,1,4,
%T 14,4,65,0,1,2,1,4,6,16,13,110,0,1,2,1,4,6,-8,10,6,185,0,1,2,1,4,6,2,
%U -6,42,-23,300,0,1,2,1,4,6,2,24,18,109,-44,481,0,1
%N Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} 1/(1 + Sum_{j=1..k} (-1)^j*j*x^(j*i))^2.
%H Seiichi Manyama, <a href="/A292577/b292577.txt">Antidiagonals n = 0..139, flattened</a>
%e Square array begins:
%e 1, 1, 1, 1, 1, ...
%e 0, 2, 2, 2, 2, ...
%e 0, 5, 1, 1, 1, ...
%e 0, 10, -2, 4, 4, ...
%e 0, 20, 4, 14, 6, ...
%e 0, 36, 13, 16, -8, ...
%Y Columns k=0..1 give A000007, A000712.
%Y Rows n=0 gives A000012.
%Y Main diagonal gives A293387.
%Y Product_{i>0} 1/(1 + Sum_{j=1..k} (-1)^j*j*x^(j*i))^m: this sequence (m=-2), A293307 (m=-1), A293305 (m=1), A293388 (m=2).
%K sign,tabl
%O 0,5
%A _Seiichi Manyama_, Oct 07 2017
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