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%I #17 Oct 09 2017 00:02:22
%S 1,1,0,1,-2,0,1,-2,1,0,1,-2,-3,-2,0,1,-2,-3,10,4,0,1,-2,-3,4,-4,-4,0,
%T 1,-2,-3,4,14,-20,5,0,1,-2,-3,4,6,-8,41,-6,0,1,-2,-3,4,6,16,-46,2,9,0,
%U 1,-2,-3,4,6,6,-30,14,-111,-12,0,1,-2,-3,4,6,6,0,-58
%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} j*x^(j*i))^2.
%H Seiichi Manyama, <a href="/A293386/b293386.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, 1, -3, -3, -3, ...
%e 0, -2, 10, 4, 4, ...
%e 0, 4, -4, 14, 6, ...
%e 0, -4, -20, -8, 16, ...
%Y Columns k=0..1 give A000007, A022597.
%Y Rows n=0 gives A000012.
%Y Main diagonal gives A252650.
%Y Product_{i>0} (1 + Sum_{j=1..k} j*x^(j*i))^m: this sequence (m=-2), A290217 (m=-1), A290216 (m=1), A293377 (m=2).
%K sign,tabl
%O 0,5
%A _Seiichi Manyama_, Oct 07 2017
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