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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 + Sum_{j=1..k} (-1)^j*j*x^(j*i))^2.
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%I #17 Oct 09 2017 10:15:16

%S 1,1,0,1,-2,0,1,-2,-1,0,1,-2,3,2,0,1,-2,3,-2,1,0,1,-2,3,-8,1,2,0,1,-2,

%T 3,-8,7,-6,-2,0,1,-2,3,-8,15,-6,14,0,0,1,-2,3,-8,15,-14,17,-20,-2,0,1,

%U -2,3,-8,15,-24,17,-14,22,-2,0,1,-2,3,-8,15,-24,27

%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 + Sum_{j=1..k} (-1)^j*j*x^(j*i))^2.

%H Seiichi Manyama, <a href="/A293388/b293388.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, -2, -8, -8, ...

%e 0, 1, 1, 7, 15, ...

%e 0, 2, -6, -6, -14, ...

%Y Columns k=0..1 give A000007, A002107.

%Y Rows n=0 gives A000012.

%Y Main diagonal gives A293389.

%Y Product_{i>0} 1/(1 + Sum_{j=1..k} (-1)^j*j*x^(j*i))^m: A292577 (m=-2), A293307 (m=-1), A293305 (m=1), this sequence (m=2).

%K sign,tabl

%O 0,5

%A _Seiichi Manyama_, Oct 07 2017