A293388 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.

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

Offset: 0

Author

Seiichi Manyama, Oct 07 2017

Keywords

• sign
• tabl

Examples

			Square array begins:
   1,  1,  1,  1,   1, ...
   0, -2, -2, -2,  -2, ...
   0, -1,  3,  3,   3, ...
   0,  2, -2, -8,  -8, ...
   0,  1,  1,  7,  15, ...
   0,  2, -6, -6, -14, ...
		

Links

• Seiichi Manyama, Antidiagonals n = 0..139, flattened

Crossrefs

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

Rows n=0 gives A000012.

Main diagonal gives A293389.

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).