A292577 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.

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, 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, -6, 42, -23, 300, 0, 1, 2, 1, 4, 6, 2, 24, 18, 109, -44, 481, 0, 1

Offset

0,5

Links

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

Example

Square array begins:
   1,  1,  1,  1,  1, ...
   0,  2,  2,  2,  2, ...
   0,  5,  1,  1,  1, ...
   0, 10, -2,  4,  4, ...
   0, 20,  4, 14,  6, ...
   0, 36, 13, 16, -8, ...

Crossrefs

Columns k=0..1 give A000007, A000712.

Rows n=0 gives A000012.

Main diagonal gives A293387.

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).

Sequence in context: A025247 A341439 A127767 * A055509 A334226 A006667

Adjacent sequences: A292574 A292575 A292576 * A292578 A292579 A292580

Keyword

sign,tabl

Author

Seiichi Manyama, Oct 07 2017

Status

approved