A284993 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1+x^j)^(j^k) in powers of x.

1, 1, -1, 1, -1, 0, 1, -1, -1, -1, 1, -1, -3, -2, 1, 1, -1, -7, -6, 1, -1, 1, -1, -15, -20, 0, 0, 1, 1, -1, -31, -66, -8, 11, 4, -1, 1, -1, -63, -212, -54, 99, 42, 2, 2, 1, -1, -127, -666, -284, 725, 455, 63, 8, -2, 1, -1, -255, -2060, -1350, 4935, 4580, 958, 73

Offset

0,13

Links

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

Formula

G.f. of column k: Product_{j>=1} 1/(1+x^j)^(j^k).

Example

Square array begins:
   1,  1,  1,   1,   1,    1, ...
  -1, -1, -1,  -1,  -1,   -1, ...
   0, -1, -3,  -7, -15,  -31, ...
  -1, -2, -6, -20, -66, -212, ...
   1,  1,  0,  -8, -54, -284, ...

Crossrefs

Columns k=0-5 give A081362, A255528, A284896, A284897, A284898, A284899.

Cf. A144048, A284992.

Sequence in context: A348177 A027082 A140736 * A292068 A350942 A140056

Adjacent sequences: A284990 A284991 A284992 * A284994 A284995 A284996

Keyword

sign,tabl

Author

Seiichi Manyama, Apr 07 2017

Status

approved