A286352 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)^k.

1, 1, 0, 1, -1, 0, 1, -2, 0, 0, 1, -3, 1, -1, 0, 1, -4, 3, -2, 1, 0, 1, -5, 6, -4, 4, -1, 0, 1, -6, 10, -8, 9, -4, 1, 0, 1, -7, 15, -15, 17, -12, 5, -1, 0, 1, -8, 21, -26, 30, -28, 15, -6, 2, 0, 1, -9, 28, -42, 51, -56, 38, -21, 9, -2, 0, 1, -10, 36, -64, 84

Offset

0,8

Links

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

Formula

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

Example

Square array begins:
   1,  1,  1,  1,  1,   1, ...
   0, -1, -2, -3, -4,  -5, ...
   0,  0,  1,  3,  6,  10, ...
   0, -1, -2, -4, -8, -15, ...
   0,  1,  4,  9, 17,  30, ...

Crossrefs

Columns k=0-32 give: A000007, A081362, A022597-A022627.

Main diagonal gives A255526.

Antidiagonal sums give A299208.

Cf. A286335.

Sequence in context: A291678 A286180 A291701 * A332898 A175045 A292377

Adjacent sequences: A286349 A286350 A286351 * A286353 A286354 A286355

Keyword

sign,tabl

Author

Seiichi Manyama, May 08 2017

Status

approved