A286950 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 - x^j)/(1 - x^(k*j))^k.

1, 1, -1, 1, 0, -1, 1, -1, 0, 0, 1, -1, 1, 0, 0, 1, -1, -1, -2, 0, 1, 1, -1, -1, 3, 3, 0, 0, 1, -1, -1, 0, -3, -4, 0, 1, 1, -1, -1, 0, 4, -2, 5, 0, 0, 1, -1, -1, 0, 0, -3, 9, -7, 0, 0, 1, -1, -1, 0, 0, 6, -4, -8, 10, 0, 0, 1, -1, -1, 0, 0, 1, -5, 1, -6, -13, 0, 0, 1

Offset

0,19

Links

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

Formula

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

Example

Square array begins:
   1, 1,  1,  1,  1, ...
  -1, 0, -1, -1, -1, ...
  -1, 0,  1, -1, -1, ...
   0, 0, -2,  3,  0, ...
   0, 0,  3, -3,  4, ...

Crossrefs

Columns k=0-4 give: A010815, A000007, A106507, A286952, A286953.

Diagonal gives A286956.

Cf. A175595.

Sequence in context: A219055 A025902 A219923 * A210638 A272903 A321458

Adjacent sequences: A286947 A286948 A286949 * A286951 A286952 A286953

Keyword

sign,tabl

Author

Seiichi Manyama, May 17 2017

Status

approved