A276554 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)^(j*k) in powers of x.

1, 1, 0, 1, -1, 0, 1, -2, -2, 0, 1, -3, -3, -1, 0, 1, -4, -3, 2, 0, 0, 1, -5, -2, 8, 6, 4, 0, 1, -6, 0, 16, 12, 12, 4, 0, 1, -7, 3, 25, 13, 9, 1, 7, 0, 1, -8, 7, 34, 5, -12, -29, -10, 3, 0, 1, -9, 12, 42, -15, -51, -78, -54, -32, -2, 0, 1, -10, 18, 48, -49, -102

Offset

0,8

Links

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

Formula

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

Example

Square array begins:
   1,  1,  1,  1,  1, ...
   0, -1, -2, -3, -4, ...
   0, -2, -3, -3, -2, ...
   0, -1,  2,  8, 16, ...
   0,  0,  6, 12, 13, ...

Crossrefs

Columns k=0-5 give: A000007, A073592, A276551, A276552, A316463, A316464.

Main diagonal gives A281267.

Antidiagonal sums give A299211.

Cf. A255961, A277938.

Sequence in context: A362686 A104245 A185287 * A297323 A257654 A167637

Adjacent sequences: A276551 A276552 A276553 * A276555 A276556 A276557

Keyword

sign,tabl

Author

Seiichi Manyama, Apr 10 2017

Status

approved