A277938 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, 5, 5, 0, 1, 4, 9, 14, 8, 0, 1, 5, 14, 28, 30, 16, 0, 1, 6, 20, 48, 72, 68, 28, 0, 1, 7, 27, 75, 141, 183, 145, 49, 0, 1, 8, 35, 110, 245, 396, 443, 298, 83, 0, 1, 9, 44, 154, 393, 751, 1058, 1026, 600, 142, 0, 1, 10, 54, 208

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,  5,  9,  14, ...
   0, 5, 14, 28,  48, ...
   0, 8, 30, 72, 141, ...

Crossrefs

Columns k=0-4 give: A000007, A026007, A026011, A027346, A027906.

Rows n=0-3 give: A000012, A001477, A000096, A005586.

Main diagonal gives A270922.

Antidiagonal sums give A299167.

Cf. A276554, A279928.

Sequence in context: A172236 A191646 A297321 * A130020 A292870 A378291

Adjacent sequences: A277935 A277936 A277937 * A277939 A277940 A277941

Keyword

nonn,tabl

Author

Seiichi Manyama, Apr 11 2017

Status

approved