A294316 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where A(n,k) is the sum of products of terms in all partitions of k*n into powers of k.

1, 1, 1, 1, 3, 1, 1, 4, 11, 1, 1, 5, 13, 27, 1, 1, 6, 21, 49, 83, 1, 1, 7, 31, 85, 157, 195, 1, 1, 8, 43, 156, 357, 481, 515, 1, 1, 9, 57, 259, 781, 1445, 1534, 1155, 1, 1, 10, 73, 400, 1555, 3931, 5797, 4693, 2899, 1, 1, 11, 91, 585, 2801, 9331, 19681, 23205

Offset

0,5

Links

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

Example

Square array A(n,k) begins:
   1,   1,   1,    1,    1, ...
   1,   3,   4,    5,    6, ...
   1,  11,  13,   21,   31, ...
   1,  27,  49,   85,  156, ...
   1,  83, 157,  357,  781, ...
   1, 195, 481, 1445, 3931, ...

Crossrefs

Columns k=1..3 give A000012, A289842, A294298.

Rows n=0 gives A000012.

Main diagonal gives A023037.

Cf. A292477.

Sequence in context: A296006 A245397 A346792 * A294761 A167284 A016463

Adjacent sequences: A294313 A294314 A294315 * A294317 A294318 A294319

Keyword

nonn,tabl

Author

Seiichi Manyama, Oct 28 2017

Status

approved