A303939 Number of partitions of n into at most 2 copies of 1, 3 copies of 2, 4 copies of 3, ... .

1, 1, 2, 2, 4, 5, 8, 10, 14, 18, 25, 32, 43, 54, 71, 88, 114, 141, 180, 221, 278, 340, 423, 515, 634, 768, 938, 1131, 1372, 1646, 1985, 2371, 2844, 3383, 4037, 4783, 5682, 6709, 7936, 9339, 11004, 12908, 15155, 17724, 20740, 24186, 28214, 32812, 38165, 44271, 51354

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Seiichi Manyama)

Formula

G.f.: Product_{k>=1} (1-x^(k*(k+2)))/(1-x^k).

Example

a(5) = 5 because we have [5], [4,1], [3,2], [3,1,1] and [2,2,1].

Crossrefs

Column k=2 of A303940.

Sequence in context: A367411 A367684 A035946 * A326446 A323530 A271593

Adjacent sequences: A303936 A303937 A303938 * A303940 A303941 A303942

Keyword

nonn

Author

Seiichi Manyama, May 03 2018

Status

approved