A393593 Number of partitions of n into distinct parts (or odd parts) with n+1 types of each part.

1, 2, 6, 24, 95, 384, 1589, 6656, 28125, 119700, 512369, 2203368, 9511944, 41197422, 178930605, 779022208, 3398860779, 14856839874, 65048680364, 285228791880, 1252351944165, 5505315501136, 24227747380447, 106727749011456, 470585836105275, 2076661051433358

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = [x^n] Product_{k>=1} (1 + x^k)^(n+1) = A286335(n,n+1).

a(n) ~ A366018 * A270914^n / sqrt(n). - Vaclav Kotesovec, Mar 02 2026

Crossrefs

Cf. A181315, A270913, A286335.

Cf. A270914, A366018.

Sequence in context: A361752 A376810 A115220 * A293185 A292984 A072854

Adjacent sequences: A393590 A393591 A393592 * A393594 A393595 A393596

Keyword

nonn

Author

Seiichi Manyama, Feb 23 2026

Status

approved