A363601 Number of partitions of n where there are k^2-1 kinds of parts k.

1, 0, 3, 8, 21, 48, 126, 288, 693, 1568, 3570, 7896, 17417, 37632, 80823, 171192, 359733, 747936, 1543192, 3155760, 6407037, 12909024, 25835649, 51359136, 101470854, 199264128, 389096028, 755591256, 1459643343, 2805471984, 5366161740, 10216161336, 19362398580

Offset

0,3

Links

Table of n, a(n) for n=0..32.

Formula

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

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} A092348(k) * a(n-k).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(1/prod(k=1, N, (1-x^k)^(k^2-1)))

Crossrefs

Cf. A023871, A092348, A253289, A363602.

Sequence in context: A007773 A071078 A179903 * A193045 A238831 A322059

Adjacent sequences: A363598 A363599 A363600 * A363602 A363603 A363604

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 10 2023

Extensions

Name suggested by Joerg Arndt, Jun 11 2023

Status

approved