A363602 Number of partitions of n where there are k^2+1 kinds of parts k.

1, 2, 8, 24, 72, 196, 532, 1368, 3467, 8520, 20580, 48664, 113330, 259588, 586692, 1308304, 2883427, 6283192, 13551344, 28940688, 61246052, 128492516, 267388008, 552126648, 1131750735, 2303690862, 4658080756, 9358912416, 18689701580, 37106245300, 73259451208

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Formula

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

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} A092345(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, A092345, A363601.

Sequence in context: A050242 A045697 A131569 * A290904 A231200 A066973

Adjacent sequences: A363599 A363600 A363601 * A363603 A363604 A363605

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 10 2023

Extensions

Name suggested by Joerg Arndt, Jun 11 2023

Status

approved