A363600 Number of partitions of n into distinct parts where there are k^2+1 kinds of part k.

1, 2, 6, 20, 52, 140, 356, 880, 2123, 5016, 11610, 26400, 59130, 130476, 284216, 611592, 1301344, 2740194, 5713930, 11806144, 24184908, 49142504, 99091244, 198360536, 394342884, 778818658, 1528531702, 2982017956, 5784365082, 11158728448, 21413292868

Offset

0,2

Links

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

Formula

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

a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d) * d * (d^2+1) ) * a(n-k).

Prog

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

Crossrefs

Cf. A027998, A219555, A255834, A363599.

Cf. A363602.

Sequence in context: A320910 A066397 A060344 * A347582 A045655 A303307

Adjacent sequences: A363597 A363598 A363599 * A363601 A363602 A363603

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 10 2023

Extensions

Name suggested by Joerg Arndt, Jun 11 2023

Status

approved