A095699 Number of partitions of n into generalized pentagonal numbers.

1, 1, 2, 2, 3, 4, 5, 7, 8, 10, 12, 14, 18, 20, 25, 29, 34, 40, 45, 53, 60, 69, 80, 89, 103, 114, 131, 147, 165, 186, 207, 232, 258, 286, 319, 352, 392, 432, 477, 525, 578, 636, 699, 765, 839, 916, 1002, 1093, 1192, 1298, 1413, 1536, 1671, 1810, 1965, 2126, 2304

Offset: 0

Author

Jon Perry, Jul 06 2004

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz)

Crossrefs

Cf. A001318, A218379, A290942.

Programs

Mathematica

nmax = 100; CoefficientList[Series[1/Product[(1-x^(k*(3*k-1)/2)) * (1-x^(k*(3*k+1)/2)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 10 2017 *)

PARI

b(n) = (3*n^2 + 2*n + (n%2) * (2*n + 1)) / 8; \\ A001318
N=66; x='x+O('x^N);
Vec(1/prod(k=1,N, (1-x^b(k))) )
\\ Joerg Arndt, Oct 13 2014

Formula

G.f.: 1/Product_{k>=1} (1-x^(k*(3*k-1)/2))*(1-x^(k*(3*k+1)/2)).