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

0,3

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A001318, A218379, A290942.

Sequence in context: A211858 A349149 A029012 * A112192 A017841 A304329

Adjacent sequences: A095696 A095697 A095698 * A095700 A095701 A095702

Keyword

nonn

Author

Jon Perry, Jul 06 2004

Status

approved