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A095699 Number of partitions of n into generalized pentagonal numbers. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A325512 A211858 A029012 * A112192 A017841 A304329

Adjacent sequences:  A095696 A095697 A095698 * A095700 A095701 A095702

KEYWORD

nonn

AUTHOR

Jon Perry, Jul 06 2004

STATUS

approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)