The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
Sequence in context: A211858 A349149 A029012 * A112192 A017841 A304329
KEYWORD
nonn
AUTHOR
Jon Perry, Jul 06 2004
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 23 17:39 EDT 2024. Contains 372765 sequences. (Running on oeis4.)