A023013 Number of partitions of n into parts of 15 kinds.

1, 15, 135, 920, 5220, 25893, 115700, 475065, 1817910, 6551390, 22414314, 73265580, 229972855, 696109950, 2039031360, 5796944357, 16036186005, 43259046975, 114012183695, 294067720380, 743368453326, 1844121021245, 4494803760045

Offset

0,2

Comments

a(n) is Euler transform of A010854. - Alois P. Heinz, Oct 17 2008

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Index entries for expansions of Product_{k >= 1} (1-x^k)^m

Formula

a(0) = 1, a(n) = (15/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

Maple

with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*15, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008

Mathematica

CoefficientList[Series[1/QPochhammer[x]^15, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)

Prog

(PARI) Vec(1/eta(x)^15 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017

Crossrefs

15th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A228583 A027630 A027629 * A036217 A022643 A125378

Adjacent sequences: A023010 A023011 A023012 * A023014 A023015 A023016

Keyword

nonn

Author

David W. Wilson

Status

approved