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A023013 Number of partitions of n into parts of 15 kinds. 2
1, 15, 135, 920, 5220, 25893, 115700, 475065, 1817910, 6551390, 22414314, 73265580, 229972855, 696109950, 2039031360, 5796944357, 16036186005, 43259046975, 114012183695, 294067720380, 743368453326, 1844121021245, 4494803760045 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 23 12:19 EDT 2019. Contains 328345 sequences. (Running on oeis4.)