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%I #25 Mar 27 2017 21:31:53
%S 1,15,135,920,5220,25893,115700,475065,1817910,6551390,22414314,
%T 73265580,229972855,696109950,2039031360,5796944357,16036186005,
%U 43259046975,114012183695,294067720380,743368453326,1844121021245,4494803760045
%N Number of partitions of n into parts of 15 kinds.
%C a(n) is Euler transform of A010854. - _Alois P. Heinz_, Oct 17 2008
%H Seiichi Manyama, <a href="/A023013/b023013.txt">Table of n, a(n) for n = 0..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>
%F a(0) = 1, a(n) = (15/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017
%p 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
%t CoefficientList[Series[1/QPochhammer[x]^15, {x, 0, 30}], x] (* _Indranil Ghosh_, Mar 27 2017 *)
%o (PARI) Vec(1/eta(x)^15 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017
%Y 15th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K nonn
%O 0,2
%A _David W. Wilson_
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