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%I #21 Mar 27 2017 21:31:29
%S 1,13,104,637,3276,14820,60697,229372,810654,2706366,8600501,26173966,
%T 76654656,216903064,594973106,1586553501,4122693185,10461067253,
%U 25967050382,63154957281,150708128116,353304272945,814564136529,1848834255034,4134822087942
%N Number of partitions of n into parts of 13 kinds.
%C a(n) is Euler transform of A010852. - _Alois P. Heinz_, Oct 17 2008
%H Alois P. Heinz, <a href="/A023011/b023011.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(0) = 1, a(n) = (13/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*13, 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]^13, {x, 0, 30}], x] (* _Indranil Ghosh_, Mar 27 2017 *)
%o (PARI) Vec(1/eta(x)^13 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017
%Y Cf. 13th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K nonn
%O 0,2
%A _David W. Wilson_
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