%I #24 Mar 27 2017 21:32:23
%S 1,19,209,1710,11495,66880,347681,1649637,7252300,29875505,116319938,
%T 430976031,1527928814,5206792965,17119704425,54484060983,168297474675,
%U 505762373795,1481733152790,4239676354650,11866652524496,32536693623850
%N Number of partitions of n into parts of 19 kinds.
%C a(n) is Euler transform of A010858. - _Alois P. Heinz_, Oct 17 2008
%H Seiichi Manyama, <a href="/A023017/b023017.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) = (19/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*19, 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]^19, {x, 0, 30}], x] (* _Indranil Ghosh_, Mar 27 2017 *)
%o (PARI) Vec(1/eta(x)^19 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017
%Y 19th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K nonn
%O 0,2
%A _David W. Wilson_