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%I #28 Feb 06 2018 09:07:23
%S 1,10,65,330,1430,5512,19415,63570,195910,573430,1605340,4322110,
%T 11240645,28341730,69488650,166096270,387890625,886698670,1987322415,
%U 4373271870,9461022285,20144164040,42254620785,87398226990,178396331100,359618772656,716409453320
%N Number of partitions of n into parts of 10 kinds.
%C a(n) is Euler transform of A010692. - _Alois P. Heinz_, Oct 17 2008
%H Seiichi Manyama, <a href="/A023009/b023009.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Alois P. Heinz)
%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 G.f.: Product_{m>=1} 1/(1-x^m)^10.
%F a(n) ~ 5^(11/4) * exp(2 * Pi * sqrt(5*n/3)) / (64 * 3^(11/4) * n^(13/4)). - _Vaclav Kotesovec_, Feb 28 2015
%F a(0) = 1, a(n) = (10/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017
%F G.f.: exp(10*Sum_{k>=1} x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 06 2018
%p with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*10, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # _Alois P. Heinz_, Oct 17 2008
%t nmax=50; CoefficientList[Series[Product[1/(1-x^k)^10,{k,1,nmax}],{x,0,nmax}],x] (* _Vaclav Kotesovec_, Feb 28 2015 *)
%Y Cf. 10th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K nonn
%O 0,2
%A _David W. Wilson_