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Number of partitions of n into parts of 20 kinds.
2

%I #23 Mar 27 2017 21:32:30

%S 1,20,230,1960,13685,82524,443870,2175800,9869990,41907380,168012824,

%T 640438680,2334121995,8171039800,27580783270,90058003200,285253928790,

%U 878572253720,2636748302650,7725084195240,22130265931900,62079251390180

%N Number of partitions of n into parts of 20 kinds.

%C a(n) is Euler transform of A010859. - _Alois P. Heinz_, Oct 17 2008

%H Seiichi Manyama, <a href="/A023018/b023018.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 G.f.: Product_{m>=1} 1/(1-x^m)^20.

%F a(0) = 1, a(n) = (20/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*20, 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]^20, {x, 0, 30}], x] (* _Indranil Ghosh_, Mar 27 2017 *)

%o (PARI) Vec(1/eta(x)^20 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017

%Y 20th column of A144064. - _Alois P. Heinz_, Oct 17 2008

%K nonn

%O 0,2

%A _David W. Wilson_