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A270241 Number of partitions of n unlabeled objects of 8 colors.

%I A270241 #7 Mar 13 2016 17:50:57
%S A270241 1,8,72,528,3582,22512,134040,760896,4152852,21897408,112037852,
%T A270241 558049096,2713386758,12907891432,60190937724,275575683576,
%U A270241 1240483837374,5496780654912,24002417723284,103380586347376,439565299059250,1846430027348704,7667597264015436
%N A270241 Number of partitions of n unlabeled objects of 8 colors.
%H A270241 Alois P. Heinz, <a href="/A270241/b270241.txt">Table of n, a(n) for n = 0..1000</a>
%F A270241 G.f.: Product_{j>=1} 1/(1-x^j)^C(j+7,7).
%p A270241 with(numtheory):
%p A270241 a:= proc(n) option remember; `if`(n=0, 1, add(add(
%p A270241       d*binomial(d+7, 7), d=divisors(j))*a(n-j), j=1..n)/n)
%p A270241     end:
%p A270241 seq(a(n), n=0..30);
%Y A270241 Column k=8 of A075196.
%K A270241 nonn
%O A270241 0,2
%A A270241 _Alois P. Heinz_, Mar 13 2016