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A270240 Number of partitions of n unlabeled objects of 7 colors.

%I A270240 #7 Mar 13 2016 17:50:08
%S A270240 1,7,56,364,2198,12292,65240,330262,1608866,7575967,34636896,
%T A270240 154235319,670752411,2855122319,11917598512,48858820584,197008297955,
%U A270240 782223365518,3061514606822,11822306812232,45080137355687,169865159676365,632916329409504,2333298558227399
%N A270240 Number of partitions of n unlabeled objects of 7 colors.
%H A270240 Alois P. Heinz, <a href="/A270240/b270240.txt">Table of n, a(n) for n = 0..1000</a>
%F A270240 G.f.: Product_{j>=1} 1/(1-x^j)^C(j+6,6).
%p A270240 with(numtheory):
%p A270240 a:= proc(n) option remember; `if`(n=0, 1, add(add(
%p A270240       d*binomial(d+6, 6), d=divisors(j))*a(n-j), j=1..n)/n)
%p A270240     end:
%p A270240 seq(a(n), n=0..30);
%Y A270240 Column k=7 of A075196.
%K A270240 nonn
%O A270240 0,2
%A A270240 _Alois P. Heinz_, Mar 13 2016