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Number of partitions of n unlabeled objects of 7 colors.
2

%I #7 Mar 13 2016 17:50:08

%S 1,7,56,364,2198,12292,65240,330262,1608866,7575967,34636896,

%T 154235319,670752411,2855122319,11917598512,48858820584,197008297955,

%U 782223365518,3061514606822,11822306812232,45080137355687,169865159676365,632916329409504,2333298558227399

%N Number of partitions of n unlabeled objects of 7 colors.

%H Alois P. Heinz, <a href="/A270240/b270240.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{j>=1} 1/(1-x^j)^C(j+6,6).

%p with(numtheory):

%p a:= proc(n) option remember; `if`(n=0, 1, add(add(

%p d*binomial(d+6, 6), d=divisors(j))*a(n-j), j=1..n)/n)

%p end:

%p seq(a(n), n=0..30);

%Y Column k=7 of A075196.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Mar 13 2016