login
Number of partitions of n unlabeled objects of 8 colors.
2

%I #7 Mar 13 2016 17:50:57

%S 1,8,72,528,3582,22512,134040,760896,4152852,21897408,112037852,

%T 558049096,2713386758,12907891432,60190937724,275575683576,

%U 1240483837374,5496780654912,24002417723284,103380586347376,439565299059250,1846430027348704,7667597264015436

%N Number of partitions of n unlabeled objects of 8 colors.

%H Alois P. Heinz, <a href="/A270241/b270241.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{j>=1} 1/(1-x^j)^C(j+7,7).

%p with(numtheory):

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

%p d*binomial(d+7, 7), d=divisors(j))*a(n-j), j=1..n)/n)

%p end:

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

%Y Column k=8 of A075196.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Mar 13 2016