cp's OEIS Frontend

A270239 Number of partitions of n unlabeled objects of 6 colors.

%I A270239 #8 Mar 13 2016 17:48:29
%S A270239 1,6,42,238,1260,6174,28784,128046,548832,2275372,9166311,35987028,
%T A270239 138069505,518758758,1912300908,6926911674,24688892511,86685575466,
%U A270239 300137463682,1025683381758,3462381505989,11553577667100,38134513479591,124575624677088,402986660479024
%N A270239 Number of partitions of n unlabeled objects of 6 colors.
%H A270239 Alois P. Heinz, <a href="/A270239/b270239.txt">Table of n, a(n) for n = 0..1000</a>
%F A270239 G.f.: Product_{j>=1} 1/(1-x^j)^C(j+5,5).
%p A270239 with(numtheory):
%p A270239 a:= proc(n) option remember; `if`(n=0, 1, add(add(
%p A270239       d*binomial(d+5, 5), d=divisors(j))*a(n-j), j=1..n)/n)
%p A270239     end:
%p A270239 seq(a(n), n=0..30);
%Y A270239 Column k=6 of A075196.
%K A270239 nonn
%O A270239 0,2
%A A270239 _Alois P. Heinz_, Mar 13 2016