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Number of partitions of n unlabeled objects of 6 colors.
2

%I #8 Mar 13 2016 17:48:29

%S 1,6,42,238,1260,6174,28784,128046,548832,2275372,9166311,35987028,

%T 138069505,518758758,1912300908,6926911674,24688892511,86685575466,

%U 300137463682,1025683381758,3462381505989,11553577667100,38134513479591,124575624677088,402986660479024

%N Number of partitions of n unlabeled objects of 6 colors.

%H Alois P. Heinz, <a href="/A270239/b270239.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{j>=1} 1/(1-x^j)^C(j+5,5).

%p with(numtheory):

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

%p d*binomial(d+5, 5), d=divisors(j))*a(n-j), j=1..n)/n)

%p end:

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

%Y Column k=6 of A075196.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Mar 13 2016