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A270242 Number of partitions of n unlabeled objects of 9 colors.

%I A270242 #4 Mar 13 2016 17:56:10
%S A270242 1,9,90,735,5535,38619,254949,1604007,9696150,56601345,320465367,
%T A270242 1765647477,9492925152,49918029894,257225030010,1301005101360,
%U A270242 6467982571350,31645832177880,152542319368640,725110153435170,3401929848645540,15764621508983883,72206209735787754
%N A270242 Number of partitions of n unlabeled objects of 9 colors.
%H A270242 Alois P. Heinz, <a href="/A270242/b270242.txt">Table of n, a(n) for n = 0..1000</a>
%F A270242 G.f.: Product_{j>=1} 1/(1-x^j)^C(j+8,8).
%p A270242 with(numtheory):
%p A270242 a:= proc(n) option remember; `if`(n=0, 1, add(add(
%p A270242       d*binomial(d+8, 8), d=divisors(j))*a(n-j), j=1..n)/n)
%p A270242     end:
%p A270242 seq(a(n), n=0..30);
%Y A270242 Column k=9 of A075196.
%K A270242 nonn
%O A270242 0,2
%A A270242 _Alois P. Heinz_, Mar 13 2016