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A270243 Number of partitions of n unlabeled objects of 10 colors.

%I A270243 #4 Mar 13 2016 17:59:55
%S A270243 1,10,110,990,8195,62854,455675,3147210,20874205,133650330,829656124,
%T A270243 5010237850,29516429335,170025614980,959521900370,5313793679524,
%U A270243 28919055049170,154857622067610,816814457097155,4247904244224630,21800095116980345,110485969920692960
%N A270243 Number of partitions of n unlabeled objects of 10 colors.
%H A270243 Alois P. Heinz, <a href="/A270243/b270243.txt">Table of n, a(n) for n = 0..1000</a>
%F A270243 G.f.: Product_{j>=1} 1/(1-x^j)^C(j+9,9).
%p A270243 with(numtheory):
%p A270243 a:= proc(n) option remember; `if`(n=0, 1, add(add(
%p A270243       d*binomial(d+9, 9), d=divisors(j))*a(n-j), j=1..n)/n)
%p A270243     end:
%p A270243 seq(a(n), n=0..30);
%Y A270243 Column k=10 of A075196.
%K A270243 nonn
%O A270243 0,2
%A A270243 _Alois P. Heinz_, Mar 13 2016