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

1, 10, 110, 990, 8195, 62854, 455675, 3147210, 20874205, 133650330, 829656124, 5010237850, 29516429335, 170025614980, 959521900370, 5313793679524, 28919055049170, 154857622067610, 816814457097155, 4247904244224630, 21800095116980345, 110485969920692960

Offset: 0

Author

Alois P. Heinz, Mar 13 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=10 of A075196.

Programs

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(
      d*binomial(d+9, 9), d=divisors(j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..30);

Formula

G.f.: Product_{j>=1} 1/(1-x^j)^C(j+9,9).