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

1, 9, 90, 735, 5535, 38619, 254949, 1604007, 9696150, 56601345, 320465367, 1765647477, 9492925152, 49918029894, 257225030010, 1301005101360, 6467982571350, 31645832177880, 152542319368640, 725110153435170, 3401929848645540, 15764621508983883, 72206209735787754

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=9 of A075196.

Programs

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(
      d*binomial(d+8, 8), 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+8,8).