A270240 Number of partitions of n unlabeled objects of 7 colors.

1, 7, 56, 364, 2198, 12292, 65240, 330262, 1608866, 7575967, 34636896, 154235319, 670752411, 2855122319, 11917598512, 48858820584, 197008297955, 782223365518, 3061514606822, 11822306812232, 45080137355687, 169865159676365, 632916329409504, 2333298558227399

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=7 of A075196.

Programs

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(
      d*binomial(d+6, 6), 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+6,6).