A270241 Number of partitions of n unlabeled objects of 8 colors.

1, 8, 72, 528, 3582, 22512, 134040, 760896, 4152852, 21897408, 112037852, 558049096, 2713386758, 12907891432, 60190937724, 275575683576, 1240483837374, 5496780654912, 24002417723284, 103380586347376, 439565299059250, 1846430027348704, 7667597264015436

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=8 of A075196.

Programs

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(
      d*binomial(d+7, 7), 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+7,7).