A270239 Number of partitions of n unlabeled objects of 6 colors.

1, 6, 42, 238, 1260, 6174, 28784, 128046, 548832, 2275372, 9166311, 35987028, 138069505, 518758758, 1912300908, 6926911674, 24688892511, 86685575466, 300137463682, 1025683381758, 3462381505989, 11553577667100, 38134513479591, 124575624677088, 402986660479024

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=6 of A075196.

Programs

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(
      d*binomial(d+5, 5), 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+5,5).