A272498 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to eight.

1, 9, 135, 1650, 23265, 316602, 4810806, 73880235, 1229123610, 21174714990, 388551217626, 7431930745668, 150102842702670, 3162843042018660, 69923464752835980, 1611044465380180974, 38759812951913315262, 969843174518264324850, 25246982138722170061950

Offset: 8

Author

Alois P. Heinz, May 01 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..450

Crossrefs

Column k=8 of A262071.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
       b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
    end:
a:= n-> (k-> b(n, k) -b(n, k-1))(8):
seq(a(n), n=8..30);

Formula

E.g.f.: x^8 * Product_{i=1..8} (i-1)!/(i!-x^i).