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

8,2

Links

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

Formula

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

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);

Crossrefs

Column k=8 of A262071.

Sequence in context: A167893 A268062 A218326 * A254282 A235339 A306848

Adjacent sequences: A272495 A272496 A272497 * A272499 A272500 A272501

Keyword

nonn

Author

Alois P. Heinz, May 01 2016

Status

approved