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A272498 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to eight. 2
1, 9, 135, 1650, 23265, 316602, 4810806, 73880235, 1229123610, 21174714990, 388551217626, 7431930745668, 150102842702670, 3162843042018660, 69923464752835980, 1611044465380180974, 38759812951913315262, 969843174518264324850, 25246982138722170061950 (list; graph; refs; listen; history; text; internal format)
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 A034723

Adjacent sequences:  A272495 A272496 A272497 * A272499 A272500 A272501

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 01 2016

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)