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A272497 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to seven. 2
1, 8, 108, 1200, 15510, 194832, 2749032, 39402792, 614555370, 9964468800, 172686804576, 3129181488576, 60039964804248, 1204868044448640, 25426155055055040, 560350692475352064, 12919636322380914984, 310342487192287684992, 7768115419959585662400 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 7..450

FORMULA

E.g.f.: x^7 * Product_{i=1..7} (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))(7):

seq(a(n), n=7..30);

CROSSREFS

Column k=7 of A262071.

Sequence in context: A326101 A300807 A301446 * A215129 A234571 A120975

Adjacent sequences:  A272494 A272495 A272496 * A272498 A272499 A272500

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 01 2016

STATUS

approved

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Last modified August 13 18:03 EDT 2022. Contains 356107 sequences. (Running on oeis4.)