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A272496 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to six. 2
1, 7, 84, 840, 9870, 113652, 1480248, 19699680, 286768482, 4358914560, 71096721696, 1216711960464, 22116370171896, 421629228820800, 8473857766133760, 178260053918650704, 3931319749640138856, 90499126549555707984, 2174651142277047610176, 54390059451824183287200 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..450

FORMULA

E.g.f.: x^6 * Product_{i=1..6} (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))(6):

seq(a(n), n=6..30);

CROSSREFS

Column k=6 of A262071.

Sequence in context: A053128 A027819 A269895 * A177009 A099674 A067413

Adjacent sequences:  A272493 A272494 A272495 * A272497 A272498 A272499

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 01 2016

STATUS

approved

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Last modified October 7 13:15 EDT 2022. Contains 357271 sequences. (Running on oeis4.)