A272496 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to six.

1, 7, 84, 840, 9870, 113652, 1480248, 19699680, 286768482, 4358914560, 71096721696, 1216711960464, 22116370171896, 421629228820800, 8473857766133760, 178260053918650704, 3931319749640138856, 90499126549555707984, 2174651142277047610176, 54390059451824183287200

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