A272497 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to seven.

1, 8, 108, 1200, 15510, 194832, 2749032, 39402792, 614555370, 9964468800, 172686804576, 3129181488576, 60039964804248, 1204868044448640, 25426155055055040, 560350692475352064, 12919636322380914984, 310342487192287684992, 7768115419959585662400

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: A300807 A301446 A363476 * A215129 A234571 A120975

Adjacent sequences: A272494 A272495 A272496 * A272498 A272499 A272500

Keyword

nonn

Author

Alois P. Heinz, May 01 2016

Status

approved