A327507 Number of set partitions of [n] where each subset is again partitioned into six nonempty subsets.

1, 0, 0, 0, 0, 0, 1, 21, 266, 2646, 22827, 179487, 1324114, 9357348, 64991927, 469882413, 4008715074, 46160063586, 691114045987, 11535301966755, 194240576089826, 3186376950695400, 50592286213334943, 780299037934036929, 11788245937182037114

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..494

Wikipedia, Partition of a set

Formula

E.g.f.: exp((exp(x)-1)^6/6!).

a(n) = Sum_{k=0..floor(n/6)} (6*k)! * Stirling2(n,6*k)/(6!^k * k!). - Seiichi Manyama, May 07 2022

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
      *binomial(n-1, j-1)*Stirling2(j, 6), j=6..n))
    end:
seq(a(n), n=0..27);

Prog

(PARI) a(n) = sum(k=0, n\6, (6*k)!*stirling(n, 6*k, 2)/(6!^k*k!)); \\ Seiichi Manyama, May 07 2022

Crossrefs

Column k=6 of A324162.

Sequence in context: A133717 A056282 A000770 * A133105 A215766 A320819

Adjacent sequences: A327504 A327505 A327506 * A327508 A327509 A327510

Keyword

nonn

Author

Alois P. Heinz, Sep 14 2019

Status

approved