A327510 Number of set partitions of [n] where each subset is again partitioned into nine nonempty subsets.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 45, 1155, 22275, 359502, 5135130, 67128490, 820784250, 9528822303, 106175420065, 1144618783815, 12011663703975, 123297356170054, 1243260840764910, 12377559175117290, 122870882863640450, 1247553197735599755, 13803307806688911225

Offset

0,11

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Wikipedia, Partition of a set

Formula

E.g.f.: exp((exp(x)-1)^9/9!).

a(n) = Sum_{k=0..floor(n/9)} (9*k)! * Stirling2(n,9*k)/(9!^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, 9), j=9..n))
    end:
seq(a(n), n=0..27);

Prog

(PARI) a(n) = sum(k=0, n\9, (9*k)!*stirling(n, 9*k, 2)/(9!^k*k!)); \\ Seiichi Manyama, May 07 2022

Crossrefs

Column k=9 of A324162.

Sequence in context: A140346 A268870 A049447 * A215769 A320822 A229796

Adjacent sequences: A327507 A327508 A327509 * A327511 A327512 A327513

Keyword

nonn

Author

Alois P. Heinz, Sep 14 2019

Status

approved