A327509 Number of set partitions of [n] where each subset is again partitioned into eight nonempty subsets.

1, 0, 0, 0, 0, 0, 0, 0, 1, 36, 750, 11880, 159027, 1899612, 20912320, 216627840, 2141770488, 20416870188, 189100389270, 1713143123640, 15314761051669, 137723007972924, 1310008783707360, 14647748873844240, 215375952901752225, 4079250159907459680

Offset: 0

Author

Alois P. Heinz, Sep 14 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..498
• Wikipedia, Partition of a set

Crossrefs

Column k=8 of A324162.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
      *binomial(n-1, j-1)*Stirling2(j, 8), j=8..n))
    end:
seq(a(n), n=0..27);

PARI

a(n) = sum(k=0, n\8, (8*k)!*stirling(n, 8*k, 2)/(8!^k*k!)); \\ Seiichi Manyama, May 07 2022

Formula

E.g.f.: exp((exp(x)-1)^8/8!).

a(n) = Sum_{k=0..floor(n/8)} (8*k)! * Stirling2(n,8*k)/(8!^k * k!). - Seiichi Manyama, May 07 2022