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

0,10

Links

Alois P. Heinz, Table of n, a(n) for n = 0..498

Wikipedia, Partition of a set

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

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);

Prog

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

Crossrefs

Column k=8 of A324162.

Sequence in context: A004329 A089909 A049434 * A215768 A320821 A144941

Adjacent sequences: A327506 A327507 A327508 * A327510 A327511 A327512

Keyword

nonn

Author

Alois P. Heinz, Sep 14 2019

Status

approved