A327508 Number of set partitions of [n] where each subset is again partitioned into seven nonempty subsets.

1, 0, 0, 0, 0, 0, 0, 1, 28, 462, 5880, 63987, 627396, 5715424, 49330996, 408921513, 3292212924, 26136933186, 211891946448, 1910903676319, 21958686224932, 338516695449108, 6257281367040396, 122152192372692405, 2369188918134769500, 44783158458575933110

Offset: 0

Author

Alois P. Heinz, Sep 14 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..496
• Wikipedia, Partition of a set

Crossrefs

Column k=7 of A324162.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
      *binomial(n-1, j-1)*Stirling2(j, 7), j=7..n))
    end:
seq(a(n), n=0..27);

PARI

a(n) = sum(k=0, n\7, (7*k)!*stirling(n, 7*k, 2)/(7!^k*k!)); \\ Seiichi Manyama, May 07 2022

Formula

E.g.f.: exp((exp(x)-1)^7/7!).

a(n) = Sum_{k=0..floor(n/7)} (7*k)! * Stirling2(n,7*k)/(7!^k * k!). - Seiichi Manyama, May 07 2022