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

0,9

Links

Alois P. Heinz, Table of n, a(n) for n = 0..496

Wikipedia, Partition of a set

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

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);

Prog

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

Crossrefs

Column k=7 of A324162.

Sequence in context: A022752 A387281 A000771 * A215767 A079518 A320820

Adjacent sequences: A327505 A327506 A327507 * A327509 A327510 A327511

Keyword

nonn

Author

Alois P. Heinz, Sep 14 2019

Status

approved