A324241 Number of set partitions of [2n] where each subset is again partitioned into n nonempty subsets.

1, 2, 10, 100, 1736, 42651, 1324114, 49330996, 2141770488, 106175420065, 5917585057033, 366282501223002, 24930204592110338, 1850568574258750360, 148782988064395367700, 12879868072770703598760, 1194461517469808134322280, 118144018577011379763287565

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..345

Wikipedia, Partition of a set

Formula

a(n) = A324162(2n,n).

a(n) = A007820(n) + A088218(n) for n > 0. - Seiichi Manyama, May 08 2022

Example

a(2) = 10: 123/4, 124/3, 12/34, 134/2, 13/24, 14/23, 1/234, 1/2|3/4, 1/3|2/4, 1/4|2/3.

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(b(n-j, k)
      *binomial(n-1, j-1)*Stirling2(j, k), j=k..n))
    end:
a:= n-> b(2*n, n):
seq(a(n), n=0..18);

Mathematica

b[n_, k_] := b[n, k] = If[n == 0, 1, If[k == 0 || k > n, 0, Sum[b[n-j, k]* Binomial[n - 1, j - 1] StirlingS2[j, k], {j, k, n}]]];
a[n_] := b[2n, n];
a /@ Range[0, 18] (* Jean-François Alcover, May 05 2020, after Maple *)

Prog

(PARI) a(n) = if(n==0, 1, stirling(2*n, n, 2)+binomial(2*n, n)/2); \\ Seiichi Manyama, May 08 2022

Crossrefs

Cf. A007820, A088218, A324162.

Sequence in context: A338193 A063959 A101686 * A188193 A228120 A377919

Adjacent sequences: A324238 A324239 A324240 * A324242 A324243 A324244

Keyword

nonn

Author

Alois P. Heinz, Sep 02 2019

Status

approved