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

Author

Alois P. Heinz, Sep 02 2019

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..345
• Wikipedia, Partition of a set

Crossrefs

Cf. A007820, A088218, A324162.

Programs

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 *)

PARI

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

Formula

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

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