A328156 Number of set partitions of [2n] with distinct block sizes and one of the block sizes is n.

1, 0, 0, 60, 280, 3780, 74844, 576576, 6949800, 110416020, 3319141540, 31333878576, 545777101324, 8349081650000, 196469122903200, 8108831645948160, 99934219113287400, 1961077012271694900, 39215221761564594900, 860948656518718429200, 25274389422461123124180

Offset: 0

Author

Alois P. Heinz, Oct 05 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..510
• Wikipedia, Partition of a set

Crossrefs

Cf. A266518, A276961, A327869.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(i*(i+1)/2 (2*n)!*(b(2*n$2, 0)-`if`(n=0, 0, b(2*n$2, n))):
seq(a(n), n=0..22);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[i (i + 1)/2 < n, 0, If[n == 0, 1, If[i < 2, 0, b[n, i - 1, If[i == k, 0, k]]] + If[i == k, 0, b[n - i, Min[n - i, i - 1], k]/i!]]];
a[n_] := (2n)! (b[2n, 2n, 0] - If[n == 0, 0, b[2n, 2n, n]]);
a /@ Range[0, 22] (* Jean-François Alcover, May 02 2020, after Maple *)

Formula

a(n) = A327869(2n,n).