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

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..510

Wikipedia, Partition of a set

Formula

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

Maple

b:= proc(n, i, k) option remember; `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!)))
    end:
a:= n-> (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 *)

Crossrefs

Cf. A266518, A276961, A327869.

Sequence in context: A100153 A333966 A059461 * A160917 A100154 A246230

Adjacent sequences: A328153 A328154 A328155 * A328157 A328158 A328159

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2019

Status

approved