A350461 Number of ways to choose a subset of size n from [2n] and arrange its elements into a set of lists.

1, 2, 18, 260, 5110, 126252, 3743124, 129156456, 5075323110, 223484406860, 10889720208796, 581327564001912, 33721264023340348, 2111076358455927800, 141812884019465389800, 10171645727323281955920, 775654703427461395949190, 62649431136582816113115660

Offset: 0

Author

Alois P. Heinz, Feb 22 2022

Keywords

• nonn

Examples

			a(2) = 18: 12, 21, 1|2, 13, 31, 1|3, 14, 41, 1|4, 23, 32, 2|3, 24, 42, 2|4, 34, 43, 3|4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..361

Crossrefs

Cf. A000262, A000984, A129652.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1, add(
      b(n-j)*binomial(n-1, j-1)*j!, j=1..n))
    end:
a:= n-> binomial(2*n, n)*b(n):
seq(a(n), n=0..20);

Mathematica

a[n_] := If[n==0, 1, ((2n)!/n!) Sum[Binomial[n-1, j]/(j+1)!, {j, 0, n-1}]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 14 2022, from 1st formula *)

Formula

a(n) = binomial(2*n,n) * A000262(n) = A000984(n) * A000262(n).

a(n) = A129652(2n,n).