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

0,2

Links

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

Formula

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

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

Example

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.

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 *)

Crossrefs

Cf. A000262, A000984, A129652.

Sequence in context: A151362 A215362 A360974 * A099880 A141009 A143154

Adjacent sequences: A350458 A350459 A350460 * A350462 A350463 A350464

Keyword

nonn

Author

Alois P. Heinz, Feb 22 2022

Status

approved