A229228 Number of set partitions of {1,...,2n} into sets of size at most n.

1, 1, 10, 166, 3795, 112124, 4163743, 190168577, 10468226150, 681863474058, 51720008131148, 4506628734688128, 445956917001833090, 49631199898024188422, 6160538225093750695800, 846748983034696433927334, 128064669166890886264698699, 21195039362681903376709497444

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = (2n)! * [x^(2n)] exp(Sum_{j=1..n} x^j/j!).

a(n) = A229223(2n,n).

Example

a(2) = 10: 1/2/3/4, 12/3/4, 13/2/4, 14/2/3, 1/23/4, 1/24/3, 1/2/34, 12/34, 13/24, 14/23.

Maple

G:= proc(n, k) option remember; local j; if k>n then G(n, n)
      elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
      for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
    end:
a:= n-> G(2*n, n):
seq(a(n), n=0..20);

Mathematica

G[n_, k_] := G[n, k] = If[n == 0, 1, If[k < 1, 0, Sum[G[n - k*j, k - 1]*n!/ k!^j/(n - k*j)!/j!, {j, 0, n/k}]]];
Table[G[2n, n], {n, 0, 20}] (* Jean-François Alcover, May 21 2018, translated from Maple *)

Crossrefs

Column k=2 of A229243.

Cf. A229223.

Sequence in context: A305604 A367444 A054688 * A112650 A006295 A006297

Adjacent sequences: A229225 A229226 A229227 * A229229 A229230 A229231

Keyword

nonn

Author

Alois P. Heinz, Sep 16 2013

Status

approved