A229229 Number of set partitions of {1,...,n^2} into sets of size at most n.

1, 1, 10, 12644, 6631556521, 3282701194678476257, 3025262978042089315465899013351, 9292286146024114784457467780130028866860171013, 158655194198118596873150397161518177395553186289541468458000908304

Offset: 0

Author

Alois P. Heinz, Sep 16 2013

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..24

Crossrefs

Main diagonal of A229243.

Cf. A229223.

Programs

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(n^2, n):
seq(a(n), n=0..10);

Mathematica

G[n_, k_] := G[n, k] = Module[{j, pc}, Which[k>n, G[n, n], n==0, 1, k<1, 0, True, pc = G[n-k, k]; For[j = k-1, j >= 1, j--, pc = pc*(n-j)/j + G[n-j, k]]; pc]]; a[n_] := G[n^2, n]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Feb 15 2017, translated from Maple *)

Formula

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

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