A229413 Number of set partitions of {1,...,3n} into sets of size at most n.

1, 1, 76, 12644, 3305017, 1245131903, 654277037674, 467728049807348, 443694809361207824, 544852927413901502514, 846359710104516310431744, 1629392161877794034658847500, 3819592516111353522143561652540, 10738740219595085951726635839975852

Offset: 0

Author

Alois P. Heinz, Sep 22 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Column k=3 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(3*n, n):
seq(a(n), n=0..20);

Mathematica

G[n_, k_] := G[n, k] = Module[{j, g}, Which[k > n, G[n, n], n == 0, 1, k < 1, 0, True, g = G[n - k, k]; For[j = k - 1, j >= 1, j--, g = g(n-j)/j + G[n - j, k]]; g]];
a[n_] := G[3n, n];
a /@ Range[0, 20] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz *)

Formula

a(n) = (3n)! * [x^(3n)] exp(Sum_{j=1..n} x^j/j!).

a(n) = A229223(3n,n).