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

0,3

Links

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

Formula

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

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

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 *)

Crossrefs

Column k=3 of A229243.

Cf. A229223.

Sequence in context: A185984 A289227 A028480 * A111682 A271242 A241878

Adjacent sequences: A229410 A229411 A229412 * A229414 A229415 A229416

Keyword

nonn

Author

Alois P. Heinz, Sep 22 2013

Status

approved