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A229413 Number of set partitions of {1,...,3n} into sets of size at most n. 2
1, 1, 76, 12644, 3305017, 1245131903, 654277037674, 467728049807348, 443694809361207824, 544852927413901502514, 846359710104516310431744, 1629392161877794034658847500, 3819592516111353522143561652540, 10738740219595085951726635839975852 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified November 27 16:20 EST 2021. Contains 349394 sequences. (Running on oeis4.)