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A229414 Number of set partitions of {1,...,3n} into sets of size at most 3. 2
1, 5, 166, 12644, 1680592, 341185496, 97620050080, 37286121988256, 18280749571449664, 11168256342434121152, 8306264068494786829696, 7380771881944947770497280, 7715405978050522488223499776, 9365880670184268387214967727104, 13058232187415887547449498864463872 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) = (3n)! * [x^(3n)] exp(x + x^2/2 + x^3/6).

a(n) = A001680(3n) = A229223(3n,3).

MAPLE

a:= proc(n) option remember; `if`(n<3, [1, 5, 166][n+1],

      ((108*n^2-72*n+4)*a(n-1)-6*(n-1)*(3*n-5)*(27*n^2-48*n+10)*a(n-2)

       +9*(n-1)*(n-2)*(3*n-1)*(3*n-7)*(3*n-5)*(3*n-8)*a(n-3))/8)

    end:

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, 3];

a /@ Range[0, 20] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz in A229243 *)

CROSSREFS

Row n=3 of A229243.

Sequence in context: A129995 A259613 A047940 * A210923 A229524 A288352

Adjacent sequences:  A229411 A229412 A229413 * A229415 A229416 A229417

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 22 2013

STATUS

approved

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Last modified December 9 06:07 EST 2021. Contains 349627 sequences. (Running on oeis4.)