

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
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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(nk, k);
for j from k1 to 1 by 1 do %*(nj)/j +G(nj, k) od; % fi
end:
a:= n> G(3*n, n):
seq(a(n), n=0..20);


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



