

A064341


Generalized Catalan numbers C(3,3; n).


1



1, 1, 6, 81, 1566, 36126, 921456, 25055001, 711951606, 20891575566, 628237506276, 19259213633226, 599654171202156, 18911332670183856, 602840023457208516, 19392890824608619401, 628769286622411762086
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OFFSET

0,3


COMMENTS

See triangle A064879 with columns m built from C(m,m; n), m >= 0, also for Derrida et al. and Liggett references.


LINKS

Table of n, a(n) for n=0..16.


FORMULA

a(n)= ((9^(n1))/(n1))*sum((m+1)*(m+2)*binomial(2*(n2)m, n2m)*((1/3)^(m+1)), m=0..n2), n >= 2, a(0) := 1=: a(1).
G.f.:(15*x*c(9*x))/(13*x*c(9*x))^2 = c(9*x)*(5+4*c(9*x))/(1+2*c(9*x))^2 = (5*c(9*x)*(3*x)^2+4*(1+4*x))/(2+3*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.


CROSSREFS

A064340.
Sequence in context: A196909 A197076 A234872 * A052756 A193265 A138457
Adjacent sequences: A064338 A064339 A064340 * A064342 A064343 A064344


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Oct 12 2001


STATUS

approved



