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%I
%S 1,1,6,81,1566,36126,921456,25055001,711951606,20891575566,
%T 628237506276,19259213633226,599654171202156,18911332670183856,
%U 602840023457208516,19392890824608619401,628769286622411762086
%N Generalized Catalan numbers C(3,3; n).
%C See triangle A064879 with columns m built from C(m,m; n), m >= 0, also for Derrida et al. and Liggett references.
%F a(n)= ((9^(n-1))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/3)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
%F G.f.:(1-5*x*c(9*x))/(1-3*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.
%Y A064340.
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, Oct 12 2001
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