%I A064341
%S A064341 1,1,6,81,1566,36126,921456,25055001,711951606,20891575566,
%T A064341 628237506276,19259213633226,599654171202156,18911332670183856,
%U A064341 602840023457208516,19392890824608619401,628769286622411762086
%N A064341 Generalized Catalan numbers C(3,3; n).
%C A064341 See triangle A064879 with columns m built from C(m,m; n), m >= 0, also 
               for Derrida et al. and Liggett references.
%F A064341 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 A064341 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 A064341 A064340.
%Y A064341 Sequence in context: A077393 A002676 A052348 this_sequence A052756 A138457 
               A076282
%Y A064341 Adjacent sequences: A064338 A064339 A064340 this_sequence A064342 A064343 
               A064344
%K A064341 nonn,easy
%O A064341 0,3
%A A064341 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 12 
               2001