%I A064346
%S A064346 1,1,16,1216,157696,25317376,4543676416,873117515776,175715349692416,
%T A064346 36562356662173696,7802094251017240576,1698089607837490610176,
%U A064346 375493988522687218057216,84121868091432283370684416
%N A064346 Generalized Catalan numbers C(8,8; n).
%C A064346 See triangle A064879 with columns m built from C(m,m; n), m >= 0, also 
               for Derrida et al. and Liggett references.
%F A064346 a(n)= ((8^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/
               8)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
%F A064346 G.f.:(1-15*x*c(64*x))/(1-8*x*c(64*x))^2 = c(64*x)*(15+49*c(64*x))/(1+7*c(64*x))^2 
               = (15*c(64*x)*(8*x)^2+7*(7+23*x))/(7+8*x)^2 with c(x)= A(x) g.f. 
               of Catalan numbers A000108.
%Y A064346 A064345.
%Y A064346 Sequence in context: A053903 A102807 A160131 this_sequence A113104 A000490 
               A027648
%Y A064346 Adjacent sequences: A064343 A064344 A064345 this_sequence A064347 A064348 
               A064349
%K A064346 nonn,easy
%O A064346 0,3
%A A064346 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 12 
               2001