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%I #8 Aug 09 2017 12:32:55
%S 1,1,16,1216,157696,25317376,4543676416,873117515776,175715349692416,
%T 36562356662173696,7802094251017240576,1698089607837490610176,
%U 375493988522687218057216,84121868091432283370684416
%N Generalized Catalan numbers C(8,8; n).
%C See triangle A064879 with columns m built from C(m,m; n), m >= 0, also for Derrida et al. and Liggett references.
%H J. Abate, W. Whitt, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Whitt/whitt6.html">Brownian Motion and the Generalized Catalan Numbers</a>, J. Int. Seq. 14 (2011) # 11.2.6, corollary 6.
%F 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 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.
%F 7*(-n+1)*a(n) +8*(223*n-560)*a(n-1) +1024*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Aug 09 2017
%Y A064345.
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, Oct 12 2001
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