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%I #8 Aug 09 2017 12:29:28
%S 1,1,8,176,5888,238848,10770432,518909952,26156466176,1362414338048,
%T 72751723839488,3961437637574656,219123329636761600,
%U 12278352550322765824,695492547259800748032,39759203500044029263872
%N Generalized Catalan numbers C(4,4; 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)= ((16^(n-1))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/4)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
%F G.f.:(1-7*x*c(16*x))/(1-4*x*c(16*x))^2 = c(16*x)*(7+9*c(16*x))/(1+3*c(16*x))^2 = (7*c(16*x)*(4*x)^2+3*(3+11*x))/(3+4*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
%F 3*(-n+1)*a(n) +4*(47*n-120)*a(n-1) +128*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Aug 09 2017
%Y A064341.
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, Oct 12 2001
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