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A064344 Generalized Catalan numbers C(6,6; n). 1

%I

%S 1,1,12,540,39744,3598992,363776832,39348690624,4456429954560,

%T 521760612125952,62642882007530496,7670452375558388736,

%U 954216689151845302272,120261048050627578368000

%N Generalized Catalan numbers C(6,6; 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)= ((6^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/6)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).

%F G.f.:(1-11*x*c(36*x))/(1-6*x*c(36*x))^2 = c(36*x)*(11+25*c(36*x))/(1+5*c(36*x))^2 = (11*c(36*x)*(6*x)^2+5*(5+17*x))/(5+6*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.

%F 5*(-n+1)*a(n) +6*(119*n-300)*a(n-1) +432*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Aug 09 2017

%Y A064343.

%K nonn,easy

%O 0,3

%A _Wolfdieter Lang_, Oct 12 2001

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Last modified June 17 17:07 EDT 2019. Contains 324196 sequences. (Running on oeis4.)