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A064347 Generalized Catalan numbers C(9,9; n). 1

%I

%S 1,1,18,1701,278478,56542698,12838905972,3121895416077,

%T 795077021525526,209364566760439038,56540432581528153788,

%U 15573764062988183490786,4358381303784085630372620,1235729432868053981694246324

%N Generalized Catalan numbers C(9,9; 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)= ((9^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/9)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).

%F G.f.:(1-17*x*c(81*x))/(1-9*x*c(81*x))^2 = c(81*x)*(17+64*c(81*x))/(1+8*c(81*x))^2 = (17*c(81*x)*(9*x)^2+16*(4+13*x))/(8+9*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.

%F 8*(-n+1)*a(n) +9*(287*n-720)*a(n-1) +1458*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Aug 09 2017

%Y A064346.

%K nonn,easy

%O 0,3

%A _Wolfdieter Lang_, Oct 12 2001

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Last modified July 15 16:29 EDT 2019. Contains 325049 sequences. (Running on oeis4.)