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A064345
Generalized Catalan numbers C(7,7; n).
1
1, 1, 14, 833, 83006, 10213854, 1404124008, 206635997673, 31844571309110, 5073749573133710, 829012595472718580, 138151786440502006186, 23390450962161609522028, 4012173837912126230070832
OFFSET
0,3
COMMENTS
See triangle A064879 with columns m built from C(m,m; n), m >= 0, also for Derrida et al. and Liggett references.
LINKS
J. Abate, W. Whitt, Brownian Motion and the Generalized Catalan Numbers, J. Int. Seq. 14 (2011) # 11.2.6, corollary 6.
FORMULA
a(n)= ((7^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/7)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
G.f.:(1-13*x*c(49*x))/(1-7*x*c(49*x))^2 = c(49*x)*(13+36*c(49*x))/(1+6*c(49*x))^2 = (13*c(49*x)*(7*x)^2+12*(3+10*x))/(6+7*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
6*(-n+1)*a(n) +7*(167*n-420)*a(n-1) +686*(2*n-3)*a(n-2)=0. - R. J. Mathar, Aug 09 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 12 2001
STATUS
approved