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)= ((4^(n-1))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/2)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1).
G.f.:(1-3*x*c(4*x))/(1-2*x*c(4*x))^2 = c(4*x)*(3+c(4*x))/(1+c(4*x))^2 = (1+5*x+3*c(4*x)*(2*x)^2)/(1+2*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108.
(-n+1)*a(n) +2*(7*n-20)*a(n-1) +16*(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