OFFSET
0,2
COMMENTS
Row sums of generalized Catalan triangle A116866 (named C(1,3)).
LINKS
J. Abate, W. Whitt, Brownian Motion and the Generalized Catalan Numbers, J. Int. Seq. 14 (2011) # 11.2.6, example after (34).
FORMULA
a(n)=sum(A116866(n,m),m=0..n), n>=0.
G.f.: ((1+3*x*c(3*x)/2)/(1+x/2))^2 = (4-3*x + 15*x*c(3*x))/(2+x)^2, with the o.g.f. c(x) of A000108 (Catalan numbers).
a(n)= sum(C(3;n-k)*C(3;k),k=0..n), n>=0, with C(3;n):= A064063(n).
2*n*a(n) +(-23*n+37)*a(n-1) +6*(-2*n+1)*a(n-2)=0. - R. J. Mathar, Aug 09 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Mar 24 2006
STATUS
approved