A116867 Convolution of generalized Catalan sequence A064063 (named C(3;n)).

1, 2, 9, 58, 446, 3792, 34369, 325538, 3184206, 31917772, 326156474, 3385065348, 35585008816, 378116619692, 4054571715729, 43820012675698, 476830454211926, 5219833626494412, 57444768682580494, 635176593108262028

Offset: 0

Author

Wolfdieter Lang, Mar 24 2006

Keywords

• nonn
• easy

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