A115194 A sequence related to A000108 (Catalan numbers).

1, 7, 45, 291, 1917, 12867, 87805, 607747, 4257789, 30140419, 215277565, 1549615107, 11230642173, 81882660867, 600196448253, 4420404117507, 32695452696573, 242766809923587, 1808890431799293, 13521381274681347

Offset: 0

Author

Wolfdieter Lang, Feb 23 2006

Keywords

• nonn
• easy

Comments

Also one fourth of third diagonal of triangle A115195, called Y(1,2).

Fourth column (m=3) of triangle A115193, called C(1,2).

Links

• L. Guo, W. Y. Sit, Enumeration and generating functions of Rota-Baxter Words, Math. Comput. Sci. 4 (2010) 313-337, sequence d(n).

Formula

G.f.: (-1+x + (1-3*x)*c(2*x))/(2*(1+x)*x^2), with the o.g.f. c(x) of A000108 (Catalan).

a(n)= A115193(n+3,3), n>=0.

D-finite with recurrence -(n+3)*(5*n-2)*a(n) +(35*n^2+31*n+18)*a(n-1) +4*(5*n+3)*(2*n+1)*a(n-2)=0. - R. J. Mathar, Jul 21 2017