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

0,2

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

Table of n, a(n) for n=0..19.

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

Crossrefs

Sequence in context: A190973 A099842 A287811 * A062274 A182556 A363570

Adjacent sequences: A115191 A115192 A115193 * A115195 A115196 A115197

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 23 2006

Status

approved