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A115194 A sequence related to A000108 (Catalan numbers). 2
1, 7, 45, 291, 1917, 12867, 87805, 607747, 4257789, 30140419, 215277565, 1549615107, 11230642173, 81882660867, 600196448253, 4420404117507, 32695452696573, 242766809923587, 1808890431799293, 13521381274681347 (list; graph; refs; listen; history; text; internal format)
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.

-(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 A219020

Adjacent sequences:  A115191 A115192 A115193 * A115195 A115196 A115197

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 23 2006

STATUS

approved

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Last modified July 24 23:25 EDT 2021. Contains 346273 sequences. (Running on oeis4.)