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%I #6 Mar 10 2022 05:52:14
%S 1,7,45,291,1917,12867,87805,607747,4257789,30140419,215277565,
%T 1549615107,11230642173,81882660867,600196448253,4420404117507,
%U 32695452696573,242766809923587,1808890431799293,13521381274681347
%N A sequence related to A000108 (Catalan numbers).
%C Also one fourth of third diagonal of triangle A115195, called Y(1,2).
%C Fourth column (m=3) of triangle A115193, called C(1,2).
%H L. Guo, W. Y. Sit, <a href="http://dx.doi.org/10.1007/s11786-010-0061-2">Enumeration and generating functions of Rota-Baxter Words</a>, Math. Comput. Sci. 4 (2010) 313-337, sequence d(n).
%F 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).
%F a(n)= A115193(n+3,3), n>=0.
%F 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
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Feb 23 2006
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