Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Feb 01 2022 01:14:40
%S 1,2,6,18,55,173,560,1858,6291,21657,75581,266797,950911,3417339,
%T 12369284,45052514,165002459,607283489,2244901889,8331383609,
%U 31030387439,115948830659,434542177289,1632963760973,6151850548775,23229299473603,87900903988155
%N a(n) = Catalan(n) + Catalan(n+1) - 1.
%H T. D. Noe, <a href="/A000778/b000778.txt">Table of n, a(n) for n = 0..200</a>
%H J. R. Stembridge, <a href="http://dx.doi.org/10.1090/S0002-9947-97-01805-9">Some combinatorial aspects of reduced words in finite Coxeter groups</a>, Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.
%F D-finite with recurrence (n+2)*a(n) +(-5*n-4)*a(n-1) +(3*n+4)*a(n-2) +(5*n-16)*a(n-3) +2*(-2*n+7)*a(n-4)=0. - _R. J. Mathar_, Jun 17 2020
%t Table[CatalanNumber[n] + CatalanNumber[n + 1] - 1, {n, 0, 200}] (* _T. D. Noe_, Jun 20 2012 *)
%Y Cf. A000108.
%Y Equals A005807(n) - 1. Cf. A071716.
%K nonn
%O 0,2
%A _N. J. A. Sloane_