A000778 a(n) = Catalan(n) + Catalan(n+1) - 1.

1, 2, 6, 18, 55, 173, 560, 1858, 6291, 21657, 75581, 266797, 950911, 3417339, 12369284, 45052514, 165002459, 607283489, 2244901889, 8331383609, 31030387439, 115948830659, 434542177289, 1632963760973, 6151850548775, 23229299473603, 87900903988155

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..200
• J. R. Stembridge, Some combinatorial aspects of reduced words in finite Coxeter groups, Trans. Amer. Math. Soc. 349 (1997), no. 4, 1285-1332.

Crossrefs

Cf. A000108.

Equals A005807(n) - 1. Cf. A071716.

Programs

Mathematica

Table[CatalanNumber[n] + CatalanNumber[n + 1] - 1, {n, 0, 200}] (* T. D. Noe, Jun 20 2012 *)

Formula

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