A026008 a(n) = T(n, floor(n/2)), where T = Catalan triangle (A008315).

1, 1, 2, 3, 5, 9, 14, 28, 42, 90, 132, 297, 429, 1001, 1430, 3432, 4862, 11934, 16796, 41990, 58786, 149226, 208012, 534888, 742900, 1931540, 2674440, 7020405, 9694845, 25662825, 35357670, 94287120, 129644790, 347993910, 477638700, 1289624490, 1767263190

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

a(n) is the number of Catalan paths in Quadrant I from (0,0) to (n, gcd(n,2)). - Clark Kimberling, Jun 26 2004

Crossrefs

a(2n) = A000108(n+1), a(2n+1) = A000245(n+1).

Formula

a(2n) = C(2n+2, n+1)/(n+2), a(2n+1) = 3C(2n+2, n)/(n+3). - Ralf Stephan, Apr 30 2004

Conjecture: (n+5)*a(n) +(n+3)*a(n-1) +(-5*n-9)*a(n-2) -4*n*a(n-3) +4*(n-2)*a(n-4)=0. - R. J. Mathar, Jun 10 2013