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

0,3

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

Links

Table of n, a(n) for n=0..36.

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

Crossrefs

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

Sequence in context: A032089 A352079 A105044 * A101461 A085897 A361906

Adjacent sequences: A026005 A026006 A026007 * A026009 A026010 A026011

Keyword

nonn

Author

Clark Kimberling

Status

approved