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 A026008 a(n) = T(n, floor(n/2)), where T = Catalan triangle (A008315). 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 13 10:55 EDT 2024. Contains 375904 sequences. (Running on oeis4.)