|
%I #16 Feb 02 2020 09:02:01
%S 1,1,2,3,5,9,14,28,42,90,132,297,429,1001,1430,3432,4862,11934,16796,
%T 41990,58786,149226,208012,534888,742900,1931540,2674440,7020405,
%U 9694845,25662825,35357670,94287120,129644790,347993910,477638700,1289624490,1767263190
%N a(n) = T(n, floor(n/2)), where T = Catalan triangle (A008315).
%C a(n) is the number of Catalan paths in Quadrant I from (0,0) to (n, gcd(n,2)). - _Clark Kimberling_, Jun 26 2004
%F a(2n) = C(2n+2, n+1)/(n+2), a(2n+1) = 3C(2n+2, n)/(n+3). - _Ralf Stephan_, Apr 30 2004
%F 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
%Y a(2n) = A000108(n+1), a(2n+1) = A000245(n+1).
%K nonn
%O 0,3
%A _Clark Kimberling_
|
