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%I #11 Sep 09 2019 01:22:54
%S 1,2,2,5,7,17,26,62,99,233,382,890,1486,3434,5812,13340,22819,52073,
%T 89846,204002,354522,801422,1401292,3155300,5546382,12444842,21977516,
%U 49155332,87167164,194392628,345994216,769547192,1374282019,3049104233
%N Number of log-concave paths of length n starting from the origin (0,0) with steps from {N=(0,1), E=(1,0) and S=(0,-1)} that stay in the second octant and never touch the line y=x except possibly at the beginning or the end.
%C The first S step can only come after an E step.
%F G.f.: (1-x)/(2-4*x) + (1+3*x)/(2*sqrt(1-4*x^2));
%F a(2n) = (1/2)*(4^(n-1) + 3*binomial(2n-2, n-1));
%F a(2n+1) = (1/2)*(2*4^(n-1) + binomial(2n, n)).
%K nonn
%O 1,2
%A _Wenjin Woan_, Feb 07 2003
%E More terms from _Max Alekseyev_, Jul 04 2009
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