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%I #6 Feb 07 2016 21:41:30
%S 1,2,5,16,53,184,654,2368,8689,32216,120434,453248,1715266,6521584,
%T 24894364,95353472,366324729,1411015064,5447548682,21074836864,
%U 81682204614,317110750672,1232951721604,4800353915264,18712880651802,73030245143792,285311648317172
%N Number of North-East paths from (0,0) to (n,n) that have even number of times bounce off y = x to the right.
%C This sequence is related to paired pattern P_2 in Section 3.2 in Pan and Remmel's link.
%H Ran Pan, Jeffrey B. Remmel, <a href="http://arxiv.org/abs/1601.07988">Paired patterns in lattice paths</a>, arXiv:1601.07988 [math.CO], 2016.
%F G.f.: (-1 + 3*f(x) - 2*x*(-2 + 5*f(x)+ 6*f(x)*x))/(2*(4*x - 1) (-1 + 4*x*(1 + x))), where f(x) = sqrt(1 - 4*x).
%F a(n) = binomial(2*n,n) - A268431(n).
%Y Cf. A268407, A268429
%K nonn
%O 0,2
%A _Ran Pan_, Feb 04 2016