This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A268430 #6 Feb 07 2016 21:41:30 %S A268430 1,2,5,16,53,184,654,2368,8689,32216,120434,453248,1715266,6521584, %T A268430 24894364,95353472,366324729,1411015064,5447548682,21074836864, %U A268430 81682204614,317110750672,1232951721604,4800353915264,18712880651802,73030245143792,285311648317172 %N A268430 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 A268430 This sequence is related to paired pattern P_2 in Section 3.2 in Pan and Remmel's link. %H A268430 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 A268430 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 A268430 a(n) = binomial(2*n,n) - A268431(n). %Y A268430 Cf. A268407, A268429 %K A268430 nonn %O A268430 0,2 %A A268430 _Ran Pan_, Feb 04 2016