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 A110199 #22 Mar 11 2020 22:58:27
%S A110199 1,1,2,2,4,4,9,9,23,23,65,65,197,197,626,626,2056,2056,6918,6918,
%T A110199 23714,23714,82500,82500,290512,290512,1033412,1033412,3707852,
%U A110199 3707852,13402697,13402697,48760367,48760367,178405157,178405157,656043857
%N A110199 a(n) = Sum_{k=0..floor(n/2)} Catalan(k).
%C A110199 Hankel transform is A166446(n+2). - _Paul Barry_, Jun 23 2010
%H A110199 Andrei Asinowski, Cyril Banderier, Valerie Roitner, <a href="https://lipn.univ-paris13.fr/~banderier/Papers/several_patterns.pdf">Generating functions for lattice paths with several forbidden patterns</a>, (2019).
%F A110199 G.f.: (1-sqrt(1-4x^2))/((1-x)2x^2);
%F A110199 a(n) = Sum_{k=0..floor(n/2)} binomial(2k, k)/(k+1).
%F A110199 Conjecture: -(n+2)*a(n) + (n+2)*a(n-1) + 4*(n-1)*a(n-2) + 4*(1-n)*a(n-3) = 0. - _R. J. Mathar_, Nov 09 2012
%F A110199 G.f.: 1/x^2 - G(0)/(1-x)/x^2, where G(k)= 1 - x/(1 - x/(1 + x/(1 + x/G(k+1) ))); (continued fraction). - _Sergei N. Gladkovskii_, Jul 17 2013
%p A110199 a:= n-> add(binomial(2*j, j)/(j+1), j=0..n/2): seq(a(n), n=0..36); # _Zerinvary Lajos_, Apr 30 2007
%Y A110199 Cf. A000108, A014137.
%K A110199 easy,nonn
%O A110199 0,3
%A A110199 _Paul Barry_, Jul 15 2005