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 A186341 #13 Oct 08 2016 08:56:53
%S A186341 1,1,3,5,15,33,95,237,667,1765,4943,13505,37967,105837,299675,847253,
%T A186341 2417903,6909409,19866303,57253165,165728475,480938693,1400391247,
%U A186341 4087481409,11963060527,35089773869,103157489499,303856951925,896755068783,2651120922081,7850714948511
%N A186341 a(n)=sum{k=0..floor(n/2), binomial(n-k,k)*A186338(k)}.
%C A186341 Hankel transform is A134751.
%F A186341 G.f.: 1/(1-x-2x^2/(1-2x^2/(1-x-x^2/(1-2x^2/(1-x-2x^2/(1-x^2/(1-x-2x^2/(1-... (continued fraction).
%F A186341 G.f.: (1-x-3x^2-sqrt((1-3x-7x^2+19x^3+15x^4-25x^5-16x^6)/(1-x)))/(2x^2(1-x-2x^2)).
%F A186341 Conjecture: (n+2)*a(n) +5*(-n-1)*a(n-1) +2*(-n+3)*a(n-2) +(38*n-59)*a(n-3) +(-22*n+41)*a(n-4) +4*(-22*n+81)*a(n-5) +3*(19*n-79)*a(n-6) +3*(29*n-164)*a(n-7) +2*(-17*n+98)*a(n-8) +16*(-2*n+15)*a(n-9)=0. - _R. J. Mathar_, Oct 08 2016
%t A186341 CoefficientList[Series[(1-x-3x^2-Sqrt[(1-3x-7x^2+19x^3+15x^4-25x^5-16x^6)/(1-x)])/(2x^2(1-x-2x^2)),{x,0,40}],x] (* _Harvey P. Dale_, Mar 04 2011 *)
%K A186341 nonn,easy
%O A186341 0,3
%A A186341 _Paul Barry_, Feb 18 2011