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 A185087 #18 Jun 23 2017 01:01:18
%S A185087 1,1,3,5,12,24,55,119,272,612,1411,3247,7565,17667,41561,98099,232696,
%T A185087 553784,1322813,3169065,7614583,18342921,44294991,107200829,259983346,
%U A185087 631718606,1537737567,3749440151,9156561590,22394270034,54845701243
%N A185087 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)*A000108(k+1).
%C A185087 Essentially identical to A090345 (=1,0,1,1,3,5,12,24...). - _Joerg Arndt_, Mar 18 2011
%C A185087 Hankel transform is A008619(n+1) (counting numbers doubled).
%H A185087 G. C. Greubel, <a href="/A185087/b185087.txt">Table of n, a(n) for n = 0..1000</a>
%F A185087 G.f.: (1-x-2x^2-sqrt(1-2x-3x^2+4x^3))/(2x^4).
%F A185087 G.f.: 1/(1-x-2x^2/(1-(1/2)x^2/(1-x-(3/2)x^2/(1-(2/3)x^2/(1-x-(4/3)x^2/(1-(3/4)x^2/(1-... (continued fraction).
%F A185087 a(n)=sum{k=0..n, sum{j=0..n, binomial(k-j,n-k-j)*binomial(k,j)*if(n-k-j>=0, A001006(n-k-j),0)}}.
%F A185087 a(n)=A090345(n+2).
%F A185087 Conjecture: (n+4)*a(n) -(2*n+5)*a(n-1) -3*(n+1)*a(n-2) +2*(2*n-1)*a(n-3)=0. - _R. J. Mathar_, Nov 16 2011
%t A185087 CoefficientList[Series[(1 - x - 2*x^2 - Sqrt[1 - 2 x - 3 x^2 + 4 x^3])/(2*x^4), {x,0,50}], x] (* _G. C. Greubel_, Jun 22 2017 *)
%o A185087 (PARI) x='x+O('x^50); Vec((1-x-2*x^2-sqrt(1-2*x-3*x^2+4*x^3))/(2*x^4)) \\ _G. C. Greubel_, Jun 22 2017
%K A185087 nonn,easy
%O A185087 0,3
%A A185087 _Paul Barry_, Feb 18 2011