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 A185089 #18 Jun 23 2017 03:43:52
%S A185089 1,1,2,3,7,14,35,81,208,517,1351,3492,9261,24521,65862,177247,481191,
%T A185089 1310338,3589143,9862257,27215012,75320969,209147407,582264200,
%U A185089 1625342649,4547350865,12750836298,35824579355,100843670951,284361285238,803170176715
%N A185089 A transform of the little Schroeder numbers.
%C A185089 Hankel transform is A060656.
%H A185089 Fung Lam, <a href="/A185089/b185089.txt">Table of n, a(n) for n = 0..2000</a>
%F A185089 G.f.: (1-x+x^2-sqrt(1-2x-5x^2+6x^3+x^4))/(4x^2(1-x)).
%F A185089 G.f.: 1/(1-x-x^2/(1-2x^2/(1-x-x^2/(1-2x^2/(1-x-x^2/(1-2x^2/(1-... (continued fraction).
%F A185089 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)*A001003(k).
%F A185089 conjecture: (n+2)*a(n) -3*(n+1)*a(n-1) +3*(2-n)*a(n-2) +(11*n-20)*a(n-3) +(11-5*n)*a(n-4) +(4-n)*a(n-5) =0. - _R. J. Mathar_, Nov 16 2011 (Formula verified and used for computations. - _Fung Lam_, Feb 24 2014)
%t A185089 CoefficientList[Series[(1-x+x^2-Sqrt[1-2*x-5*x^2+6*x^3+x^4])/(4*x^2*(1-x)), {x,0,50}], x] (* _G. C. Greubel_, Jun 22 2017 *)
%o A185089 (PARI) x='x+O('x^50); Vec((1-x+x^2-sqrt(1-2*x-5*x^2+6*x^3+x^4))/(4*x^2*(1-x))) \\ _G. C. Greubel_, Jun 22 2017
%K A185089 nonn,easy
%O A185089 0,3
%A A185089 _Paul Barry_, Feb 18 2011