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 A190733 #26 Jan 30 2020 21:29:16
%S A190733 1,3,5,15,49,175,657,2559,10241,41855,173953,732927,3123457,13439743,
%T A190733 58307841,254779391,1120247809,4952864767,22005184513,98196398079,
%U A190733 439923990529,1977917169663,8921667641345,40361657696255,183092192411649,832634240106495,3795237359190017
%N A190733 Expansion of (4*x+2)/(1+sqrt(1-4*x-4*x^2)).
%H A190733 Vincenzo Librandi, <a href="/A190733/b190733.txt">Table of n, a(n) for n = 0..100</a>
%F A190733 a(n) = (n+1)*sum(k=1..n+1,binomial(k,n-k+1)*Catalan(k-1)/k).
%F A190733 D-finite with recurrence: (n+1)*a(n) +(-n+1)*a(n-1) +14*(-n+2)*a(n-2) +20*(-n+3)*a(n-3) +8*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Jan 25 2020
%t A190733 CoefficientList[Series[(4x+2)/(1+Sqrt[1-4x-4x^2]),{x,0,40}],x] (* _Harvey P. Dale_, Mar 20 2015 *)
%o A190733 (Maxima)
%o A190733 a(n):=(n+1)*sum(binomial(k,n-k+1)/k*binomial(2*k-2,k-1)/k,k,1,(n+1))
%o A190733 (PARI) x='x+O('x^66); /* that many terms */
%o A190733 Vec((4*x+2)/(1+sqrt(1-4*x-4*x^2))) /* show terms */ /* _Joerg Arndt_, May 27 2011 */
%K A190733 nonn
%O A190733 0,2
%A A190733 _Dmitry Kruchinin_, May 26 2011