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 A126115 #28 Mar 22 2020 12:40:40
%S A126115 1,3,11,69,537,5475,64755,916965,14536305,263680515,5239150875,
%T A126115 115916048325,2768235849225,72290366223075,2016224400665475,
%U A126115 60700190066641125,1936215798778886625,66023235942444655875,2370503834057244760875,90300788789652000685125,3603830757053442135845625
%N A126115 E.g.f.: sqrt(1+2*x)/(1-2*x).
%C A126115 Old name: Numerators of sequence of fractions with e.g.f. sqrt(1+x)/(1-x).
%C A126115 Denominators are successive powers of 2.
%H A126115 Robert Israel, <a href="/A126115/b126115.txt">Table of n, a(n) for n = 0..403</a>
%F A126115 b(n) = a(n)/n! satisfies b(n) = (3*b(n-1) + 2*(2*n-3)*b(n-2))/n, b(0)=1, b(1)=3. - _Sergei N. Gladkovskii_, Jul 22 2012, corrected by _Robert Israel_, Mar 12 2018
%F A126115 D-finite with recurrence: a(n+2) = (2*(n+1))*(1+2*n)*a(n)+3*a(n+1). - _Robert Israel_, Mar 12 2018
%F A126115 E.g.f.: sqrt(1+2*x)/(1-2*x). - _Sergei N. Gladkovskii_, Jul 22 2012
%e A126115 The fractions are 1, 3/2, 11/4, 69/8, 537/16, 5475/32, 64755/64, 916965/128, ...
%p A126115 f:= gfun:-rectoproc({-2*(n+1)*(1+2*n)*a(n)-3*a(n+1)+a(n+2), a(0)=1,a(1)=3},a(n),remember):
%p A126115 map(f, [$0..30]); # _Robert Israel_, Mar 12 2018
%t A126115 With[{nn=20},CoefficientList[Series[Sqrt[1+2x]/(1-2x),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Sep 21 2018 *)
%Y A126115 Cf. A001147, A126119.
%K A126115 nonn,frac
%O A126115 0,2
%A A126115 _N. J. A. Sloane_, Mar 22 2007
%E A126115 Better name by _Sergei N. Gladkovskii_, Jul 22 2012
%E A126115 Edited by _Robert Israel_, Mar 12 2018