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 A228156 #13 Sep 29 2019 10:31:20
%S A228156 1,2,0,8,2,68,32,720,464,8480,6656,106368,95912,1390928,1392512,
%T A228156 18734144,20371650,257955716,300101760,3613109008,4448177412,
%U A228156 51302395528,66289160512,736588435360,992578330048,10674012880512,14924667774976,155890890782720,225244659392784,2291995151532576,3410654921389824
%N A228156 Expansion of sqrt((1+4*x)/AGM(1+4*x,1-4*x)) where AGM denotes the arithmetic-geometric mean.
%C A228156 Convolution square is A092266.
%H A228156 Vaclav Kotesovec, <a href="/A228156/b228156.txt">Table of n, a(n) for n = 0..1000</a>
%F A228156 a(n) ~ 2^(2*n - 1/2) / (n*sqrt(Pi*log(n))) * (1 - (gamma + 3*log(2)) / (2*log(n)) + (3*gamma^2/8 + 9*gamma*log(2)/4 + 27*log(2)^2/8 - 1/16*Pi^2) / log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Sep 29 2019
%t A228156 CoefficientList[Series[Sqrt[2*(1 + 4*x)*EllipticK[1 - (1 + 4*x)^2/(1 - 4*x)^2] / (Pi*(1 - 4*x))], {x, 0, 30}], x] (* _Vaclav Kotesovec_, Sep 27 2019 *)
%o A228156 (PARI) Vec( 1/agm(1,(1-4*x)/(1+4*x)+O(x^66))^(1/2) ) \\ _Joerg Arndt_, Aug 14 2013
%Y A228156 Cf. A092266 (1+4*x)/AGM(1+4*x,1-4*x).
%Y A228156 Cf. A081085 1/AGM(1,1-8*x), A053175 1/AGM(1,1-16*x), A090004 1/AGM(1,1-16*x)^(1/2), A089602 1/AGM(1,1-16*x)^(1/4).
%K A228156 nonn
%O A228156 0,2
%A A228156 _Joerg Arndt_, Aug 14 2013