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 A171454 #15 Nov 15 2023 04:51:15
%S A171454 1,4,16,80,448,2672,16640,106944,704000,4722608,32166784,221865280,
%T A171454 1546491904,10876777024,77091573760,550088739584,3948410757120,
%U A171454 28489277352112,206520803651712,1503353875355200,10984898330047488,80540719266134080,592362120108263424,4369140213882013440
%N A171454 G.f. satisfies: A(x) = 1 + 4*x*AGM(1, A(x)^2).
%H A171454 Vaclav Kotesovec, <a href="/A171454/b171454.txt">Table of n, a(n) for n = 0..400</a>
%F A171454 a(n) ~ c * d^n / n^(3/2), where d = 7.862810359254200633908490328120234046255594283562932892563... and c = 1.2926544621133576475917023125188188972684483736846308027... - _Vaclav Kotesovec_, Nov 15 2023
%e A171454 G.f.: A(x) = 1 + 4*x + 16*x^2 + 80*x^3 + 448*x^4 + 2672*x^5 + ...
%e A171454 A(x)^2 = 1 + 8*x + 48*x^2 + 288*x^3 + 1792*x^4 + 11488*x^5 + ...
%e A171454 AGM(1, A(x)^2) = 1 + 4*x + 20*x^2 + 112*x^3 + 668*x^4 + 4160*x^5 + ...
%t A171454 (* Calculation of constants {d,c}: *) {1/r, Sqrt[r*s*(-1 - s + s^4 + s^5) / (2*Pi*r*(-1 - 4*s^2 + s^4) + 8*s*EllipticK[(-1 + s^2)^2/(1 + s^2)^2])]} /. FindRoot[{(s - 1)/(4*r) == Pi*s^2/(2*EllipticK[1 - 1/s^4]), EllipticE[(-1 + s^2)^2/(1 + s^2)^2] == Pi*r*s}, {r, 1/8}, {s, 3}, WorkingPrecision -> 70] (* _Vaclav Kotesovec_, Nov 15 2023 *)
%o A171454 (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+4*x*agm(1,A^2));polcoeff(A,n)}
%Y A171454 Cf. A060691.
%K A171454 nonn
%O A171454 0,2
%A A171454 _Paul D. Hanna_, Dec 09 2009
%E A171454 More terms from _Jinyuan Wang_, Feb 25 2020