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 A060691 #19 Jul 02 2025 19:28:19
%S A060691 1,-4,-4,-16,-84,-496,-3120,-20416,-137300,-942384,-6572336,-46432960,
%T A060691 -331580272,-2389352256,-17351364160,-126851634432,-932823545428,
%U A060691 -6895102385072,-51199649648048,-381738099675840,-2856639909232112
%N A060691 Expansion of AGM(1,1-8x) (where AGM denotes the arithmetic-geometric mean).
%H A060691 Vaclav Kotesovec, <a href="/A060691/b060691.txt">Table of n, a(n) for n = 0..1000</a>
%F A060691 G.f.: AGM(1, 1-8x).
%F A060691 a(n) ~ -Pi * 2^(3*n-1) / (n * log(n)^2) * (1 - (2*gamma + 4*log(2))/log(n) + (3*gamma^2 + 12*log(2)*gamma + 12*log(2)^2 - Pi^2/2) / log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Sep 29 2019
%t A060691 CoefficientList[Series[1/Hypergeometric2F1[1/2, 1/2, 1, 16*x*(1 - 4*x)], {x, 0, 20}], x] (* _Vaclav Kotesovec_, Jan 13 2019 *)
%t A060691 CoefficientList[Series[Pi*(1 - 4*x)/(2*EllipticK[1/(1 - 1/(4*x))^2]), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Jan 13 2019 *)
%o A060691 (PARI) a(n)=if(n<0,0,polcoeff(agm(1,1-8*x+x*O(x^n)),n))
%Y A060691 Cf. A081085.
%K A060691 sign
%O A060691 0,2
%A A060691 _Roland Bacher_, Apr 20 2001
%E A060691 Edited by _Michael Somos_, Jul 19 2002