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%I #12 Sep 29 2019 08:16:08
%S 1,4,4,16,84,496,3120,20416,137300,942384,6572336,46432960,331580272,
%T 2389352256,17351364160,126851634432,932823545428,6895102385072,
%U 51199649648048,381738099675840,2856639909232112,21447771308542784
%N Expansion of 2-AGM(1,1-8x) (where AGM denotes the arithmetic-geometric mean).
%F G.f.: 2-AGM(1, 1-8x).
%F 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 CoefficientList[Series[2 - Pi*(1 - 8*x) / (2*EllipticK[1 - 1/(1 - 8*x)^2]), {x, 0, 25}], x] (* _Vaclav Kotesovec_, Sep 28 2019 *)
%o (PARI) a(n)=if(n<0,0,polcoeff(2-agm(1,1-8*x+x*O(x^n)),n))
%Y Cf. A060691. a(n)=-A060691(n) if n>0.
%K nonn
%O 0,2
%A _Michael Somos_, Sep 11 2002
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