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 A328046 G.f.: 1/2 + 1/(1 + AGM(1, sqrt(1-16*x))). 2

%I

%S 1,1,7,68,763,9276,118656,1572024,21368155,296187164,4169180104,

%T 59420124472,855590919392,12425933510200,181787367119112,

%U 2676258927443328,39615617922076635,589234154312057436,8801406013366190952,131964659304934491576,1985338775295068132520

%N G.f.: 1/2 + 1/(1 + AGM(1, sqrt(1-16*x))).

%C AGM(x,y) = AGM((x+y)/2,sqrt(x*y)) is the arithmetic-geometric mean.

%H Vaclav Kotesovec, <a href="/A328046/b328046.txt">Table of n, a(n) for n = 0..830</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Arithmetic-GeometricMean.html">Arithmetic-Geometric Mean</a>

%F a(n) ~ Pi * 16^n / (n * (log(n) + Pi)^2) * (1 - (2*gamma + 8*log(2)) / (log(n) + Pi) + (3*gamma^2 + 48*log(2)^2 + 24*gamma*log(2) - Pi^2/2) / (log(n) + Pi)^2), where gamma is the Euler-Mascheroni constant A001620.

%t CoefficientList[Series[1/2 + 1/(1 + (Pi*Sqrt[1 - 16*x])/(2*EllipticK[1 - 1/(1 - 16*x)])), {x, 0, 25}], x]

%Y Cf. A188267.

%Y Cf. A060691, A081085, A323385.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 03 2019

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Last modified April 4 08:58 EDT 2020. Contains 333213 sequences. (Running on oeis4.)