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A328046 G.f.: 1/2 + 1/(1 + AGM(1, sqrt(1-16*x))). 2
1, 1, 7, 68, 763, 9276, 118656, 1572024, 21368155, 296187164, 4169180104, 59420124472, 855590919392, 12425933510200, 181787367119112, 2676258927443328, 39615617922076635, 589234154312057436, 8801406013366190952, 131964659304934491576, 1985338775295068132520 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
AGM(x,y) = AGM((x+y)/2,sqrt(x*y)) is the arithmetic-geometric mean.
LINKS
Eric Weisstein's World of Mathematics, Arithmetic-Geometric Mean
FORMULA
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.
MATHEMATICA
CoefficientList[Series[1/2 + 1/(1 + (Pi*Sqrt[1 - 16*x])/(2*EllipticK[1 - 1/(1 - 16*x)])), {x, 0, 25}], x]
CROSSREFS
Cf. A188267.
Sequence in context: A120079 A297502 A087567 * A306386 A136629 A197525
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 03 2019
STATUS
approved

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Last modified February 24 22:04 EST 2024. Contains 370307 sequences. (Running on oeis4.)