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

1, 1, 7, 68, 763, 9276, 118656, 1572024, 21368155, 296187164, 4169180104, 59420124472, 855590919392, 12425933510200, 181787367119112, 2676258927443328, 39615617922076635, 589234154312057436, 8801406013366190952, 131964659304934491576, 1985338775295068132520

Offset

0,3

Comments

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

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..830

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.

Cf. A060691, A081085, A323385.

Sequence in context: A120079 A297502 A087567 * A371392 A306386 A136629

Adjacent sequences: A328043 A328044 A328045 * A328047 A328048 A328049

Keyword

nonn

Author

Vaclav Kotesovec, Oct 03 2019

Status

approved