OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..500
Eric Weisstein's World of Mathematics, Arithmetic-geometric mean
Wikipedia, Arithmetic-geometric mean
FORMULA
Convolution inverse of A089603.
a(n) ~ -sqrt(Pi) * 2^(3*n - 3/2) / (n * log(n)^(3/2)) * (1 - 3*(gamma/2 + log(2)) / log(n) + (15*gamma^2/8 + 15*log(2)*gamma/2 + 15*log(2)^2/2 - 5*Pi^2/16) / log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Sep 29 2019
MATHEMATICA
CoefficientList[Series[Sqrt[Pi*(1 - 8*x) / (2*EllipticK[1 - 1/(1 - 8*x)^2])], {x, 0, 25}], x] (* Vaclav Kotesovec, Sep 28 2019 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 24 2018
STATUS
approved