|
%I #20 Sep 29 2019 08:24:29
%S 1,-2,-4,-16,-82,-476,-2968,-19360,-130220,-895592,-6264656,-44411968,
%T -318300080,-2302042400,-16777460032,-123084642048,-908175062994,
%U -6734680013532,-50164119638328,-375134475461088,-2815268948389212,-21195313970398536
%N Expansion of sqrt(agm(1, 1 - 8*x)) in powers of x.
%H Seiichi Manyama, <a href="/A300100/b300100.txt">Table of n, a(n) for n = 0..500</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Arithmetic-GeometricMean.html">Arithmetic-geometric mean</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_mean">Arithmetic-geometric mean</a>
%F Convolution inverse of A089603.
%F 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
%t CoefficientList[Series[Sqrt[Pi*(1 - 8*x) / (2*EllipticK[1 - 1/(1 - 8*x)^2])], {x, 0, 25}], x] (* _Vaclav Kotesovec_, Sep 28 2019 *)
%Y Cf. A060691, A089603.
%K sign
%O 0,2
%A _Seiichi Manyama_, Feb 24 2018
|
