A089603 G.f.: sqrt(1/agm(1, 1-8*x)) = sqrt(o.g.f. for A081085).

1, 2, 8, 40, 226, 1380, 8880, 59280, 406416, 2842400, 20186752, 145119616, 1053575336, 7711639760, 56834201280, 421327859520, 3139306406850, 23494847031300, 176526280319120, 1330929290036560, 10065855468854980, 76341682531733960, 580460500453098080

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

a(n) ~ 2^(3*n - 1/2) / (n * sqrt(Pi*log(n))) * (1 - (gamma/2 + log(2))/log(n) + (3*gamma^2/8 + 3*log(2)*gamma/2 + 3*log(2)^2/2 - Pi^2/16) / log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Sep 29 2019

Mathematica

CoefficientList[Series[Sqrt[2*EllipticK[1/(1 - 1/(4*x))^2]/(Pi*(1 - 4*x))], {x, 0, 25}], x] (* Vaclav Kotesovec, Sep 26 2019 *)
nmax = 25; CoefficientList[Series[Sqrt[Hypergeometric2F1[1/2, 1/2, 1, 16*x*(1 - 4*x)]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 26 2019 *)

Prog

(PARI) Vec( 1/agm(1, 1-8*x+O(x^66))^(1/2) ) \\ Joerg Arndt, Aug 14 2013

Crossrefs

Cf. A081085, A089602.

Sequence in context: A289431 A337912 A085485 * A343146 A209358 A116456

Adjacent sequences: A089600 A089601 A089602 * A089604 A089605 A089606

Keyword

nonn

Author

N. J. A. Sloane, Dec 31 2003

Status

approved