A075225 Expansion of 2-AGM(1,1-8x) (where AGM denotes the arithmetic-geometric mean).

1, 4, 4, 16, 84, 496, 3120, 20416, 137300, 942384, 6572336, 46432960, 331580272, 2389352256, 17351364160, 126851634432, 932823545428, 6895102385072, 51199649648048, 381738099675840, 2856639909232112, 21447771308542784

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

G.f.: 2-AGM(1, 1-8x).

a(n) ~ Pi * 2^(3*n-1) / (n * log(n)^2) * (1 - (2*gamma + 4*log(2))/log(n) + (3*gamma^2 + 12*log(2)*gamma + 12*log(2)^2 - Pi^2/2) / log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Sep 29 2019

Mathematica

CoefficientList[Series[2 - Pi*(1 - 8*x) / (2*EllipticK[1 - 1/(1 - 8*x)^2]), {x, 0, 25}], x] (* Vaclav Kotesovec, Sep 28 2019 *)

Prog

(PARI) a(n)=if(n<0, 0, polcoeff(2-agm(1, 1-8*x+x*O(x^n)), n))

Crossrefs

Cf. A060691. a(n)=-A060691(n) if n>0.

Sequence in context: A204295 A203101 A060691 * A204078 A284494 A091541

Adjacent sequences: A075222 A075223 A075224 * A075226 A075227 A075228

Keyword

nonn

Author

Michael Somos, Sep 11 2002

Status

approved