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A075225 Expansion of 2-AGM(1,1-8x) (where AGM denotes the arithmetic-geometric mean). 0
1, 4, 4, 16, 84, 496, 3120, 20416, 137300, 942384, 6572336, 46432960, 331580272, 2389352256, 17351364160, 126851634432, 932823545428, 6895102385072, 51199649648048, 381738099675840, 2856639909232112, 21447771308542784 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 17 18:24 EST 2019. Contains 329241 sequences. (Running on oeis4.)