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 A060691 Expansion of AGM(1,1-8x) (where AGM denotes the arithmetic-geometric mean). 12
 1, -4, -4, -16, -84, -496, -3120, -20416, -137300, -942384, -6572336, -46432960, -331580272, -2389352256, -17351364160, -126851634432, -932823545428, -6895102385072, -51199649648048, -381738099675840, -2856639909232112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 FORMULA G.f.: 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[1/Hypergeometric2F1[1/2, 1/2, 1, 16*x*(1 - 4*x)], {x, 0, 20}], x] (* Vaclav Kotesovec, Jan 13 2019 *) CoefficientList[Series[Pi*(1 - 4*x)/(2*EllipticK[1/(1 - 1/(4*x))^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Jan 13 2019 *) PROG (PARI) a(n)=if(n<0, 0, polcoeff(agm(1, 1-8*x+x*O(x^n)), n)) CROSSREFS Cf. A081085. Sequence in context: A010099 A204295 A203101 * A075225 A204078 A284494 Adjacent sequences: A060688 A060689 A060690 * A060692 A060693 A060694 KEYWORD sign AUTHOR Roland Bacher, Apr 20 2001 EXTENSIONS Edited by Michael Somos, Jul 19, 2002 STATUS approved

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)