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 A323385 Expansion of AGM(1,1-16*x) (where AGM denotes the arithmetic-geometric mean). 2
 1, -8, -16, -128, -1344, -15872, -199680, -2613248, -35148800, -482500608, -6730072064, -95094702080, -1358152794112, -19573573681152, -284284750397440, -4156674357067776, -61133523873169408, -903754859816157184, -13421680957337894912, -200140704802846801920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Robert Israel, Table of n, a(n) for n = 0..833 Eric Weisstein's World of Mathematics, Arithmetic-geometric mean Wikipedia, Arithmetic-geometric mean FORMULA a(n) = 2^n * A060691(n). a(n) ~ -Pi * 2^(4*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 MAPLE R:= Pi*(1-8*x)/(2*EllipticK(-8*x/(1-8*x))): S:= series(R, x, 31): seq(coeff(S, x, j), j=0..30); # Robert Israel, Jan 13 2019 MATHEMATICA CoefficientList[Series[Pi*(1 - 16*x) / (2*EllipticK[1 - 1/(1 - 16*x)^2]), {x, 0, 25}], x] (* Vaclav Kotesovec, Sep 28 2019 *) PROG (PARI) N=66; x='x+O('x^N); Vec(agm(1, 1-16*x)) CROSSREFS Convolution inverse of A053175. Cf. A060691, A089602, A090004. Sequence in context: A278312 A107906 A328127 * A061359 A330150 A340586 Adjacent sequences:  A323382 A323383 A323384 * A323386 A323387 A323388 KEYWORD sign AUTHOR Seiichi Manyama, Jan 13 2019 STATUS approved

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Last modified January 25 16:01 EST 2022. Contains 350572 sequences. (Running on oeis4.)