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 A092266 Expansion of (1+4x)/AGM(1+4x,1-4x) where AGM denotes the arithmetic-geometric mean. 2
 1, 4, 4, 16, 36, 144, 400, 1600, 4900, 19600, 63504, 254016, 853776, 3415104, 11778624, 47114496, 165636900, 662547600, 2363904400, 9455617600, 34134779536, 136539118144, 497634306624, 1990537226496, 7312459672336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA G.f.: (1+4x)/AGM(1+4x, 1-4x) where AGM(x, y) is the arithmetic-geometric mean of Gauss and Legendre. a(n) = A063886(n)^2. a(2n) = A002894(n); a(2n+1) = 4*a(2n). a(n) ~ 2^(2*n + 1) / (Pi*n). - Vaclav Kotesovec, Sep 27 2019 MATHEMATICA CoefficientList[Series[2*(1 + 4*x)*EllipticK[1 - (1 + 4*x)^2/(1 - 4*x)^2] / (Pi*(1 - 4*x)), {x, 0, 30}], x] (* Vaclav Kotesovec, Sep 27 2019 *) PROG (PARI) a(n)=((n==0)+2*binomial(n-1, (n-1)\2))^2; (PARI) Vec( 1/agm(1, (1-4*x)/(1+4*x)+O(x^66)) ) \\ Joerg Arndt, Aug 14 2013 CROSSREFS Sequence in context: A038234 A099462 A218051 * A257606 A219398 A222104 Adjacent sequences: A092263 A092264 A092265 * A092267 A092268 A092269 KEYWORD nonn AUTHOR Michael Somos, Feb 16 2004 STATUS approved

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Last modified January 28 12:46 EST 2023. Contains 359892 sequences. (Running on oeis4.)