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A038535
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Numerators of coefficients of EllipticE/Pi.
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4
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1, -1, -3, -5, -175, -441, -4851, -14157, -2760615, -8690825, -112285459, -370263621, -19870814327, -67607800225, -931331941875, -3241035157725, -2913690606794775, -10313859829588425, -147068001273760875, -527570807893408125, -30451387031607516975
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OFFSET
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0,3
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COMMENTS
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a(n)/A056982(n) = -(binomial(2*n,n)^2)/((2*n-1)*2^(4*n)), n>=0, are the coefficients of x^n of hypergeometric([1/2,-1/2],[1],x).
The series hypergeometric([1/2,-1/2],[1],e^2)=L/(2*Pi*a) with L the perimeter of an ellipse with major axis a and numerical eccentricity e. (End)
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LINKS
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FORMULA
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a(n) = 2^(-2 w[n])binomial[2n, n]^2 (-1)^(2n)/(1-2n) with w[n]=A000120 = number of 1's in binary expansion of n
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MATHEMATICA
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Numerator[CoefficientList[Series[EllipticE[m]/Pi, {m, 0, 25}], m]] (* Harvey P. Dale, Dec 16 2011 *)
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CROSSREFS
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KEYWORD
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frac,sign
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AUTHOR
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STATUS
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approved
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