cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A038535 Numerators of coefficients of EllipticE/Pi.

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%I A038535 #12 Nov 21 2013 12:46:44
%S A038535 1,-1,-3,-5,-175,-441,-4851,-14157,-2760615,-8690825,-112285459,
%T A038535 -370263621,-19870814327,-67607800225,-931331941875,-3241035157725,
%U A038535 -2913690606794775,-10313859829588425,-147068001273760875,-527570807893408125,-30451387031607516975
%N A038535 Numerators of coefficients of EllipticE/Pi.
%C A038535 Contribution from _Wolfdieter Lang_, Nov 08 2010: (Start)
%C A038535 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).
%C A038535 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)
%F A038535 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
%t A038535 Numerator[CoefficientList[Series[EllipticE[m]/Pi,{m,0,25}],m]] (* _Harvey P. Dale_, Dec 16 2011 *)
%Y A038535 Cf. A038533, A038534.
%Y A038535 a(n) divides A000891(n+1).
%K A038535 frac,sign
%O A038535 0,3
%A A038535 _Wouter Meeussen_, revised Jan 03 2001