OFFSET
0,3
COMMENTS
Contribution from Wolfdieter Lang, Nov 08 2010: (Start)
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)
FORMULA
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
MATHEMATICA
Numerator[CoefficientList[Series[EllipticE[m]/Pi, {m, 0, 25}], m]] (* Harvey P. Dale, Dec 16 2011 *)
CROSSREFS
KEYWORD
frac,sign
AUTHOR
Wouter Meeussen, revised Jan 03 2001
STATUS
approved