The function df(x) = 2^(x/2)*(2/Pi)^(sin(Pi*x/2)^2/2)*Gamma(x/2+1) interpolates the double factorials A006882 and extends them analytically. df(-1/2) is the given constant. Extending also the notation this can be written as (-1/2)!! = (-1/4)!/Pi^(1/4).