def alpha_coeff(ellipsoid):
    """
    Computes the set of Alpha coefficients of an Ellipsoid with specified
    Inverse Flattening (See Ref 2 Equation 5)
    :param ellipsoid: Ellipsoid Object
    :return: Alpha coefficients a2, a4 ... a16
    """
    nval = ellipsoid.n
    a2 = nval * (nval * (nval * (nval * (nval * (nval * ((37884525 - 
        75900428 * nval) * nval + 42422016) - 89611200) + 46287360) + 
        63504000) - 135475200) + 101606400) / 203212800.0
    a4 = nval ** 2 * (nval * (nval * (nval * (nval * (nval * (148003883 *
        nval + 83274912) - 178508970) + 77690880) + 67374720) - 104509440) +
        47174400) / 174182400.0
    a6 = nval ** 3 * (nval * (nval * (nval * (nval * (318729724 * nval - 
        738126169) + 294981280) + 178924680) - 234938880) + 81164160
        ) / 319334400.0
    a8 = nval ** 4 * (nval * (nval * ((14967552000 - 40176129013 * nval) *
        nval + 6971354016) - 8165836800) + 2355138720) / 7664025600.0
    a10 = nval ** 5 * (nval * (nval * (10421654396 * nval + 3997835751) - 
        4266773472) + 1072709352) / 2490808320.0
    a12 = nval ** 6 * (nval * (175214326799 * nval - 171950693600) + 
        38652967262) / 58118860800.0
    a14 = nval ** 7 * (13700311101 - 67039739596 * nval) / 12454041600.0
    a16 = 1424729850961 * nval ** 8 / 743921418240.0
    return a2, a4, a6, a8, a10, a12, a14, a16
