  A simple recurrence relation for the even order moments of the Fabius
function is proven. Also, a very similar formula for the odd order moments in
terms of the even order moments is proved. The matrices corresponding to these
formulas (and their inverses) are multiplied so as to obtain a matrix that
correspond to a recurrence relation for the odd order moments in terms of
themselves. The theorem at the end gives a closed-form for the coefficients.
