A recurrence relation for the odd order moments of the Fabius function

Abstract: 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.