  The determinant of an $N \times N$ circulant matrix $M = {\rm CIRC}[x_0, x_1,
..., x_{N-1}$] can be expanded in the form det$ ~M= \sum C_{a_0 a_1 ...a_{N-1}}
x_{a_0} x_{a_1}...x_{a_{N-1}}$. By using the generating function of a
restricted, mod-$N$ partition function, we derive a formula for the
coefficients in this expansion as finite sums over products of binomial
coefficients with integer variables.
