  Let $G$ be a finite group. A contravariant functor from the category of
finite free $G$-sets to vector spaces has an associated Hilbert series, which
records the underlying sequence of $G^n$ representations, $n \in \mathbb N$. We
prove that this Hilbert series is rational with denominator given by linear
polynomials with coefficients in the field generated by the character table of
$G$.
