  A numerical semigroup $S$ is a subset of the non-negative integers containing
$0$ that is closed under addition. The Hilbert series of $S$ (a formal power
series equal to the sum of terms $t^n$ over all $n \in S$) can be expressed as
a rational function in $t$ whose numerator is characterized in terms of the
topology of a simplicial complex determined by membership in $S$. In this
paper, we obtain analogous rational expressions for the related power series
whose coefficient of $t^n$ equals $f(n)$ for one of several semigroup-theoretic
invariants $f:S \to \mathbb R$ known to be eventually quasipolynomial.
