  The resonance arrangement $\mathcal{A}_n$ is the arrangement of hyperplanes
in $\mathbb{R}^n$ given by all hyperplanes of the form $\sum_{i \in I} x_i =
0$, where $I$ is a nonempty subset of $\{1,\dots,n\}$. We consider the
characteristic polynomial $\chi(\mathcal{A}_n; t)$ of the resonance
arrangement, whose value $R_n$ at $-1$ is of particular interest, and
corresponds to counts of generalized retarded functions in quantum field
theory, among other things. No formula is known for either the characteristic
polynomial or $R_n$, though $R_n$ has been computed up to $n=8$. By exploiting
symmetry and using computational methods, we compute the characteristic
polynomial of $\mathcal{A}_9$, and thus obtain $R_9$. The coefficients of the
characteristic polynomial are also equal to the so-called Betti numbers of the
complexified hyperplane arrangement; that is, the coefficient of $t^{n-i}$ is
denoted by the Betti number $b_i(\mathcal{A}_n)$. Explicit formulas are known
for the Betti numbers up to $b_3(\mathcal{A}_n)$. Using computational methods,
we also obtain an explicit formula for $b_4(\mathcal{A}_n)$, which gives the
$t^{n-4}$ coefficient of the characteristic polynomial.
