  Consider the collection of hyperplanes in $\mathbb{R}^n$ whose defining
equations are given by $\{x_i + x_j = 0\mid 1\leq i<j\leq n\}$. This
arrangement is called the threshold arrangement since its regions are in
bijection with labeled threshold graphs on $n$ vertices. Zaslavsky's theorem
implies that the number of regions is the sum of coefficients of the
characteristic polynomial of the arrangement. In the present article we give a
combinatorial meaning to these coefficients as the number of labeled threshold
graphs with a certain number of `odd anchors', thus answering a question posed
by Stanley.
