  The derangement polynomial for the symmetric group enumerates derangements by
the number of excedances. It can be interpreted as the local $h$-polynomial, in
the sense of Stanley, of the barycentric subdivision of the simplex. Motivated
by this interpretation, we define a derangement polynomial for the even-signed
permutation group. The coefficients of this polynomial are nonnegative,
symmetric and unimodal. We show that they enumerate derangements in the
even-signed permutation group according to a notion of excedance, which is
analogous to the one introduced by Brenti for signed permutations. We also give
an explicit formula for the corresponding exponential generating function.
