  Hetyei recently introduced a hyperplane arrangement (called the homogenized
Linial arrangement) and used the finite field method of Athanasiadis to show
that its number of regions is a median Genocchi number. These numbers count a
class of permutations known as Dumont derangements. Here, we take a different
approach, which makes direct use of Zaslavsky's formula relating the
intersection lattice of this arrangement to the number of regions. We refine
Hetyei's result by obtaining a combinatorial interpretation of the M\"obius
function of this lattice in terms of variants of the Dumont permutations. This
enables us to derive a formula for the generating function of the
characterisitic polynomial of the arrangement. The M\"obius invariant of the
lattice turns out to be a (nonmedian) Genocchi number. Our techniques also
yield type B, and more generally Dowling arrangement, analogs of these results.
