Arithmetic Properties of Generalized Euler Numbers
The generalized Euler number E_{n|k} counts
the number of permutations of {1,2,...,n} which have a descent in
position m if and only if m is divisible by k.
The classical Euler numbers are the special case when k=2.
In this paper, we study divisibility properties of a q-analog of
E_{n|k}. In particular, we generalize two theorems of
Andrews and Gessel about factors of the q-tangent numbers.