On cographic regular matroids

The presentation of alternating permutatioas via labelled binary trees is used to define polynomials H_2n?1(x) as enumerating polynomials for the height of peaks in alternating permutations of length 2n?1. A divisibility property of the coefficients of these polynomials is proved, which generalizes and explains combinatirially a well-known property of the tangent numbers. Furthermore, a version of the exponential generating function for the H_2n?1(x) is given, leading to a new combinatorial interpretation of Dumont's modified Ghandi-polynomials.