  Recently, Lazar and Wachs (arXiv:1910.07651) showed that the (median)
Genocchi numbers play a fundamental role in the study of the homogenized Linial
arrangement and obtained two new permutation models (called D-permutations and
E-permutations) for (median) Genocchi numbers. They further conjecture that the
distributions of cycle numbers over the two models are equal. In a follow-up,
Eu et al. (arXiv:2103.09130) further proved the gamma-positivity of the descent
polynomials of even-odd descent permutations, which are in bijection with
E-permutations by Foata's fundamental transformation. This paper merges the
above two papers by considering a general moment sequence which encompasses the
number of cycles and number of drops of E-permutations. Using the combinatorial
theory of continued fraction, the moment connection enables us to confirm
Lazar-Wachs' conjecture and obtain a natural $(p,q)$-analogue of Eu et al's
descent polynomials. Furthermore, we show that the $\gamma$-coefficients of our
$(p,q)$-analogue of descent polynomials have the same factorization flavor as
the $\gamma$-coeffcients of Br\"and\'en's $(p,q)$-Eulerian polynomials.
