We study the GMa degenerations Fa λ of the type A flag varieties Fλ. We describe these degenerations explicitly as subvarieties in the products of Grassmannians. We construct cell decompositions of Fa λ and show that for complete flags the number of cells is equal to the normalized median Genocchi numbers hn. This leads to a new combinatorial definition of the numbers hn. We also compute the Poincaré polynomials of the complete degenerate flag varieties via a natural statistics on the set of Dellac's configurations, similar to the length statistics on the set of permutations. We thus obtain a natural q-version of the normalized median Genocchi numbers.