#####
Séminaire Lotharingien de Combinatoire, B31e (1993).

[Formerly: Publ. I.R.M.A. Strasbourg, 1987, 1994/021, p.
103-126.]

# Arthur Randrianarivony and Jiang Zeng

# Une famille de polynômes qui interpole plusieurs suites
classiques de nombres

**Abstract.**
We give a common polynomial extension of the Euler numbers, Genocchi
numbers, Eulerian polynomials, and the recent median Euler
numbers. We first study some general algebraic properties of
these polynomials, which include the continued fraction
expansion of its ordinary generating function, and by
establishing the connection with a generating function of some
staircases introduced by Dumont, we get several combinatorial
interpretations of these polynomials and then several new
combinatorial interpretations of the above classical
numbers. Finally, we study also a similar extension of
Springer numbers.

The paper has been finally published under the same title in
*Adv. Appl. Math.* **17** (1996), 1-26.