Séminaire Lotharingien de Combinatoire, B30f (1993), 14 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1993, 1993/034, p. 97-110.]

Arthur Randrianarivony and Jiang Zeng

Sur une extension des nombres d'Euler et les records des permutations alternantes

Abstract. We study the sequence of polynomials Cn(x,y) defined through the recurrence C0(x,y)=1, Cn(x,y)=x(y+1)Cn-1(x+2,y+2)-xyCn-1(x,y), which turns out to be an extension of Euler numbers. We give a combinatorial interpretation of these numbers in terms of down-up permutations with respect to the numbers of even and odd upper records, and a continued fraction expansion for their ordinary generating function.

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