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.
The following versions are available: