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Séminaire Lotharingien de Combinatoire, B42e (1999), 22 pp.

# G.-N. Han, A. Randrianarivony, J. Zeng

#
Un autre *q*-analogue des nombres d'Euler

**Abstract.**
The ordinary generating functions of the secant and tangent numbers have very
simple continued fraction expansions. However, the classical *q*-secant
and *q*-tangent numbers do not give a natural *q*-analogue of these
continued fractions. In this paper, we introduce a different
*q*-analogue of Euler numbers using *q*-difference operator and show that
their generating functions
have simple continued fraction expansions. Furthermore,
by establishing an explicit bijection between some Motzkin paths
and (*k*,r)-multipermutations we derive combinatorial
interpretations for these *q*-numbers. Finally the allied
*q*-Euler median numbers are also studied.

Received: December 16, 1998; Accepted: February 24, 1999.

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