##### Quarterly J. Math., 62(2), 2011, p. 417-432; first published online
December 19, 2009 doi:10.1093/qmath/hap043

# Dominique Foata, Guo-Niu Han

#
DOUBLOONS AND NEW q-TANGENT NUMBERS

**Abstract.**
We introduce new q-tangent numbers based on the Carlitz
q-analog of the Eulerian polynomial and the so-called doubloons
combinatorial set-up. Those new q-tangent numbers are polynomials
with positive integral coefficients. They are divisible by products of
binomials of the form 1+q(to the power i), the quotients being
q-analogs of the reduced tangent numbers having an explicit
combinatorial interpretation.

foata at unistra dot fr,
guoniu at math unistra dot fr

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