DOUBLOONS AND NEW Q-TANGENT NUMBERS.

We introduce new q-tangent numbers based on the Carlitz q-analog of the Eulerian polynomial and the so-called doubloon 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 + qi, the quotients being q-analogs of the reduced tangent numbers having an explicit combinatorial interpretation. [ABSTRACT FROM PUBLISHER]