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Dominique Foata, Guo-Niu Han, DOUBLOONS AND NEW Q-TANGENT NUMBERS, The Quarterly Journal of Mathematics, Volume 62, Issue 2, June 2011, Pages 417–432, https://doi.org/10.1093/qmath/hap043
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Abstract
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.
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