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Poly-Bernoulli numbers are one of generalizations of the classical Bernoullinumbers. Since a negative index poly-Bernoulli number is an integer, it is aninteresting problem to study this number from combinatorial viewpoint. In thisshort article, we give a new combinatorial relation between symmetrizedpoly-Bernoulli numbers and the Dumont-Foata polynomials.

Symmetrized poly-Bernoulli numbers and combinatorics