# Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers

@article{Komatsu2015IncompletePN, title={Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers}, author={T. Komatsu and K{\'a}lm{\'a}n Liptai and Istv'an MezHo}, journal={arXiv: Number Theory}, year={2015} }

By using the associated and restricted Stirling numbers of the second kind, we give some generalizations of the poly-Bernoulli numbers. We also study their arithmetical and combinatorial properties. As an application, at the end of the paper we present a new infinite series representation of the Riemann zeta function via the Lambert $W$.

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