Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers

@article{Komatsu2015IncompletePN,
  title={Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers},
  author={Takao 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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