Journal of Integer Sequences, Vol. 17 (2014), Article 14.4.5

Multi-Poly-Bernoulli Numbers and Finite Multiple Zeta Values

Kohtaro Imatomi, Masanobu Kaneko, and Erika Takeda
Graduate School of Mathematics
Kyushu University
Motooka 744, Nishi-ku
Fukuoka 819-0395


We define the multi-poly-Bernoulli numbers slightly differently from similar numbers given in earlier papers by Bayad, Hamahata, and Masubuchi, and study their basic properties. Our motivation for the new definition is the connection to finite multiple zeta values, which have been studied by Hoffman and Zhao, among others, and are recast in a recent work by Zagier and the second author. We write the finite multiple zeta value in terms of our new multi-poly-Bernoulli numbers.

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(Concerned with sequences A027643 A027644 A027645 A027646 A027647 A027648 A027649 A027650 A027651.)

Received October 24 2013; revised version received February 17 2014. Published in Journal of Integer Sequences, February 17 2014.

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