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Poly-Bernoulli numbers $B_n^{(k)}\in\mathbb{Q}$\,($n \geq 0$,\,$k \in\mathbb{Z}$) are defined by Kaneko in 1997. Multi-Poly-Bernoullinumbers\,$B_n^{(k_1,k_2,\ldots, k_r)}$, defined by using multiplepolylogarithms, are generations of Kaneko's Poly-Bernoullinumbers\,$B_n^{(k)}$. We researched relations between Multi-Poly-Bernoullinumbers and Poly-Bernoulli numbers of negative index in particular. In section2, we introduce a identity for Multi-Poly-Bernoulli numbers of negative indexwhich was proved by Kamano. In section 3, as main results, we introduce somerelations between Multi-Poly-Bernoulli numbers and Poly-Bernoulli numbers ofnegative index in particular.

Relations between Multi-Poly-Bernoulli numbers and Poly-Bernoulli numbers of negative index