We study the function ζ(k1, . . . , kn - 1 ; s) = Σ0<m1<m2⋯<mn 1/mk11⋯mkn - 1 n - 1 msn and show that the poly-Bernoulli numbers introduced in our previous paper are expressed as special values at negative arguments of certain combinations of these functions. As a consequence of our study, we obtain a series of relations among multiple zeta values.
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