In mathematics, poly-Bernoulli numbers, denoted as , were defined by M. Kaneko as where Li is the polylogarithm. The are the usual Bernoulli numbers. Moreover, the Generalization of Poly-Bernoulli numbers with a,b,c parameters defined as follows where Li is the polylogarithm. Kaneko also gave two combinatorial formulas: where is the number of ways to partition a size set into non-empty subsets (the Stirling number of the second kind). The Poly-Bernoulli number satisfies the following asymptotic: For a positive integer n and a prime number p, the poly-Bernoulli numbers satisfy