Arithmetic Properties of Bernoulli–Padé Numbers and Polynomials

Abstract

A class of generating functions based on the Padé approximants of the exponential function gives a doubly infinite class of number and polynomial sequences. These generalize the Bernoulli numbers and polynomials, as well as other sequences found in the literature. We derive analogues of the Kummer congruences, the von Staudt–Clausen Theorem, and other properties also satisfied by the ordinary Bernoulli numbers and polynomials.