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Abstract. Following earlier research of ours, we propose a new method for obtaining the complete Padé table of the exponential function. It is based on an explicit construction of certain Padé approximants not for the usual power series for exp at 0 but for a formal power series related in a simple way to the remainder term of the power series for exp. This surprising and non trivial coincidence is proved more generally for type II simultaneous Padé approximants for a family (exp(a j z)) j=1,...,r with distinct complex a's and we recover Hermite's classical formulae. The proof uses certain discrete multiple orthogonal polynomials recently introduced by Arvesú, Coussement and van Assche, which generalise the classical Charlier orthogonal polynomials.

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