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Let P = p n (x) ∞ n=0 be a sequence of polynomials such that deg p n (x) = n, p 0 (x) = 1. The aim of this paper is to study the Stirling numbers of the second kind associated with P and of the first kind associated with P, in a unified and systematic way with the help of umbral calculus technique. This generalizes enormously the 'classical' Stirling numbers of both kinds, which correspond to the sequence x n ∞ n=0. Our results are illustrated with many examples which give rise to interesting inverse relations in each case.
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