Weighted Derangements and the Linearization Coefficients of Orthogonal Sheffer Polynomials

The present paper is devoted to a systematic study of the combinatorial interpretations of the moments and the linearization coefficients of the orthogonal Sheffer polynomials, i.e., Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. In particular, we show that Viennot's combinatorial interpretations of the moments can be derived directly from their classical analytical expressions and that the linearization coefficients of Meixner-Pollaczek polynomials have an interpretation in the model of derangements analogous to those of Laguerre and Meixner polynomials.

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