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Starting from the moment sequences of classical orthogonal polynomials wederive the orthogonality purely algebraically. We consider also the moments of($q=1$) classical orthogonal polynomials, and study those cases in which theexponential generating function has a nice form. In the opposite direction, weshow that the generalized Dumont-Foata polynomials with six parameters are themoments of rescaled continuous dual Hahn polynomials. Finally we show that oneof our methods can be applied to deal with the moments of Askey-Wilsonpolynomials.

Moments of Orthogonal Polynomials and Exponential Generating Functions