We prove that the V(n, k) are also related to the numbers W(n, k) defined by fc! 2 W(n, k)x"/n< = [(*-2)(e*-l)]fc n=0 in much the same way the associated Stirling numbers are related to the Stirling numbers. Finally, we examine, more generally, the Bell polynomials Bn k(ax, a2, 3-a, 4-a, 5-a, ...) and show how the methods of this paper can be used to prove several formulas involving the Bernoulli and Stirling numbers.

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ABSTRACT. In this paper we examine the polynomials Wn

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