The Dickson polynomial Dn (x, a) of degree n is defined by Dn (x, a) = ∑i=0[n/2] n/n-i (in-i) (-a)i xn-21, where ⌊⌋ denotes the greatest integer function. In particular, we define D0 (x, a) = 2 for all real x and a. By using Dickson polynomials we present new types of generalized Stirling numbers of the first and second kinds. Some basic properties of these numbers and a combinatorial application to the enumeration of functions on finite sets in terms of their range values is also given.
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