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The Wiener index is a graphical invariant which has found many applications in chemistry. The Wiener Polynomial of a connected graph G is the generating function of the sequence (C(G,k)) whose derivative at x=1 is the Wiener index W(G) of G, in which C(G,k) is the number of pairs of vertices distance k apart. The Wiener Polynomials of star-like trees and other special trees are found in this paper; and hence a formula of the Wiener index for each such trees is obtained .