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Recently Han obtained a general formula for the weight function correspondingto the expansion of a generating function in terms of hook lengths of binarytrees. In this paper, we present formulas for k-ary trees, plane trees, planeforests, labeled trees and forests. We also find appropriate generatingfunctions which lead to unifications of the hook length formulas due to Du andLiu, Han, Gessel and Seo, and Postnikov.

Hook Length Formulas for Trees by Han's Expansion