We define a new class of generating function transformations related to polylogarithm functions, Dirichlet series, and Euler sums. These transformations are given by an infinite sum over the jth derivatives of a sequence generating function and sets of generalized coefficients satisfying a non-triangular recurrence relation in two variables. The generalized transformation coefficients share a number of analogous properties with the Stirling numbers of the second kind and the known harmonic… CONTINUE READING