Expansions of certain inverse factorial series via series and sequence transformations

In this study, factorial series involving generalizations of the harmonic numbers are investigated. New expressions for the Dirichlet series (also called Euler sums) associated with hyperharmonic and skew-harmonic numbers are obtained. In addition, the relationships between the inverse factorial series of a given sequence and the inverse factorial series of the binomial, Stirling and Lah transformations of that sequence are investigated. Furthermore, closed form formulas are derived for inverse factorial series whose coefficients are given by the p-Stirling numbers.