  In this paper we consider a transformation $L_a$ of sequences of complex
numbers. We find the inverse transformation of $L_a$ as well as the inverse of
a related transformation $\tilde{L}_a$. We explore a connection to the binomial
transform and significantly generalize a previously known result. We also
obtain new relations among many classical hypergeometric orthogonal polynomials
as well as new formulas for sums involving terminating hypergeometric series.
