Inverse binomial coefficients in Egorychev method

A certain residue representation of the inverse binomial coefficients makes them amenable to Egorychev method for the reduction of sums by analytic methods, wherein the main idea is to identify parts of the summands as residues of analytic functions. We illustrate the use of such residue representation on some instances varying in complexity, including a generalization of an identity by Sung Sik U and Kyu Song Chae in [13].