An application of Jacobi's residue formula and proofs of some other conjectures on binomial coefficients

Abstract

We prove seven conjectures involving binomial coefficients. These conjectures appear in The On-Line Encyclopedia of Integer Sequences (OEIS). Among these is an application of Jacobi's residue formula. We also apply MacMahon's master theorem to give a new and independently obtained proof of a recently established result.

27 pages; v2: added a reference and updated a remark