A Family of Generating Functions for Reciprocal Binomial Coefficients and Its Applications

A generating function for reciprocal binomial coefficients is written down, integral representations of this function are obtained, generating functions for sums of reciprocal binomial coefficients are derived, new identities are obtained, including identities connecting reciprocal binomial coefficients with harmonic numbers and Fibonacci numbers. The application of the found functions for evaluating infinite numerical sequences involving reciprocal binomial coefficients is demonstrated.

💡 Research Summary

The paper introduces a comprehensive generating‑function framework for reciprocal binomial coefficients, i.e. the entries (T(n,m)=\binom{n}{m}^{-1}) of the triangle listed as OEIS A098361. The authors first construct an explicit bivariate generating function
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