New sums mixing harmonic numbers and central binomial coefficients

We study two new classes of sums with inverse binomial coefficients and harmonic numbers. In addition we establish recursive solutions to the following power sums \begin{equation*} U_d(n) = \sum_{k=1}^n \frac{2^{2k}}{\binom{2k}{k}} \cdot k^d \quad \mbox{and}\quad V_d(n) = \sum_{k=1}^n \frac{2^{2k}}{\binom{2k}{k}}\cdot k^d,H_k, \end{equation*} where $d$ is a positive integer.

💡 Research Summary

The paper investigates two new families of finite sums that combine inverse central binomial coefficients with harmonic numbers. The authors first recall classical identities involving reciprocals of central binomial coefficients, such as
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