Series with Central Binomial Coefficients, Catalan Numbers, and Harmonic Numbers
Khristo N. Boyadzhiev
Department of Mathematics and Statistics
Ohio Northern University
Ada, Ohio 45810
USA
mailto:k-boyadzhiev@onu.eduk-boyadzhiev@onu.edu

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Abstract:

We present several generating functions for sequences involving the central binomial coefficients and the harmonic numbers. In particular, we obtain the generating functions for the sequences $\binom{2n}{n} H_{n}$, $\binom{2n}{n} \frac{1}{n} H_{n}$, $\binom{2n}{n} \frac{1}{n+1} H_{n}$ , and $\binom{2n}{n} n^{m}$. The technique is based on a special Euler type series rasformation formula.