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arXiv · 2604.01249

On Series Involving Cubed Catalan Numbers

Kunle Adegoke
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Abstract

Using generalized binomial coefficient identities and some results of John Dougall, we derive some families of series involving the cubes of Catalan numbers. We also establish a family of series containing fourth powers of Catalan numbers. Finally, we find a generalization of the Bauer series for $1/\pi$ and obtain some Ramanujan-like series for $1/\pi^2$ and~$1/\pi^3$.

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Kunle Adegoke. 2026-04-01. On Series Involving Cubed Catalan Numbers. https://arxiv.org/abs/2604.01249

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