Journal of Integer Sequences, Vol. 25 (2022), Article 22.6.5

Infinite Series Associated with the Ratio and Product of Central Binomial Coefficients

Narendra Bhandari
Department of Mathematics
University of Delhi
Budhiganga-01, Bajura


We establish several interesting series associated with the ratio and the product of central binomial coefficients, namely ${2n\choose n}$ and ${4n\choose 2n} $. Series involving the product of central binomial coefficients can be found in the papers of Campbell, D'Aurizio, and Sondow. In this paper, through the application of integration methods, we address broad generalizations of both classes. The techniques involved in constructing the integrals for the corresponding series are based on the use of the ordinary generating functions of central binomial coefficients and Wallis' well-known integral formulas.

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(Concerned with sequence A000984.)

Received April 15 2022; revised versions received April 27 2022; June 22 2022; June 26 2022; June 27 2022. Published in Journal of Integer Sequences, June 29 2022.

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