Journal of Integer Sequences, Vol. 16 (2013), Article 13.9.5

Curious Relations and Identities Involving the Catalan Generating Function and Numbers

Asamoah Nkwanta
Department of Mathematics
Morgan State University
Baltimore, MD 21251

Akalu Tefera
Department of Mathematics
Grand Valley State University
Allendale, MI 49401


Riordan matrix methods and manipulation of various generating functions are used to find curious relations among the Catalan, central binomial, and RNA generating functions. In addition, the Wilf-Zeilberger method is used to find identities where the gamma function and Catalan numbers are expressed in terms of the Gauss hypergeometric function. As a consequence of the identities, new recurrence relations are obtained. In particular, a new recurrence relation is given for the RNA numbers. Furthermore, other representations of π and the Catalan numbers are obtained.

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(Concerned with sequences A000012 A000027 A000045 A000108 A000957 A001477 A004148 A007318 A039598 A053121 A097724 A111418.)

Received July 14 2013; revised version received October 6 2013. Published in Journal of Integer Sequences, October 13 2013.

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