Research Article

On some properties of generalized Narayana numbers

Published in: Quaestiones Mathematicae
Volume 45 , issue 12 , 2022 , pages: 1949–1963

DOI: 10.2989/16073606.2021.1980448

Author(s): Dmitry Kruchinin Tomsk State University of Control Systems and Radioelectronics, Russia , Vladimir Kruchinin Tomsk State University of Control Systems and Radioelectronics, Russia , Yuriy Shablya Tomsk State University of Control Systems and Radioelectronics, Russia

Keywords: 05E05 , 05A15 , 11B65 , Narayana numbers , generalized Narayana numbers , explicit formula , generating function , composition

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Abstract

In this paper, we consider a three-parameter generalization of the Narayana numbers that is related to the powers of the generating function for the Narayana numbers. We find a multivariate generating function for these generalized Narayana numbers. For the composition of generating functions where the inner function is the generating function for the Narayana numbers, we obtain an explicit formula for calculating its coefficients. We also consider several examples of applying the obtained results and derive new generating functions.

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