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Kruchinin, Dmitry; Kruchinin, Vladimir; Shablya, Yuriy

On some properties of generalized Narayana numbers. (English) Zbl 1505.05007

Quaest. Math. 45, No. 12, 1949-1963 (2022).
Summary: 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.

MSC:

05A10 Factorials, binomial coefficients, combinatorial functions
05A15 Exact enumeration problems, generating functions
11B65 Binomial coefficients; factorials; \(q\)-identities
11B75 Other combinatorial number theory

Keywords:

Narayana numbers; generalized Narayana numbers; explicit formula; generating function; composition

Software:

OEIS
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References:

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