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arXiv · 1803.01975

Exponential Riordan arrays and generalized Narayana polynomials

E. Burlachenko
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Abstract

Generalized Euler polynomials ${{\alpha }_{n}}\left( x \right)={{\left( 1-x \right)}^{n+1}}\sum\nolimits_{m=0}^{\infty }{{{p}_{n}}}\left( m \right){{x}^{m}}$, where ${{p}_{n}}\left( x \right)$ is the polynomial of degree $n$, are the numerator polynomials of the generating functions of diagonals of the ordinary Riordan arrays. Generalized Narayana polynomials ${{\varphi }_{n}}\left( x \right)={{\left( 1-x \right)}^{2n+1}}\sum\nolimits_{m=0}^{\infty }{\left( m+1 \right)...\left( m+n \right){{p}_{n}}}\left( m \right){{x}^{m}}$ are the numerator polynomials of the generating functions of diagonals of the exponential Riordan arrays. In present paper we consider the constructive relationship between these two types of numerator polynomials.

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E. Burlachenko. 2018-03-06. Exponential Riordan arrays and generalized Narayana polynomials. https://arxiv.org/abs/1803.01975

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