Exponential Riordan arrays and generalized Narayana polynomials

2018/03/06 by Burlachenko, E.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1803.01975

Abstract

Generalized Euler polynomials α_n( x )=( 1-x )ⁿ⁺¹∑\nolimits_m=0^∞ p_n( m )x^m, where p_n( x ) is the polynomial of degree n, are the numerator polynomials of the generating functions of diagonals of the ordinary Riordan arrays. Generalized Narayana polynomials φ_n( x )=( 1-x )²ⁿ⁺¹∑\nolimits_m=0^∞ ( m+1 )...( m+n )p_n( m )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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