  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.
