Identities for generalized Euler polynomials

For $N\in \mathbb{N}$, let $T_N$ be the Chebyshev polynomial of the first kind. Expressions for the sequence of numbers $p_{\mathrm{\ell }}^{(N)}$, defined as the coefficients in the expansion of $1\mathrm{/}{T}_N(1\mathrm{/}z)$, are provided. These coefficients give formulas for the classical Euler polynomials in terms of the so-called generalized Euler polynomials. The proofs are based on a probabilistic interpretation of the generalized Euler polynomials recently given by Klebanov et al. Asymptotics of $p_{\mathrm{\ell }}^{(N)}$ are also provided.