Asymptotic Normality of the Coefficients of the Morgan-Voyce Polynomials

Abstract

We study arithmetic and asymptotic properties of polynomials provided by $Q_n(x):=x{\sum }_{k=1}^{n}k{Q}_{n-k}(x)$ with initial value $Q_0(x)=1$. The coefficients satisfy a central limit theorem and a local limit theorem involving Fibonacci numbers. We apply methods of Berry and Esseen, Harper, Bender, and Canfield.