Asymptotic normality of the coefficients of the Morgan-Voyce polynomials (Q6579973)

In this paper, the authors study arithmetic and asymptotic properties of polynomials defined by \N\[\NQ_n(x):= x \sum_{k=1}^n k \, Q_{n-k}(x),\N\]\Nwith initial condition \(Q_0(x)=1\).\N\NThe coefficients satisfy a central limit theorem and a local limit theorem involving Fibonacci numbers.\N\NSeveral methods are used, namely, those by \textit{E.R. Canfield} [in: Handbook of enumerative combinatorics. Boca Raton, FL: CRC Press. 255--280 (2015; Zbl 1351.05024)], \textit{L.H. Harper} [Ann. Math. Stat. 38, 410--414 (1967; Zbl 0154.43703)], and \textit{E.A. Bender} [J. Comb. Theory, Ser. A 15, 91--111 (1973; Zbl 0242.05006)].