  Let $g$ and $h$ be real-valued arithmetic functions, positive and normalized.
Specific choices within the following general scheme of recursively defined
polynomials \begin{equation*} P_n^{g,h}(x):= \frac{x}{h(n)} \sum_{k=1}^{n} g(k)
\, P_{n-k}^{g,h}(x), \end{equation*} with initial value $P_{0}^{g,h}(x)=1$
encode information about several classical, widely studied polynomials. This
includes Chebyshev polynomials of the second kind, associated Laguerre
polynomials, and the Nekrasov--Okounkov polynomials. In this paper we prove
that for $g(n)=n$ and fixed $h$ we obtain orthogonal polynomial sequences for
positive definite functionals. Let $h(n)=n^s$ with $0 \leq s \leq 1 $. Then the
sequence satisfies Tur\'an inequalities for $x \geq 0$.
