Maximizing weighted sums of binomial coefficients using generalized continued fractions

S. P. Glasby, G. R. Paseman

Let $m,r\in \mathbb{Z}$ and $\omega \in \mathbb{R}$ satisfy $0⩽r⩽m$ and $\omega ⩾1$. Our main result is a generalized continued fraction for an expression involving the…