Binomial convolutions for rational power series

Ira M. Gessel, Ishan Kar

The binomial convolution of two sequences $\{a_n\}$ and $\{b_n\}$ is the sequence whose $n$th term is ${\sum }_{k=0}^n\left(\genfrac{}{}{0ex}{}{n}{k}\right)a_k{b}_{n-k}$. If $\{a_n\}$ and $\{b_n\}$ have rat…