Congruences for sums involving $\left(\genfrac{}{}{0ex}{}{rk}{k}\right)$

Sandro Mattarei, Roberto Tauraso

We primarily investigate congruences modulo $p$ for finite sums of the form ${\sum }_k\left(\genfrac{}{}{0ex}{}{rk}{k}\right)x^k/k$ over the ranges $0<k<p$ and $0<k<p/r$, where $p$ is a prime larger than the p…