Congruences involving Delannoy numbers and Schröder numbers

Chen-Bo Jia, Jia-Qing Huang

The central Delannoy numbers $D_n={\sum }_{k=0}^n\left(\genfrac{}{}{0ex}{}{n}{k}\right)\left(\genfrac{}{}{0ex}{}{n+k}{k}\right)$ and the little Schröder number $s_n={\sum }_{k=1}^n\frac{1}{n}\left(\genfrac{}{}{0ex}{}{n}{k}\right)\left(\genfrac{}{}{0ex}{}{n}{k-1}\right)2^{n-k}$ are impo…