Diff m mth Row $\left(\begin{array}{c}m\\ 0\end{array}\right){z}_{m}-\left(\begin{array}{c}m\\ 1\end{array}\right){z}_{m-1}+\left(\begin{array}{c}m\\ 2\end{array}\right){z}_{m-2}+\cdots +{\left(-1\right)}^{m}\left(\begin{array}{c}m\\ m\end{array}\right){z}_{0}$ (m + 1)th Row $\left(\begin{array}{c}m\\ 0\end{array}\right){z}_{m+1}-\left(\begin{array}{c}m\\ 1\end{array}\right){z}_{m}+\left(\begin{array}{c}m\\ 2\end{array}\right){z}_{m-1}+\cdots +{\left(-1\right)}^{m}\left(\begin{array}{c}m\\ m\end{array}\right){z}_{1}$ $\cdots$ $\cdots$ kth Row $\left(\begin{array}{c}m\\ 0\end{array}\right){z}_{k}-\left(\begin{array}{c}m\\ 1\end{array}\right){z}_{k-1}+\left(\begin{array}{c}m\\ 2\end{array}\right){z}_{k-2}+\cdots +{\left(-1\right)}^{m}\left(\begin{array}{c}m\\ m\end{array}\right){z}_{k-m}$ $\cdots$ $\cdots$ (n − 1)th Row $\left(\begin{array}{c}m\\ 0\end{array}\right){z}_{n-1}-\left(\begin{array}{c}m\\ 1\end{array}\right){z}_{n-2}+\left(\begin{array}{c}m\\ 2\end{array}\right){z}_{n-3}+\cdots +{\left(-1\right)}^{m}\left(\begin{array}{c}m\\ m\end{array}\right){z}_{n-1-m}$