xiaoyaowudi's blog线性求欧拉数单项 & 具体数学 6.67
证明:
$\displaystyle\sum_{k}\left\{\begin{matrix}n+1\\k+1\end{matrix}\right\}\binom{n-k}{m-k}\left(-1\right)^{m-k}k!=\left\langle\begin{matrix}n\\m\end{matrix}\right\rangle$
具体数学 5.83
证明:
$\displaystyle\sum_{j,k} (-1)^{j+k}\binom{j+k}{k+l}\binom{r}{j}\binom{n}{k}\binom{s+n-j-k}{m-j}=\left(-1\right)^l\binom{n+r}{n+l}\binom{s-r}{m-n-l}$