设$m\geqslant n\geqslant1$,则
\begin{equation}
\sum_{k=m}^{m+n} \frac{(-1)^{k-1}(k-1)!}{(k-m)!(k-n)!(m+n-k)!}=0\nonumber
\end{equation}
I found a formula
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Origin www.cnblogs.com/zcmath/p/11320385.html
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