Sum over j, k of -1^j+k by j+j Choose k+l by r Choose j by n Choose k by s+n-j-k Choose m-j

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Theorem

Let $l, m, n \in \Z$ be integers such that $n \ge 0$.

Then:

$\ds \sum_{j, \ k \mathop \in \Z} \paren {-1}^{j + k} \dbinom {j + k} {k + l} \dbinom r j \dbinom n k \dbinom {s + n - j - k} {m - j} = \paren {-1}^l \dbinom {n + r} {n + l} \dbinom {s - r} {m - n - l}$


Proof


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Sources

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