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Combinatorial identity


Let n\in \mathbb{N}^*. Prove the identity
\displaystyle \sum_{j+h=n \ j \geq h} (-1)^h \frac{1}{j}\begin{pmatrix}j\\ h \end{pmatrix}2^{j-h}=\frac{2}{n}.
Ioan Tomescu, Romanian TST 1991

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