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Let $L_n$ be the Lucas numbers, defined by $L_n = F_{n-1} + F_{n+1}$ where f is the Fibonacci numbers.

How to prove that

$L_{2n+1} = \displaystyle \sum_{k=0}^{\lfloor n + 1/2\rfloor}\frac{2n+1}{2n+1 - k}{2n+1 - k \choose k} $

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    Induction?${}{}$2011-07-04

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