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Prove inequality:

$ S(n,k-1)\cdot S(n,k+1) \le (S(n,k))^2 $

for $n,k\in\mathbb{N}$, where $S(n,k)$ is the Stirling number of the second kind.

I think induction is the last resort. I don't know if it will work but I rather want to avoid it.

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