Prove inequality:
$ S(n,k1)\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.
Prove inequality: $ S(n,k1)\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. 

