I need to prove such a formula:
$$
{n\brace k-1}\cdot{n\brace k+1}\leqslant{n\brace k}^2
$$
Where {} are Stirling numbers of the second kind.
(number of ways to partition a set of $n$ objects into $k$ non-empty subsets).
I tried to figure out some combinatorial proof, but failed.
I'd be grateful for any help.