I'm pretty sure this is unknown, though it would be great if I'm wrong.

Asymptotically there is a function $A(n)$ such that $M(n,n/2+t)\sim  e^{-2t^2}A(n)$ for $t=o(n^{1/2})$, which follows from [this paper][1].

It is also known to be true for $n\le 20$.

  [1]: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v12i1r29