My acceleration is using the formula of minors of the inverse:
$\det{A}=\frac{\det{A(\alpha)}}{\det{A^{-1}(\alpha')}}$
In which, $\alpha\subset\{1,2,...,n\}$, $\alpha'$ is its complement and $A(\alpha)$ is a sub-matrix of $A$.
This way I need only to compute the determinants of two n/2-by-n/2 matrices.