Calculer : \[ D_n = \begin{vmatrix} 1 & a_1 & a_1^2 & \cdots & a_1^{n-2} & a_1^n \\ 1 & a_2 & a_2^2 & \cdots & a_2^{n-2} & a_2^n \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ 1 & a_n & a_n^2 & \cdots & a_n^{n-2} & a_n^n \end{vmatrix} \]