计算 $$D_{n+1}=\left|\begin{array}{cccc}
a^n & (a-1)^n & \cdots & (a-n)^n \\
a^{n-1} & (a-1)^{n-1} & \cdots & (a-n)^{n-1} \\
\vdots & \vdots & & \vdots \\
a & a-1 & \cdots & a-n \\
1 & 1 & \cdots & 1
\end{array}\right|
$$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$