计算 $\left|\begin{array}{ccccc}
a_0 & 1 & 1 & \cdots & 1 \\
1 & a_1 & 0 & \cdots & 0 \\
1 & 0 & a_2 & \cdots & 0 \\
\cdots & \cdots & \cdots & \\
1 & 0 & 0 & \cdots & a_n
\end{array}\right| $
$ \left(a_1 a_2 \cdots a_n \neq 0\right)$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$
$\text{E.}$
$\text{F.}$