How can I calculate this determinant? Please can you give me some hints to deal with this :
$\displaystyle \text{Let } a_1, a_2, ..., a_n \in \mathbb{R}$
$\displaystyle \text{ Calculate } \det A \text{ where }$ $\displaystyle A=(a_{ij})_{1\leqslant i,j\leqslant n} \text{ and }$ $\displaystyle \lbrace_{\alpha_{ij}=0,\text{ otherwise}}^{\alpha_{ij}=a_i,\text{ for } i+j=n+1}$

Hint: The matrix looks like the following (for $n=4$; it gives the idea though):
$$
\begin{bmatrix}
0 & 0 & 0 & a_1\\
0 & 0 & a_2 & 0\\
0 & a_3 & 0 & 0\\
a_4 & 0 & 0 & 0
\end{bmatrix}
$$
What happens if you do a cofactor expansion in the first column? Try using induction.
