For $n \geq 2,$ consider the following square matrix of order $(n-1)$
\begin{array}{cccccc}
3 & 1 & 1 & 1 & & 1 \\
1 & 4 & 1 & 1 & \dots & 1 \\
1 & 1 & 5 & 1 & \cdots & 1 \\
1 & 1 & 1 & 6 & & 1 \\
& & & & \ddots & \vdots \\
1 & 1 & 1 & 1 & \cdots & n+1
\end{array}
Find its determinant using only elementary row operations and denote it by $A_{n}$. Hence or otherwise, check whether the sequence $\left\{^{A_{n}} / n_{1}\right\}_{n>2}$ is bounded
