Putnam 1992 B5

Let $D_n$ denote the value of the $(n-1) \times (n-1)$ determinant $$\left[ \begin{array}{cccccc} 3 & 1 & 1 & 1 & \cdots & 1 \\ 1 & 4 & 1 & 1 & \cdots & 1 \\ 1 & 1 & 5 & 1 & \cdots & 1 \\ 1 & 1 & 1 & 6 & \cdots & 1 \\ \vdots & \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & 1 & 1 & 1 & \cdots & n+1 \end{array} \right].$$ Is the set $\left\{ \frac{D_n}{n!} \right\}_{n \geq 2}$ bounded?