Take the number $192$ and multiply it by each of $1$, $2$, and $3$:

$$\begin{array}{rl}192\times 1& =192\\ 192\times 2& =384\\ 192\times 3& =576\end{array}$$

By concatenating each product we get the $1$ to $9$ pandigital, $192384576$. We will call $192384576$ the concatenated product of $192$ and $(1,2,3)$.

The same can be achieved by starting with $9$ and multiplying by $1$, $2$, $3$, $4$, and $5$, giving the pandigital, $918273645$, which is the concatenated product of $9$ and $(1,2,3,4,5)$.

What is the largest $1$ to $9$ pandigital $9$-digit number that can be formed as the concatenated product of an integer with $(1,2,\dots ,n)$ where $n>1$?