Find a simplified form for $n!+(n-1)!+(n-2)!+(n-3)!+ \dots +1!$ . Find a simplified form for $n!+(n−1)!+(n−2)!+(n−3)!+\dots+1!$ .

By simplified, I mean that there should not be "..." in the equation.

If there isn't one, prove it. Thanks!

Edit 1: Is it possible not to have $\sum$ in it?
This number is just
$$1111\cdots1111$$
with $n+1$ digits in factorial number system.
∑(2-k)!

This is a simplified form of n!+(n−1)!+(n−2)!+(n−3)!+...+1!