Writing an expression in summation notation

[SithsNGiggles]

How would I write

1 + n + n(n - 1) + n(n - 1)(n - 2) + ･･･ + n!

in sigma notation? If it's possible.

 

[JHamm]

\sum_{i = 0}^{n} \frac{n!}{(n - i)!}