Simpler expression for $\sum_{k=1}^{n}{k!}$

Question

Is there a way to express $$\sum_{k=1}^{n}{k!}$$ in a simpler way that doesn't use sums up to n ?

I've searched for this around the web and found that the subfactorial function can help with this, however, it's also defined by a sum, so this does not meet the criteria.

Answer 1

If you plug it in wolfram Alpha, you get an alternate expression without the subfactorial, but it has the gamma function which by definition is still a sum (integral).

http://www.wolframalpha.com/input/?i=summation+from+1+to+n+of++k+factorial+