Solving the Series: sum_{r=0}^{+\infty}1/(r*r!)

[mathsnerd]

I'm trying to find the sum of the following series and am a bit stuck:

sum_{r=0}^{+\infty}1/(r*r!)

It looks a bit like e^1 but the extra r in the denominator is causing problems. Can anyone help?

 

[dirk_mec1]

Where does this problem originates from?

 

[mathsnerd]

It's part of a birth rate for a birth and death process in a particular special case. The series looks like it should be summable but I can't think how to do it.