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.
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?