exponential generating function of $n^n$

Question

Question is simple: What's the EGF of $n^n$? I would also like to know the regular generating function too, but the first is a priority.

Standard operations on GF's have failed to yield adequate results with me

Answer 1

With an offset of $1 $, the EGF is $$1-e^{W(-x)}$$ where $W(.) is the principal branch of Lambert function.