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

This is pretty close https://en.wikipedia.org/wiki/Lambert_W_function#Asymptotic_expansions ... integrate this ? — Donald Splutterwit, Oct 07 '20 at 10:33
It's related to the Lambert W-function https://en.wikipedia.org/wiki/Lambert_W_function — Angina Seng, Oct 07 '20 at 10:34

score 1 · Accepted Answer · answered Oct 07 '20 at 12:07

1

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

answered Oct 07 '20 at 12:07

Claude Leibovici

1 Answers1