Round table exponential generating function

Question

Let $r(n)$ be the number of different ways to seat $n$ people around a round table. Find the exponential generating function for $r$.

I believe $r(n)$ is just equal to $n!/n = (n-1)!$. So then I plugged it into the equation for the exponential generating function and I get that $R(x)= \sum _{n \ge 0} x^n/n$ which doesn't simplify into anything nice. Did I approach this problem correctly? Any help is appreciated.

Answer 1

Note that $$\frac{d}{dx}{\sum{\frac{x^n}{n}}}=\sum{x^{n-1}}=1+x+x^2+\cdots=\frac{1}{1-x}$$ so integrating gives $$-\ln(1-x)$$ as the generating function.

In other words, you were right, but it does simplify.