Polynomial sequence?

[Joshua Zucker]

If I understand correctly, the observation below also means that it is
the number of labeled rooted trees with n nodes except for the ones
that are some particular tree (say the one where the nodes are all in
a straight line)?

--Joshua Zucker

On 12/17/06, Jonathan Post <jvospost3 at gmail.com> wrote:
> a(n) = (n+1)^n - n! = A000169(n) - A000142(n).
>
>  Since A000169 is the number of labeled rooted trees with n nodes, you
> should be able to come up with a pure graph enumeration description of your
> sequence.  When you do, I agree that it is nice.
>