Polynomial sequence?

[Jonathan Post]

Exactly. I would call this: "The number of  labeled rooted non-path-graph
trees on n nodes."


On 12/18/06, Joshua Zucker <joshua.zucker at gmail.com> wrote:
>
> 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.
> >
>
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