[seqfan] Re: Number of ways to decompose K_2n into n spanning trees (unlabeled nodes)

[Giovanni Resta]

  07/08/2015 21:27, Andrew Weimholt:
> So far, I have
>
> 1 way to decompose k0 (null graph) into 0 trees.
> 1 way to decompose k2 into 1 tree.
> 1 way to decompose k4 into 2 trees.
I think I'm  missing something.

K_4 has 4 nodes. I always make confusion between labeled and unlabeled
graphs, but here I expected at least two decompositions, instead of one.
Namely, a decomposition into two trees of 2 nodes each and one
decomposition into a tree of 3 nodes and a tree of 1 node.
Could you explain better your sequence ?
Giovanni