  In the work [4] tree-rooted planar cubic maps with marked directed edge (not
in this tree) were enumerated. The number of such objects with $2n$ vertices is
$C_{2n}\cdot C_{n+1}$, where $C_k$ is Catalan number. In this work a marked
directed edge is not demanded, i.e. we enumerate tree-rooted planar cubic maps.
Formulas are more complex, of course, but not significantly.
