Editing Cayley's formula (section)

=== Generalizations ===

The following generalizes Cayley's formula to labelled forests:
Let ''T''<sub>''n'',''k''</sub> be the number of labelled forests on ''n'' vertices with ''k'' connected components,
such that vertices 1, 2, ..., ''k'' all belong to different connected components.
Then {{math|''T''<sub>''n'',''k''</sub> {{=}} ''k'' ''n''<sup>''n'' − ''k'' − 1</sup>}}.<ref>{{cite journal|last1=Takács|first1=Lajos|title=On Cayley's formula for counting forests|journal=Journal of Combinatorial Theory, Series A|date=March 1990|volume=53|issue=2|pages=321–323|doi=10.1016/0097-3165(90)90064-4|doi-access=free}}</ref>