A forest is an acyclic graph (i.e., a graph without any graph cycles). Forests therefore consist only of (possibly
disconnected) trees, hence the name "forest."

A forest with
components and
nodes has graph edges.
The numbers of forests on ,
2, ... nodes are 1, 2, 3, 6, 10, 20, 37, ... (OEIS A005195).

A graph can be tested to determine if it is acyclic (i.e., a forest) in the Wolfram Language using AcylicGraphQ[g].
A collection of acyclic graphs is available as GraphData["Acyclic"]
or GraphData["Forest"].

The total numbers of trees in all the forests of orders , 2, ... are 1, 3, 6, 13, 24, 49, 93, 190, 381, ... (OEIS
A005196). The average numbers of trees are
therefore 1, 3/2, 2, 13/6, 12/5, 49/20, 93/37, 5/2, ... (OEIS A095131
and A095132).

The triangle of numbers of -node
forests containing
trees is 1; 1, 1; 1, 1, 1; 2, 2, 1, 1; 3, 3, 2, 1, 1; ... (OEIS A095133).