The numbers of acyclic graphs (forests) on , 2, ... are 1, 2, 3, 6, 10, 20, 37, 76, 153, ... (OEIS A005195), and the corresponding numbers of connected
acyclic graphs (trees) are 1, 1, 1, 2, 3, 6, 11, 23, 47, 106, ... (OEIS A000055).

A graph can be tested in the Wolfram Language to see if it is acyclic using AcyclicGraphQ[g],
and a collection of acyclic graphs are available as GraphData["Acyclic"].