In tree enumeration, we usually use the algorithms BFG and BFG --> TGA in cooperation; In the rooted tree case, we only need to use one of these. This is due to the fact that there are actually no restrictive conditions in the forests of rooted trees.
Here is an example of the case v = 10:
In other words, r10 = 719. In the next post I will show how the values r1-r9 are enumerated with the BFG, and will also show how the procedure of the case v = 10 is done with the algorithm BFG --> TGA.