Some care is needed when encountering pseudotrees as some authors use the term to mean "a pseudotree that is not a tree." Such graphs are perhaps better
known as connected unicyclic graphs for clarity.

The numbers of pseudotrees on 1, 2, 3, ... vertices are 1, 1, 2, 4, 8, 19, 44, 112, ... (OEIS A005703), the first few of which
are illustrated above.