Let $X_n$ denote the number of acyclic connected gentle tree algebras (given by quiver and admissible relations over a field) with $n$ simple modules. Those are also exactly the connected quiver algebras derived equivalent to a Dynkin type $A_n$ path algebra.
Question: Is there a nice formula for $X_n$?
ChatGPT suggests via some program that the sequence is equal to https://oeis.org/A296532 (but it can not prove it). Is this true?
