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Maybe something like this

sage: def banana(n): 
....:     for P in posets(n): 
....:         if not P.is_connected(): 
....:             continue 
....:         H = P.hasse_diagram() 
....:         if H.to_undirected().is_tree(): 
....:             continue 
....:         dg = H.transitive_closure() 
....:         if any(dg.degree(x) == n - 1 for x in dg): 
....:             continue 
....:         yield P