Lagrange Inversion Counts $3\bar{5}241$-Avoiding Permutations
  In a previous paper, we showed that $3\bar{5}241$-avoiding permutations are counted by the unique sequence that starts with a 1 and shifts left under the self-composition transform. The proof uses a complicated bijection. Here we give a much simpler proof based on Lagrange inversion. 
David Callan
math.CO