Lagrange inversion counts $3\overline5241$-avoiding permutations
Journal of integer sequences, Tome 14 (2011) no. 9.

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Summary: In a previous paper, we showed that 35241-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.
Classification : 05A15
Keywords: eigensequence, barred pattern, Lagrange inversion
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     author = {Callan, David},
     title = {Lagrange inversion counts $3\overline5241$-avoiding permutations},
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Callan, David. Lagrange inversion counts $3\overline5241$-avoiding permutations. Journal of integer sequences, Tome 14 (2011) no. 9. http://geodesic.mathdoc.fr/item/JIS_2011__14_9_a2/