The number of \bar{2}413\bar{5}-avoiding permutations
  We answer a question of R. J. Mathar and confirm that the counting sequence for $\bar{2}413\bar{5}$-avoiding permutations is the Invert transform of the Bell numbers. The proof relies on a simple decomposition of these permutations and the known fact that $\bar{2}413$-avoiding permutations are counted by the Bell numbers. 
David Callan
math.CO