Mathematics · Permutations

A permutation σ of [n] = {1, 2, ..., n} is called irreducible if the restriction σ| [k] is not a permutation of [k] for any 1 ≤ k < n. Let a n be the number of irreducible permutations of [n]. If a 1 = 1, a 2 = 1, and a 3 = 3, then the value of a 4 is:

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A permutation &sigma; of [n] = {1, 2, ..., n} is called irreducible if the restriction &sigma;| [k] is not a permutation of [k] for any 1 &le; k < n. Let a n be the number of irreducible permutations of [n]. If a 1 = 1, a 2 = 1, and a 3 = 3, then the value of a 4 is: