On the number of even permutations with roots

Let π be an even permutation on n letters which has a root, that is, there exists an even permutation ξ such that π = ξ. In this article the number of this kind of π is found by using generating function techniques. This is the analogue of a result for the number of all permutations with roots.

[1]  Miklós Bóna,et al.  Permutations with roots , 2000, Random Struct. Algorithms.

[2]  Nicolas Pouyanne.  On the Number of Permutations Admitting an m-th Root , 2002, Electron. J. Comb..

[3]  Joseph Blum,et al.  Enumeration of the Square Permutations in Sn , 1974, J. Comb. Theory, Ser. A.

[4]  E. Bender.  Asymptotic Methods in Enumeration , 1974 .