Necessary conditions for reversed Dickson polynomials of the second kind to be permutational

In this paper, we present several necessary conditions for the reversed Dickson polynomial En(1,x)En(1,x) of the second kind to be a permutation of FqFq. In particular, we give explicit evaluation of the sum ∑a∈FqEn(1,a)∑a∈FqEn(1,a).