The number of permutations of {1,2,...,n,1,2,...,n} with the property that there are k numbers between the two k's in the set for k=1,...,n, as n runs through the positive integers congruent to -1 or 0 mod 4.

A268536

The number of permutations of {1,2,...,n,1,2,...,n} with the property that there are k numbers between the two k's in the set for k=1,...,n, as n runs through the positive integers congruent to -1 or 0 mod 4.