Find the number of all permutations of the set $\left\{ 1,2,...,2n \right\}$ such that does not have compact subsequence: $\langle i, \ i+1\rangle$ or $\langle i+1, \ i\rangle$ for all $1\le i\le 2n-1$.
I'm not sure if I translated above text properly, so please correct me if needed. For example, for $n=3$ permutation: $1,6,4,2,5,3$ is ok, but $4,6,2,1,3,5$ is not.
I've tried inclusion-exclusion principle, but it didn't help. Probably because I was always weak at this principle. How can I solve this problem?