We say a permutation `\sigma=\sigma_{1}\sigma_2\cdots\sigma_n` is log-concave if for any `2\le k\le n-1`, `\sigma_{k-1}\sigma_{k+1}<\sigma_k^2`.
We say a permutation `\sigma=\sigma_{1}\sigma_2\cdots\sigma_n` is weakly log-concave if for any `2\le k\le n-1`, `\sigma_{k-1}\sigma_{k+1}\le\sigma_k^2`.
For example, `\sigma=1\ 2\ 4\ 3` is not log-concave but weakly log-concave.
`a(n)` is the number of log-concave permutations of length `n`.
`b(n)` is the number of weakly log-concave permutations of length `n`.
Find `a(n)` and `b(n)`.