Use dynamic programming to store the number of unique BSTs for smaller values of `n` to avoid recomputation.

For each possible root `i` (from `1` to `n`), the number of unique BSTs is the product of the number of BSTs in the left subtree (with `i-1` nodes) and the right subtree (with `n-i` nodes).

Recognize that the solution follows the Catalan number sequence, where the `n`-th Catalan number is given by the formula: `C(n) = (2n)! / (n+1)!n!`.