The follow up question to the previous blog https://mirror.codeforces.com/blog/entry/78752

I still don't really understand the permutation formula for numbers with duplicates. (I googled but didn't get the intuition besides it saying to account for repetitions we divide). Sorry for the silly question.

Calculate the number of ways a rooted tree can be reconstructed (by adding one node at a time) such that it remains connected.