How many ways can you insert a series of values into a BST to form a specific tree?

Question

This earlier question asked how many ways there were to insert the values 1 - 7 into a binary search tree that would result in the following tree:

       4
              


        

Answer 1

This is an interesting question. I implemented this idea in python and this recursion plus memorization has pretty good performance. The "seq" is the input list of unique integers

def answer(seq):
    from math import factorial
    BStore = dict() # store binomsial coefficient
    Store = dict() # store the recusion step 
    def TreeGenerator(a,L): # for a given number a and a list L, this functions returns the left tree (a list) and the right tree (a list)
        LT = []
        RT = []
        for i in L:
            if i