Your task is to count how many balanced parenthesis sequences of length n have at most k nested pairs of parenthesis.
You may assume that 2 \le n \le 16 and that 1 \le k \le n/2. The algorithm should be efficient in all these cases.
In a file brackets.py, implement a function count that returns the desired count.
def count(n, k):
# TODO
if __name__ == "__main__":
print(count(6, 1)) # 1
print(count(6, 2)) # 4
print(count(6, 3)) # 5
print(count(9, 1)) # 0
print(count(16, 4)) # 1094