Catalan number

In combinatorics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. The nth Catalan number C_n (0-indexed) is defined by the recurrence: C_0 = 1 C_n = sum_{i=0}^{n-1} C_i * C_{n-1-i} for n >= 1 Your task is to implement the function `catalan_number(n: int) -> int` that returns C_n. The input n will be a non-negative integer. Use dynamic programming (or any correct method) to compute the value efficiently. The result will fit within the standard integer range in Python. You must write the function with the exact signature `catalan_number(n: int) -> int`.

>>> catalan_number(0)
1
>>> catalan_number(1)
1
>>> catalan_number(2)
2
>>> catalan_number(3)
5
>>> catalan_number(10)
16796