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Nth Catalan Number

The Catalan numbers are a sequence of natural numbers that have many applications in combinatorial mathematics. The nth Catalan number can be defined recursively as:

\[
C(n) = \sum_{i=0}^{n-1} C(i) \cdot C(n-i-1), \text{ for } n > 0, \text{ and } C(0) = 1.
\]

Write a Python function `catalan_number(n)` that computes the nth Catalan number using recursion.

#### Example Usage
```python [main.nopy]
print(catalan_number(0))  # Output: 1
print(catalan_number(3))  # Output: 5
print(catalan_number(5))  # Output: 42
```

#### Constraints
- The input `n` will be a non-negative integer.
- The function should use recursion to compute the result.
def catalan_number(n):
    """
    Compute the nth Catalan number using recursion.

    Args:
        n (int): The index of the Catalan number to compute.

    Returns:
        int: The nth Catalan number.
    """
    # Base case
    if n == 0:
        return 1

    # Recursive case
    # Placeholder for the recursive computation
    pass
Intermediate recursionmath
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