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Count Balanced Binary Sequences

Write a function `count_balanced_binary_sequences(n)` that calculates the number of binary sequences of length `2n` such that the sum of the first `n` bits is equal to the sum of the last `n` bits.

#### Example Usage
```python [main.nopy]
count_balanced_binary_sequences(1)  # Output: 2
count_balanced_binary_sequences(2)  # Output: 6
count_balanced_binary_sequences(3)  # Output: 20
```
def count_balanced_binary_sequences(n):
    """
    Calculate the number of binary sequences of length 2n such that the sum of the first n bits
    is equal to the sum of the last n bits.

    Args:
    n (int): The half-length of the binary sequence.

    Returns:
    int: The count of such balanced binary sequences.
    """
    # Placeholder for the solution
    pass