------
## 最终结论
```python
def count_binary_seq(n):
    from math import comb
    
    total_count = 0
    
    for k in range(n + 1):
        total_count += comb(n, k) * comb(n, k)
    
    return float(total_count)

# Test cases
assert count_binary_seq(1) == 2.0
assert count_binary_seq(2) == 6.0
assert count_binary_seq(3) == 20.0
```