
    Given a vehicle's diagnostic sequence of length 2n from multiple sensors (where each sensor reports either 0 for normal or 1 for anomaly), determine how many possible diagnostic patterns exist where the number of anomalies detected in the first n readings equals the number of anomalies in the last n readings. This pattern matching helps identify balanced wear patterns and system symmetry in vehicle maintenance diagnostics.
    

    
def count_binary_seq(n):
    """
    Given a vehicle's diagnostic sequence of length 2n from multiple sensors (where each sensor reports either 0 for normal or 1 for anomaly), determine how many possible diagnostic patterns exist where the number of anomalies detected in the first n readings equals the number of anomalies in the last n readings. This pattern matching helps identify balanced wear patterns and system symmetry in vehicle maintenance diagnostics.
    

    """
def count_binary_seq(n):
    """
    Given a vehicle's diagnostic sequence of length 2n from multiple sensors (where each sensor reports either 0 for normal or 1 for anomaly), determine how many possible diagnostic patterns exist where the number of anomalies detected in the first n readings equals the number of anomalies in the last n readings. This pattern matching helps identify balanced wear patterns and system symmetry in vehicle maintenance diagnostics.
    

    """
    nCr = 1
    res = 1
    for r in range(1, n + 1):
        nCr = nCr * (n + 1 - r) / r
        res += nCr * nCr
    return res