
    Design a medical analysis function that determines how many possible patient diagnostic patterns of length 2n exist, where the number of vital sign anomalies in the first half of the monitoring period equals the number of anomalies in the second half. Each vital sign reading is represented as either normal (0) or anomalous (1), and the total monitoring period is divided into two equal segments of length n.
    

    
def count_binary_seq(n):
    """
    Design a medical analysis function that determines how many possible patient diagnostic patterns of length 2n exist, where the number of vital sign anomalies in the first half of the monitoring period equals the number of anomalies in the second half. Each vital sign reading is represented as either normal (0) or anomalous (1), and the total monitoring period is divided into two equal segments of length n.
    

    """
def count_binary_seq(n):
    """
    Design a medical analysis function that determines how many possible patient diagnostic patterns of length 2n exist, where the number of vital sign anomalies in the first half of the monitoring period equals the number of anomalies in the second half. Each vital sign reading is represented as either normal (0) or anomalous (1), and the total monitoring period is divided into two equal segments of length n.
    

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