
    In a hospital's vital signs monitoring system, determine how many possible sequences of 2n patient status readings can occur where the count of abnormal readings in the first n timepoints exactly matches the count in the last n timepoints. Each reading is binary (normal/abnormal), and this pattern recognition helps identify stable versus deteriorating patient conditions over equal time intervals.
    

    
def count_binary_seq(n):
    """
    In a hospital's vital signs monitoring system, determine how many possible sequences of 2n patient status readings can occur where the count of abnormal readings in the first n timepoints exactly matches the count in the last n timepoints. Each reading is binary (normal/abnormal), and this pattern recognition helps identify stable versus deteriorating patient conditions over equal time intervals.
    

    """
def count_binary_seq(n):
    """
    In a hospital's vital signs monitoring system, determine how many possible sequences of 2n patient status readings can occur where the count of abnormal readings in the first n timepoints exactly matches the count in the last n timepoints. Each reading is binary (normal/abnormal), and this pattern recognition helps identify stable versus deteriorating patient conditions over equal time intervals.
    

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