
    Given a patient's daily medication schedule tracking record of length 2n, where each entry is marked as 1 for a taken dose or 0 for a missed dose, determine the number of possible scenarios where the count of medications taken in the first n time slots equals the count of medications taken in the last n time slots. This analysis helps identify balanced medication adherence patterns between different parts of the day.
    

    
def count_binary_seq(n):
    """
    Given a patient's daily medication schedule tracking record of length 2n, where each entry is marked as 1 for a taken dose or 0 for a missed dose, determine the number of possible scenarios where the count of medications taken in the first n time slots equals the count of medications taken in the last n time slots. This analysis helps identify balanced medication adherence patterns between different parts of the day.
    

    """
def count_binary_seq(n):
    """
    Given a patient's daily medication schedule tracking record of length 2n, where each entry is marked as 1 for a taken dose or 0 for a missed dose, determine the number of possible scenarios where the count of medications taken in the first n time slots equals the count of medications taken in the last n time slots. This analysis helps identify balanced medication adherence patterns between different parts of the day.
    

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