
    Write a function to analyze patient post-discharge monitoring data of length 2n days, where each day is marked as compliant (1) or non-compliant (0) with prescribed care protocols, and determine the count of all possible monitoring sequences where the number of compliant days in the first n days equals the number of compliant days in the last n days. This analysis helps identify balanced adherence patterns that may indicate stable recovery trajectories.
    

    
def count_binary_seq(n):
    """
    Write a function to analyze patient post-discharge monitoring data of length 2n days, where each day is marked as compliant (1) or non-compliant (0) with prescribed care protocols, and determine the count of all possible monitoring sequences where the number of compliant days in the first n days equals the number of compliant days in the last n days. This analysis helps identify balanced adherence patterns that may indicate stable recovery trajectories.
    

    """
def count_binary_seq(n):
    """
    Write a function to analyze patient post-discharge monitoring data of length 2n days, where each day is marked as compliant (1) or non-compliant (0) with prescribed care protocols, and determine the count of all possible monitoring sequences where the number of compliant days in the first n days equals the number of compliant days in the last n days. This analysis helps identify balanced adherence patterns that may indicate stable recovery trajectories.
    

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