
    Given a patient's binary health profile of length 2n where each digit represents the presence (1) or absence (0) of specific risk factors, determine how many possible profile combinations exist where the sum of historical risk factors (first n digits) equals the sum of current risk factors (last n digits). This analysis helps identify patterns where past and present health indicators show similar risk levels.
    

    
def count_binary_seq(n):
    """
    Given a patient's binary health profile of length 2n where each digit represents the presence (1) or absence (0) of specific risk factors, determine how many possible profile combinations exist where the sum of historical risk factors (first n digits) equals the sum of current risk factors (last n digits). This analysis helps identify patterns where past and present health indicators show similar risk levels.
    

    """
def count_binary_seq(n):
    """
    Given a patient's binary health profile of length 2n where each digit represents the presence (1) or absence (0) of specific risk factors, determine how many possible profile combinations exist where the sum of historical risk factors (first n digits) equals the sum of current risk factors (last n digits). This analysis helps identify patterns where past and present health indicators show similar risk levels.
    

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