
    Design a fraud detection algorithm that analyzes credit card transaction security patterns of length 2n, where each position represents a pass/fail security check result, and determines how many possible patterns exist where the number of failed checks in the first n historical validations equals the number of failed checks in the n most recent validations. The matching patterns could indicate potential systematic fraud attempts that need investigation.
    

    
def count_binary_seq(n):
    """
    Design a fraud detection algorithm that analyzes credit card transaction security patterns of length 2n, where each position represents a pass/fail security check result, and determines how many possible patterns exist where the number of failed checks in the first n historical validations equals the number of failed checks in the n most recent validations. The matching patterns could indicate potential systematic fraud attempts that need investigation.
    

    """
def count_binary_seq(n):
    """
    Design a fraud detection algorithm that analyzes credit card transaction security patterns of length 2n, where each position represents a pass/fail security check result, and determines how many possible patterns exist where the number of failed checks in the first n historical validations equals the number of failed checks in the n most recent validations. The matching patterns could indicate potential systematic fraud attempts that need investigation.
    

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