
    Design a fraud detection algorithm that analyzes transaction security patterns of length 2n, where each security check generates either a pass (1) or fail (0) flag, and determines how many possible patterns exist where the number of passed checks in the first n validations equals the number of passed checks in the last n validations. The security checks include location verification, amount validation, activity pattern analysis, and other fraud prevention measures, with the goal of identifying balanced security validation sequences.
    

    
def count_binary_seq(n):
    """
    Design a fraud detection algorithm that analyzes transaction security patterns of length 2n, where each security check generates either a pass (1) or fail (0) flag, and determines how many possible patterns exist where the number of passed checks in the first n validations equals the number of passed checks in the last n validations. The security checks include location verification, amount validation, activity pattern analysis, and other fraud prevention measures, with the goal of identifying balanced security validation sequences.
    

    """
def count_binary_seq(n):
    """
    Design a fraud detection algorithm that analyzes transaction security patterns of length 2n, where each security check generates either a pass (1) or fail (0) flag, and determines how many possible patterns exist where the number of passed checks in the first n validations equals the number of passed checks in the last n validations. The security checks include location verification, amount validation, activity pattern analysis, and other fraud prevention measures, with the goal of identifying balanced security validation sequences.
    

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