
    Develop a function for a bank's fraud detection system that calculates the total risk score by summing the coefficients of even-indexed transaction patterns from n possible combinations. Given n transaction patterns, the system needs to evaluate only the even-indexed pattern combinations (based on binomial coefficients) as they historically correlate with fraudulent activities.
    

    
import math

def even_binomial_Coeff_Sum(n):
    """
    Develop a function for a bank's fraud detection system that calculates the total risk score by summing the coefficients of even-indexed transaction patterns from n possible combinations. Given n transaction patterns, the system needs to evaluate only the even-indexed pattern combinations (based on binomial coefficients) as they historically correlate with fraudulent activities.
    

    """
import math

def even_binomial_Coeff_Sum(n):
    """
    Develop a function for a bank's fraud detection system that calculates the total risk score by summing the coefficients of even-indexed transaction patterns from n possible combinations. Given n transaction patterns, the system needs to evaluate only the even-indexed pattern combinations (based on binomial coefficients) as they historically correlate with fraudulent activities.
    

    """
    return 1 << n - 1