
    Design a function for an early intervention system that calculates the total number of significant dropout risk patterns by analyzing combinations of n risk factors, where only patterns with even-indexed combinations are considered valid predictors. The function should take the total number of monitored risk factors as input and return the sum of the statistically significant combination patterns that occur at even indices in the Pascal's triangle representation of risk factor combinations.
    

    
import math

def even_binomial_Coeff_Sum(n):
    """
    Design a function for an early intervention system that calculates the total number of significant dropout risk patterns by analyzing combinations of n risk factors, where only patterns with even-indexed combinations are considered valid predictors. The function should take the total number of monitored risk factors as input and return the sum of the statistically significant combination patterns that occur at even indices in the Pascal's triangle representation of risk factor combinations.
    

    """
import math

def even_binomial_Coeff_Sum(n):
    """
    Design a function for an early intervention system that calculates the total number of significant dropout risk patterns by analyzing combinations of n risk factors, where only patterns with even-indexed combinations are considered valid predictors. The function should take the total number of monitored risk factors as input and return the sum of the statistically significant combination patterns that occur at even indices in the Pascal's triangle representation of risk factor combinations.
    

    """
    return 1 << n - 1