
    In a personalized learning analytics system, develop a function that calculates the total weight of balanced assessment combinations from a student's n performance indicators, where only combinations at even indices are considered significant for learning path optimization. The balanced combinations are represented by binomial coefficients, and the function should return their sum for even indices only.
    

    
import math

def even_binomial_Coeff_Sum(n):
    """
    In a personalized learning analytics system, develop a function that calculates the total weight of balanced assessment combinations from a student's n performance indicators, where only combinations at even indices are considered significant for learning path optimization. The balanced combinations are represented by binomial coefficients, and the function should return their sum for even indices only.
    

    """
import math

def even_binomial_Coeff_Sum(n):
    """
    In a personalized learning analytics system, develop a function that calculates the total weight of balanced assessment combinations from a student's n performance indicators, where only combinations at even indices are considered significant for learning path optimization. The balanced combinations are represented by binomial coefficients, and the function should return their sum for even indices only.
    

    """
    return 1 << n - 1