
    Design a function for a learning management system that calculates the total number of possible study material combinations at even-numbered complexity levels, given a student's maximum proficiency parameter n. The function should use binomial coefficients to determine these combinations, considering only even-indexed difficulty levels up to the student's proficiency level.
    

    
import math

def even_binomial_Coeff_Sum(n):
    """
    Design a function for a learning management system that calculates the total number of possible study material combinations at even-numbered complexity levels, given a student's maximum proficiency parameter n. The function should use binomial coefficients to determine these combinations, considering only even-indexed difficulty levels up to the student's proficiency level.
    

    """
import math

def even_binomial_Coeff_Sum(n):
    """
    Design a function for a learning management system that calculates the total number of possible study material combinations at even-numbered complexity levels, given a student's maximum proficiency parameter n. The function should use binomial coefficients to determine these combinations, considering only even-indexed difficulty levels up to the student's proficiency level.
    

    """
    return 1 << n - 1