
    Design a function that calculates the total number of balanced learning patterns in a student's personalized curriculum containing n modules, where balanced patterns occur at even-indexed combinations of learning activities. Given n learning modules, find the sum of binomial coefficients at even indices to determine the optimal distribution of balanced learning activities.
    

    
import math

def even_binomial_Coeff_Sum(n):
    """
    Design a function that calculates the total number of balanced learning patterns in a student's personalized curriculum containing n modules, where balanced patterns occur at even-indexed combinations of learning activities. Given n learning modules, find the sum of binomial coefficients at even indices to determine the optimal distribution of balanced learning activities.
    

    """
import math

def even_binomial_Coeff_Sum(n):
    """
    Design a function that calculates the total number of balanced learning patterns in a student's personalized curriculum containing n modules, where balanced patterns occur at even-indexed combinations of learning activities. Given n learning modules, find the sum of binomial coefficients at even indices to determine the optimal distribution of balanced learning activities.
    

    """
    return 1 << n - 1