
    In a personalized learning system with n difficulty levels, calculate the total weighted importance score by summing the assessment values at even-numbered transition points between levels. Each transition point's value is determined by its corresponding binomial coefficient, representing the number of possible learning paths through that particular milestone.
    

    
import math

def even_binomial_Coeff_Sum(n):
    """
    In a personalized learning system with n difficulty levels, calculate the total weighted importance score by summing the assessment values at even-numbered transition points between levels. Each transition point's value is determined by its corresponding binomial coefficient, representing the number of possible learning paths through that particular milestone.
    

    """
import math

def even_binomial_Coeff_Sum(n):
    """
    In a personalized learning system with n difficulty levels, calculate the total weighted importance score by summing the assessment values at even-numbered transition points between levels. Each transition point's value is determined by its corresponding binomial coefficient, representing the number of possible learning paths through that particular milestone.
    

    """
    return 1 << n - 1