
    Design a function that determines the number of possible learning paths of length 2n, where each position represents a mastered (1) or unmastered (0) learning objective, such that the number of mastered objectives in the first half of the path equals the number of mastered objectives in the second half. This balanced achievement pattern ensures consistent learning progress across the entire educational sequence.
    

    
def count_binary_seq(n):
    """
    Design a function that determines the number of possible learning paths of length 2n, where each position represents a mastered (1) or unmastered (0) learning objective, such that the number of mastered objectives in the first half of the path equals the number of mastered objectives in the second half. This balanced achievement pattern ensures consistent learning progress across the entire educational sequence.
    

    """
def count_binary_seq(n):
    """
    Design a function that determines the number of possible learning paths of length 2n, where each position represents a mastered (1) or unmastered (0) learning objective, such that the number of mastered objectives in the first half of the path equals the number of mastered objectives in the second half. This balanced achievement pattern ensures consistent learning progress across the entire educational sequence.
    

    """
    nCr = 1
    res = 1
    for r in range(1, n + 1):
        nCr = nCr * (n + 1 - r) / r
        res += nCr * nCr
    return res