
    Given a student's learning sequence of length 2n where each position represents a completed (1) or incomplete (0) module, determine the total number of possible sequences where the count of completed modules in the first n modules equals the count of completed modules in the last n modules. This balanced completion pattern helps ensure consistent progress throughout the learning path.
    

    
def count_binary_seq(n):
    """
    Given a student's learning sequence of length 2n where each position represents a completed (1) or incomplete (0) module, determine the total number of possible sequences where the count of completed modules in the first n modules equals the count of completed modules in the last n modules. This balanced completion pattern helps ensure consistent progress throughout the learning path.
    

    """
def count_binary_seq(n):
    """
    Given a student's learning sequence of length 2n where each position represents a completed (1) or incomplete (0) module, determine the total number of possible sequences where the count of completed modules in the first n modules equals the count of completed modules in the last n modules. This balanced completion pattern helps ensure consistent progress throughout the learning path.
    

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