
    In an adaptive learning system, determine the number of possible ways a student can answer a sequence of 2n questions (with binary correct/incorrect outcomes) where the number of correct answers in the first half of the assessment equals the number of correct answers in the second half. This pattern analysis helps evaluate whether the student's performance remains consistent across the assessment duration.
    

    
def count_binary_seq(n):
    """
    In an adaptive learning system, determine the number of possible ways a student can answer a sequence of 2n questions (with binary correct/incorrect outcomes) where the number of correct answers in the first half of the assessment equals the number of correct answers in the second half. This pattern analysis helps evaluate whether the student's performance remains consistent across the assessment duration.
    

    """
def count_binary_seq(n):
    """
    In an adaptive learning system, determine the number of possible ways a student can answer a sequence of 2n questions (with binary correct/incorrect outcomes) where the number of correct answers in the first half of the assessment equals the number of correct answers in the second half. This pattern analysis helps evaluate whether the student's performance remains consistent across the assessment duration.
    

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