
    Design an algorithm that analyzes student assessment sequences of length 2n, where each position represents a correct (1) or incorrect (0) answer, to identify sequences where the number of correct answers in the first half matches the number of correct answers in the second half. This pattern analysis helps determine if students maintain consistent performance levels throughout the assessment period.
    

    
def count_binary_seq(n):
    """
    Design an algorithm that analyzes student assessment sequences of length 2n, where each position represents a correct (1) or incorrect (0) answer, to identify sequences where the number of correct answers in the first half matches the number of correct answers in the second half. This pattern analysis helps determine if students maintain consistent performance levels throughout the assessment period.
    

    """
def count_binary_seq(n):
    """
    Design an algorithm that analyzes student assessment sequences of length 2n, where each position represents a correct (1) or incorrect (0) answer, to identify sequences where the number of correct answers in the first half matches the number of correct answers in the second half. This pattern analysis helps determine if students maintain consistent performance levels throughout the assessment period.
    

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