
    Design an algorithm to determine how many possible learning paths exist for a student completing 2n modules, where each module is either completed (1) or incomplete (0), such that the number of completed modules in the first n modules equals the number of completed modules in the last n modules. This balanced completion pattern ensures consistent learning progress across both halves of the curriculum.
    

    
def count_binary_seq(n):
    """
    Design an algorithm to determine how many possible learning paths exist for a student completing 2n modules, where each module is either completed (1) or incomplete (0), such that the number of completed modules in the first n modules equals the number of completed modules in the last n modules. This balanced completion pattern ensures consistent learning progress across both halves of the curriculum.
    

    """
def count_binary_seq(n):
    """
    Design an algorithm to determine how many possible learning paths exist for a student completing 2n modules, where each module is either completed (1) or incomplete (0), such that the number of completed modules in the first n modules equals the number of completed modules in the last n modules. This balanced completion pattern ensures consistent learning progress across both halves of the curriculum.
    

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