def part(n):
    """Return the number of partitions of positive integer n.

    >>> part(5)
    7
    >>> part(10)
    42
    >>> part(15)
    176
    >>> part(20)
    627
    """
    def helper(ls, n):
        if n == 0:
            return 1
        if len(ls) == 0 or n < 0:
            return 0
        return helper(ls[1:], n) + helper(ls, n-ls[0])
    integers = []
    for i in range(n+1):
        if i > 0:
            integers.append(i)
    return helper(integers, n)