🚀 go-pugleaf

Dear Netters:
    I have a question about random walk.
    Those interested, would you please reply me by e-mail?
    The problem is :
    If a drunk man start from a position x=0 when time is t=0, in the every
following unit time interval he takes either a right step or a left step and
 position of the drunk man is limited to N steps from the starting
point(x=0), we want to know, the drunk man has how many different ways to
arrive at x=i(i<N) when time t=n(n>N)?  An expression in terms of N and n
is needed.
    This is equivalent to ask the number of random walk in a limited distance.
    Thank you for you attention and I am looking forward to receiving your 
answers.
                                                    Sincerely,

                                                    QZ