The explicit formula is: P[N_m=n]=(m/n)P[S_n=m] where P[N_m=n] is the probability the position m is hitted after exactly n steps, S_n=X_1+X_2+..X_n and  P[S_n=m] is the probablity after n steps the path to be at the position m. This last is well known and is given by P[S_n=m]=(n!/([(n+m)/2]![(n-m)/2]!))p^{(n+m)/2}q^{(n-m)/2}. This is true when n and m have the same parity else the probability is zero. Additionally m is positive and n is greater or equal to m. A similar eapression can be found for negative m.