For example, the coefficient of \(x^3\) will come from the n ways of multiplying the coefficients \(x^3, x^0, ..., x^0\) and \(x^2, x^1, x^0, ..., x^0\) and \(x^1, x^1, x^1, x^0,..., x^0\text{.}\) This is equivalent to finding the number of ways to write the number k as a sum of nonnegative integers. The possible set of nonnegative integers is {0,1,2,...,k} and one way to count the combinations is to separate k *’s by n-1 |’s. For example, if k = 3 then *|*|* means \(x^1 x^0 x^2 = x^3\text{.}\) Similarly for k = 5 and |**|*|**| implies \(x^0 x^2 x^1 x^2 x^0 = x^5\text{.}\) The number of ways to interchange the identical *’s among the idential |’s is \(\binom{n+k-1}{k}\text{.}\)