In how many ways can a positive integer n be broken into a sum of k positive integers ? ( While representing the number as a sum the order in which the addends are arranged for each of the ways is not taken into consideration)

I know that we denote the number of ways to do this as $\displaystyle p(n,k)$ and I tried an inductive approach to the problem , i.e, I was able to figure out that ,

$\displaystyle p(n,1) = 1 $

$\displaystyle p(n,2) = \left\lceil\frac{n-1}{2}\right\rceil $

$\displaystyle p(n,3) = \sum_{i=1}^{\left\lfloor\frac{n}{2}\right\rfloor} {\left\lceil\frac{i-1}{2}\right\rceil + \left\lceil\frac{n-i-1}{2}\right\rceil }$

But I cant seem to figure out $\displaystyle p(n,4)$ and so on....And I need a closed-form solution, not recurrence relations..So, please help . Thanks in advance .