# The Summation of a Summation in Mathematica

I am trying to input $\sum_{a_1=1}^{n-1}$$\sum_{a_2=1}^{{a_1}-1}$$\sum_{a_3=1}^{{a_2}-1}$$\sum_{a_4=1}^{{a_3}-1}$$...f({{a_1},{a_2},{a_3},{a_4}...})$ into Mathematica. The number of sums should be a variable, not a constant.

I do not know how to nest a variable amount of sums without having to modify the code every time that variable changes. Could someone please give me an example?

With[{m = 4},

$$\sum_{\tt K[1]=1}^{\tt -1+n} \sum_{\tt K[2]=1}^{\tt -1+K[1]} \sum_{\tt K[3]=1}^{\tt -1+K[2]} \sum_{\tt K[4]=1}^{\tt -1+K[3]} {\tt F[K[1],K[2],K[3],K[4]]}$$