Base cases:
$F(n,k,d) = 0$ if $d=0$ and $n>0$
$F(n,k,d) = 1$ if $n=0$
Expression:
$$F(n,k,d) = \sum_{s=0}^{\min(k,n)}\binom{n}{s}F(n-s,k,d-1)$$
I am trying to compute the value of $F(n,k,10)$ where $n$ is a large positive integer and $k$ is a positive integer (can be small or large). As you can see, the inner loop can possibly take a very long time. Is there any way I can simplify?