we are given a function $$f(n,k) = \sum_{s=0}^{s=n} \sum_{r=s}^{r=n} \sum_{t=0}^{t=s} \frac {\binom nr \binom rs \binom st t(3k^2)^{t/2} I(t)}{(s+1)} $$. $ (n c r)$ known as Binomial Coefficient denotes the number of ways to choose an unordered subset of r elements from a fixed set of n elements.
$$I(x) = \begin{cases} 1 & x \equiv 0\ (mod\ 4) \\ 0 & x \equiv 1\ (mod\ 4) \\ -1 & x \equiv 2\ (mod\ 4) \\ 0 & x \equiv 3\ (mod\ 4) \\ \end{cases} $$.
We have to find the value of f(n,k) (modulo 10^9+21). Integers n and k are given to us.
Can anyone please help to simplify the above-given function?