The function implements the following relationship from Nagaraja (2013)
for the symmetric triangular distribution:
$$
\text{E}[X_{r:n}^k] = \frac{n!}{(r-1)!(n-r)!} \left\{
(\frac{1}{2})^{k/2} B\left(\frac{1}{2}; \frac{k}{2} + r, n - r + 1\right) +
\sum_{j=0}^k (-1)^j \binom{k}{j} (\frac{1}{2})^{j/2}
B\left(\frac{1}{2}; \frac{j}{2} + n - r + 1, r\right)
\right\}.
$$
Here, \(B(x; a, b)\) is the incomplete Beta function.