Implement Fast Hartley Transform
First of all, I'm pretty sure that $H_e(k)$ is the $N/2$ point DHT of the even elements of the original sequence to be transformed, not of $H(k)$. The same is true for $H_o(k)$. As for the index $k$, when used with $H_e(k)$ and $H_o(k)$, it is evaluated modulo $N/2$, so it ranges from $0$ to $N/2-1$. So the index $k=N/2$ is mapped to the index $0$ when evaluating $H_e(k)$ and $H_o(k)$.