Nothing, as far as I can tell*. That is, I think you're right. Congratulations! You've found a mistake in H, which is not that easy to do**. (I suspect it was more of a typo. He probably left out a twist or something, but I'm not really sure what he intended.)
- Actually, I only checked your $h^0$. It does seem that there is a jump in $h^1$ and $h^2$ as Sándor points out. So his explanation 1 of the typo seems highly plausible.
** I have to confess that I'm amazed by just how few errors there are.