I was reading these notes on mathematical population genetics, and they have a derivation of the mean time ($\tau$) until either of the alleles fix, in the Wright-Fisher model. They get, in page 12, after equation (2.1.10):
$$E(\tau|H_0) = 2NH_0$$
where $H_0$ is the initial heterozygocity, defined there as:
$$H_n = \frac{2X_n (2N-X_n)}{2N(2N-1)}$$
although, sometimes it is defined instead as $H_n = \frac{2X_n (2N-X_n)}{(2N)^2}$. However, as said here, Kimura and Ohta showed
$$E(\tau|p)=-4N\cdot \left((1-p)\cdot \ln(1-p)+p\cdot \ln(p)\right)$$
where $p = X_0/N$ is the initial frequency of the allele.
So, I just want to check if the notes I'm reading are wrong, or I'm just missing something?