expected time for all balls to be put in urn 2 Ehrenfest model

Question

I am trying to calculate the maximal hitting time of the Lazy Random Walk on the $n$-dimensional hypercube(I know it is $2^n$). I'm using the Ehrenfest urn model. Let $X_t$ be the number of balls in Urn 1 in time $t$, $\tau_x=\inf\{t>0|X_t=x\}$ the hitting time of $x$. The question is how to calculate the expected time, so that starting with all balls in Urn $1$, we end with all the balls in Urn $2$ and more precisely $\mathbb{E}_n(\tau_0)=$?

Thank you in advance!

Answer 1

This is solved Section 4 of Blom's (very short) 1989 article: Mean Transition Times for the Ehrenfest urn Model