I don't know exactly how they arrive at that expression, but it could be due to some conversion that is related to the double factorial.
See: https://en.wikipedia.org/wiki/Double_factorial
We can write the recurrence relation as K_l = \frac{2l}{2l+1} K_{l-1}.
We get the formula on the left-hand side when we substitute K_{l-1} with K_{l-1} = \frac{2l-1}{2(l-1)+1} K_{l-1-1}.
We can repeat this process until we get to l = 1 and K_0 (because of the assumption just below the grey box)...
I am not sure if this is what you are looking for.
In digital architectures, jitter of ring oscillators (ROs) are popular sources for entropy.
You can get an introduction about ROs here:
https://en.wikipedia.org/wiki/Ring_oscillator
ROs for hardware TRNGs are actively being researched.
Also...