Hjort and Stoltenberg have discovered the square root of 2¦Ð

Probability Proofs for Stirling (and More):
the Ubiquitous Role of ¡Ì2¦Ð 

I think all of this is understandable for stk4011 students (whether this makes it "exam relevant" or not).

To be arXiv'd and submited to a journal in a day or two.

https://www.mn.uio.no/math/english/research/projects/focustat/publications_2/stirling11.pdf