Last night I answered this question with a formula and a rationale. A little later someone else answered the same question using a different method with a formula that looks very different, which is fine. This morning, I found a direct combinatorial proof that the two formulas are equivalent. What should I do? What is proper MSE etiquette? Do I
add a comment to one of our posts (which one?) with the proof of equivalence, or
amend my answer with proof of equivalence, or
set up a community wiki, or
do nothing, or
do something else?
After considering the responses thru 11/12/17 noon I followed the second proposal on the list as suggested by @J. M. is not a mathematician. You can see the result by using the link above.