Consider a new office building with n floors and k offices per floor in which you must assign 2nk people to work, each sharing an office with exactly one other person

Math Oct 29, 2020

Consider a new office building with n floors and k offices per floor in which you must assign 2nk people to work, each sharing an office with exactly one other person. Find a closed form solution for the number of ways there are to assign offices if from floor to floor the offices are distinguishable but any two offices on a given floor are not.