  In this memorial tribute to Joe Gillis, who taught us that Special Functions
count, we show how the seminal Even-Gillis integral formula for the number of
derangements of a multiset, in terms of Laguerre polynomials, can be used to
efficiently compute not only the number of the title, but much harder ones,
when it is interfaced with Wilf-Zeilberger algorithmic proof theory.
