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

There are EXACTLY 1493804444499093354916284290188948031229880469556 Ways  to Derange a Standard Deck of Cards (ignoring suits) [and many other such  useful facts]