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

By Shalosh B. Ekhad, Christoph Koutschan, and Doron Zeilberger

.pdf    .tex   

Posted: Jan. 25, 2021

[Published in Enumerative Combinatorics and Applidcations v. 1, issue 3, article S2A17]

In fond memoroy of Joe Gillis (3 Aug. 1911- 18 Nov. 1993), who taught us that Special Functions Count

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.

Maple package

Sample Input and Output for MultiDer.txt