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A102263
Denominators of probabilities in gift exchange problem with n people.
3
1, 4, 36, 144, 1800, 43200, 705600, 705600, 2116800, 127008000, 23051952000, 6638962176000, 280496151936000, 31415569016832000, 471233535252480000, 471233535252480000, 54474596675186688000, 3268475800511201280000
OFFSET
2,2
COMMENTS
n friends organize a gift exchange. The n names are put into a hat and the first person draws one. If she picks her own name, then she returns it to the bag and draws again, repeating until she has a name that is not her own. Then the second person draws, again returning his own name if it is drawn. This continues down the line. What is the probability p(n) that when the n-th person draws, only her own name will be left in the bag?
I heard about the problem from Gary Thompson at Grove City College in PA.
LINKS
Math Forum at Drexel, A variant on the "Secret Santa"
FORMULA
See A102262 for formula for p(n).
EXAMPLE
p(2) through p(10) are 0, 1/4, 5/36, 19/144, 203/1800, 4343/43200, 63853/705600, 58129/705600, 160127/2116800.
CROSSREFS
Sequence in context: A183354 A204504 A083223 * A103931 A334580 A068589
KEYWORD
nonn,frac
AUTHOR
Jerrold Grossman, Feb 17 2005
EXTENSIONS
More terms from Jon E. Schoenfield, Sep 30 2006
STATUS
approved