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 A102263 Denominators of probabilities in gift exchange problem with n people. 1
 1, 4, 36, 144, 1800, 43200, 705600, 705600, 2116800, 127008000, 23051952000, 6638962176000, 280496151936000, 31415569016832000, 471233535252480000, 471233535252480000, 54474596675186688000, 3268475800511201280000 (list; graph; refs; listen; history; text; internal format)
 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. As n increases, p(n) approaches 1/(n + log(n) + EulerGamma), where EulerGamma = 0.5772156649015... (the Euler-Mascheroni constant). - Jon E. Schoenfield, Sep 30 2006 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 Cf. A102262. Sequence in context: A183354 A204504 A083223 * A103931 A068589 A120077 Adjacent sequences:  A102260 A102261 A102262 * A102264 A102265 A102266 KEYWORD nonn,frac AUTHOR Jerrold Grossman, Feb 17 2005 EXTENSIONS More terms from Jon E. Schoenfield, Sep 30 2006 STATUS approved

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Last modified October 23 05:50 EDT 2018. Contains 316519 sequences. (Running on oeis4.)