

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
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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 nth 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 EulerMascheroni constant).  Jon E. Schoenfield, Sep 30 2006


LINKS

Table of n, a(n) for n=2..19.
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



