

A162682


If S is countable finite set, we can define n as number of elements in S. There are n^n distinct functions f(S)>S. Each function has a fixed point, or an orbit in S. This sequence is a number of distinct functions g(S)>S, with largest orbit.


3



1, 1, 1, 2, 6, 20, 840, 420, 2688, 18144, 120960, 15966720, 7983360, 1349187840, 1037836800, 12454041600, 149448499200, 1693749657600, 579262382899200, 289631191449600, 115852476579840000, 26822744640147456000, 4750241170964889600000, 30776210403434496000
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OFFSET

0,4


COMMENTS

Sizes of orbits are given by A000793.


LINKS



FORMULA



EXAMPLE

For S={a}, n=1 and only one operation possible {a>a}. For S={a,b}, n=2 and possible operations are {a>a,b>a}, {a>a,b>b}, {a>b,b>a},{a>b,b>b}. Longest orbit generated by applying operation {a>b,b>a}: initial set (a,b), applying function gives orbit  (b,a), (a,b). All other possible functions are generating fixed points.


CROSSREFS



KEYWORD

nonn


AUTHOR

Dmitriy Samsonov (dmitriy.samsonov(AT)gmail.com), Jul 10 2009


EXTENSIONS



STATUS

approved



