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.

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

Offset

0,4

Comments

Sizes of orbits are given by A000793.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..130

Formula

a(n) = A222029(n,A000793(n)). - Alois P. Heinz, Aug 14 2017

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

Cf. A000793, A074115, A074859, A222029.

Sequence in context: A082690 A104861 A074859 * A103160 A242819 A126099

Adjacent sequences: A162679 A162680 A162681 * A162683 A162684 A162685

Keyword

nonn

Author

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

Extensions

a(0), a(10)-a(23) from Alois P. Heinz, Jul 12 2017

a(21)-a(22) corrected by Alois P. Heinz, Aug 16 2017

Status

approved