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

Author

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

Keywords

• nonn

Comments

Sizes of orbits are given by A000793.

Examples

			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.
		

Links

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

Crossrefs

Cf. A000793, A074115, A074859, A222029.

Formula

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

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