cp's OEIS Frontend

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.

%I A162682 #14 Jan 24 2019 19:00:34
%S A162682 1,1,1,2,6,20,840,420,2688,18144,120960,15966720,7983360,1349187840,
%T A162682 1037836800,12454041600,149448499200,1693749657600,579262382899200,
%U A162682 289631191449600,115852476579840000,26822744640147456000,4750241170964889600000,30776210403434496000
%N 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.
%C A162682 Sizes of orbits are given by A000793.
%H A162682 Alois P. Heinz, <a href="/A162682/b162682.txt">Table of n, a(n) for n = 0..130</a>
%F A162682 a(n) = A222029(n,A000793(n)). - _Alois P. Heinz_, Aug 14 2017
%e A162682 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.
%Y A162682 Cf. A000793, A074115, A074859, A222029.
%K A162682 nonn
%O A162682 0,4
%A A162682 Dmitriy Samsonov (dmitriy.samsonov(AT)gmail.com), Jul 10 2009
%E A162682 a(0), a(10)-a(23) from _Alois P. Heinz_, Jul 12 2017
%E A162682 a(21)-a(22) corrected by _Alois P. Heinz_, Aug 16 2017