%I A076728
%S A076728 1,12,144,2000,32400,605052,12845056,306110016,8100000000,235794769100,
%T A076728 749200,1071104,258071096741328,9581271191425024,381454233398437500,
%U A076728 1621295865853378,5600,732780301186512843008,35096024486915738763264
%N A076728 a(n) = (n-1)^2 * n^(n-2)
%C A076728 Smallest integer value of the form 1/z(k,n) where z(k,x)=x/(x-1)^2-sum(i=1,
               k,i/x^i).
%C A076728 For any x>1 lim k -> infinity z(k,x)=0. More generally if p is an integer 
               >=2, 1/z(u(k),p) is an integer for any k>=2 where u(k)=(p-1)^2*p^((p^k-(p-1)*k-p)/
               (p-1)). u(k) can also be written : u(k)=(p-1)^2*p^(1+p+p^2+...+p^(k-2))
%C A076728 For n>=2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,
               2,...,n} such that for fixed, different x_1, x_2 in {1,2,...,n} and 
               fixed y_1, y_2 in {1,2,...,n} we have f(x_1)<>y_1 and f(x_2)<> y_2. 
               - Milan R. Janjic (agnus(AT)blic.net), May 10 2007
%H A076728 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas 
               for Some Functions on Finite Sets</a>
%o A076728 (PARI) a(n) = (n-1)^2*n^(n-2)
%Y A076728 Sequence in context: A001021 A159490 A000468 this_sequence A123237 A143248 
               A138444
%Y A076728 Adjacent sequences: A076725 A076726 A076727 this_sequence A076729 A076730 
               A076731
%K A076728 nonn
%O A076728 2,2
%A A076728 Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 25 2002