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A076728 a(n) = (n-1)^2 * n^(n-2).

%I A076728 #31 May 22 2016 17:53:18
%S A076728 0,1,12,144,2000,32400,605052,12845056,306110016,8100000000,
%T A076728 235794769100,7492001071104,258071096741328,9581271191425024,
%U A076728 381454233398437500,16212958658533785600,732780301186512843008,35096024486915738763264,1775645341922275908244236
%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 Janjic_, May 10 2007
%C A076728 a(n+1) = Sum_{k=0...n} binomial(n,k)*n^k*k, which enumerates the total number of elements in the domain of definition over all partial functions on n labeled objects. - _Geoffrey Critzer_, Feb 08 2012
%C A076728 Also, the number of possible negation tables in the n-valued logics (cf. A262458 and A262459). - _Max Alekseyev_, Sep 23 2015
%H A076728 Alois P. Heinz, <a href="/A076728/b076728.txt">Table of n, a(n) for n = 1..386</a>
%H A076728 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%t A076728 Table[Sum[Binomial[n,k] n^k k, {k,0,n}], {n,1,20}] (* _Geoffrey Critzer_, Feb 08 2012 *)
%o A076728 (PARI) a(n) = (n-1)^2*n^(n-2)
%Y A076728 Column k=0 of A245692.
%K A076728 nonn
%O A076728 1,3
%A A076728 _Benoit Cloitre_, Oct 25 2002
%E A076728 a(1)=0 prepended by _Max Alekseyev_, Sep 23 2015
%E A076728 Some terms corrected by _Alois P. Heinz_, May 22 2016