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

0, 1, 12, 144, 2000, 32400, 605052, 12845056, 306110016, 8100000000, 235794769100, 7492001071104, 258071096741328, 9581271191425024, 381454233398437500, 16212958658533785600, 732780301186512843008, 35096024486915738763264, 1775645341922275908244236

Offset

1,3

Comments

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).

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)).

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

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

Also, the number of possible negation tables in the n-valued logics (cf. A262458 and A262459). - Max Alekseyev, Sep 23 2015

Links

Alois P. Heinz, Table of n, a(n) for n = 1..386

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Mathematica

Table[Sum[Binomial[n, k] n^k k, {k, 0, n}], {n, 1, 20}] (* Geoffrey Critzer, Feb 08 2012 *)

Prog

(PARI) a(n) = (n-1)^2*n^(n-2)

Crossrefs

Column k=0 of A245692.

Sequence in context: A159490 A245853 A000468 * A123237 A143248 A138444

Adjacent sequences: A076725 A076726 A076727 * A076729 A076730 A076731

Keyword

nonn

Author

Benoit Cloitre, Oct 25 2002

Extensions

a(1)=0 prepended by Max Alekseyev, Sep 23 2015

Some terms corrected by Alois P. Heinz, May 22 2016

Status

approved