The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A076728 a(n) = (n-1)^2 * n^(n-2). 5
 0, 1, 12, 144, 2000, 32400, 605052, 12845056, 306110016, 8100000000, 235794769100, 7492001071104, 258071096741328, 9581271191425024, 381454233398437500, 16212958658533785600, 732780301186512843008, 35096024486915738763264, 1775645341922275908244236 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)