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A054652 Acyclic orientations of the Hamming graph (K_2) x (K_n). 2


%S 1,2,14,204,5016,185520,9595440,659846880,58130513280,6376568728320,

%T 851542303852800,135930981520857600,25547289000870067200,

%U 5581430113409537587200,1402137089367777207244800,401230026747563176171008000,129714370868892377008336896000

%N Acyclic orientations of the Hamming graph (K_2) x (K_n).

%C This number is equivalent to the number of plans (i.e. structural solutions) of the open shop problem with n jobs and 2 machines - see problems in scheduling theory.

%D H. Braesel, M. Kleinau, On the number of feasible schedules of the open shop problem - an application of special Latin rectangles, Optimization 23 (1992) 251-260

%D M. Harborth, Structural analysis of shop scheduling problems, PhD thesis, Otto-von-Guericke-Univ. Magdeburg, GCA-Verlag, 1999 (in German)

%H Alois P. Heinz, <a href="/A054652/b054652.txt">Table of n, a(n) for n = 0..250</a>

%H <a href="http://www.math.uni-magdeburg.de/publ/diss/sources/harborth_diss.ps.gz">Structural analysis of shop scheduling problems (PhD thesis in German with English abstract)</a>

%F a(n) = n! * Sum_{k=0..n} n!/k! * binomial(n,k).

%F a(n) = n! * A002720(n).

%p a:= n-> (n!)^2 * add(binomial(n,k)/k!, k=0..n):

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Feb 10 2017

%t Table[n!*Sum[n!/k!*Binomial[n, k], {k, 0, n}], {n, 0, 20}]

%Y Cf. A002720, A054653, A053870, A054583.

%K nonn,easy

%O 0,2

%A M. Harborth (Martin.Harborth(AT)vt.siemens.de)

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)