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%I #18 Oct 26 2023 08:26:57
%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.
%H Alois P. Heinz, <a href="/A054652/b054652.txt">Table of n, a(n) for n = 0..250</a>
%H H. Bräsel and M. Kleinau, <a href="https://doi.org/10.1080/02331939208843762">On the number of feasible schedules of the open shop problem - an application of special Latin rectangles</a>, Optimization 23 (1992) 251-260.
%H Martin Harborth, <a href="https://web.archive.org/web/20070610185300/http://www.math.uni-magdeburg.de/publ/diss/shadows/19990831-Harborth-diss.html">Structural analysis of shop scheduling problems</a>, PhD thesis, Otto-von-Guericke-Univ. Magdeburg, GCA-Verlag, 1999. (in German with English abstract)
%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}]
%o (PARI) a(n) = n!^2 * sum(k=0, n, binomial(n,k)/k!); \\ _Michel Marcus_, Oct 26 2023
%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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