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A054652 Acyclic orientations of the Hamming graph (K_2) x (K_n). 2
1, 2, 14, 204, 5016, 185520, 9595440, 659846880, 58130513280, 6376568728320, 851542303852800, 135930981520857600, 25547289000870067200, 5581430113409537587200, 1402137089367777207244800, 401230026747563176171008000, 129714370868892377008336896000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

REFERENCES

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

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

Structural analysis of shop scheduling problems (PhD thesis in German with English abstract)

FORMULA

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

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

MAPLE

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

seq(a(n), n=0..20);  # Alois P. Heinz, Feb 10 2017

MATHEMATICA

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

CROSSREFS

Cf. A002720, A054653, A053870, A054583.

Sequence in context: A123543 A279452 A262008 * A122647 A158097 A262003

Adjacent sequences:  A054649 A054650 A054651 * A054653 A054654 A054655

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified February 21 18:45 EST 2019. Contains 320376 sequences. (Running on oeis4.)