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

1, 2, 14, 204, 5016, 185520, 9595440, 659846880, 58130513280, 6376568728320, 851542303852800, 135930981520857600, 25547289000870067200, 5581430113409537587200, 1402137089367777207244800, 401230026747563176171008000, 129714370868892377008336896000

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.

Links

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

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

Martin Harborth, Structural analysis of shop scheduling problems, PhD thesis, Otto-von-Guericke-Univ. Magdeburg, GCA-Verlag, 1999. (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}]

Prog

(PARI) a(n) = n!^2 * sum(k=0, n, binomial(n, k)/k!); \\ Michel Marcus, Oct 26 2023

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