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
KEYWORD
nonn,easy
AUTHOR
M. Harborth (Martin.Harborth(AT)vt.siemens.de)
STATUS
approved