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A054652
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Number of acyclic orientations of the Hamming graph (K_2) x (K_n).
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2
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1, 2, 14, 204, 5016, 185520, 9595440, 659846880, 58130513280, 6376568728320, 851542303852800, 135930981520857600, 25547289000870067200, 5581430113409537587200, 1402137089367777207244800, 401230026747563176171008000, 129714370868892377008336896000
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = n! * Sum_{k=0..n} n!/k! * binomial(n,k).
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MAPLE
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a:= n-> (n!)^2 * add(binomial(n, k)/k!, k=0..n):
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MATHEMATICA
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Table[n!*Sum[n!/k!*Binomial[n, k], {k, 0, n}], {n, 0, 20}]
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PROG
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(PARI) a(n) = n!^2 * sum(k=0, n, binomial(n, k)/k!); \\ Michel Marcus, Oct 26 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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M. Harborth (Martin.Harborth(AT)vt.siemens.de)
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STATUS
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approved
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