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A055533
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Number of labeled order relations on n nodes in which longest chain has n-1 nodes.
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8
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1, 12, 108, 960, 9000, 90720, 987840, 11612160, 146966400, 1995840000, 28979596800, 448345497600, 7366565606400, 128152088064000, 2353813862400000, 45527990796288000, 925143000477696000
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OFFSET
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2,2
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COMMENTS
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Also number of labeled acyclic digraphs with n nodes and binomial(n,2)-1 arcs, cf. A081064. - Vladeta Jovovic, Jul 14 2008
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 60.
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LINKS
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FORMULA
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E.g.f.: (x^2/2)(1+x)/(1-x)^3. a(n)=n!(n-1)^2/2, if n>1. - Vladeta Jovovic, Dec 01 2002
D-finite with recurrence (n-2)^2*a(n) -n*(n-1)^2*a(n-1)=0. - R. J. Mathar, Mar 08 2021
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PROG
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(PARI) a(n)=if(n<2, 0, n!/2*(n-1)^2) /* Michael Somos, Mar 06 2004 */
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CROSSREFS
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A column or diagonal of triangle in A342587.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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