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A357257
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Number of n-node tournaments that have exactly three circular triads.
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2
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240, 2880, 33600, 403200, 5093760, 68275200, 972787200, 14724864000, 236396160000, 4016659046400, 72067387392000, 1362306097152000, 27071765360640000, 564357385912320000, 12317692759916544000, 280955128203509760000
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OFFSET
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5,1
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LINKS
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FORMULA
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a(n) = n!*(2*(n-4) + (1/3)*(n-5)*(n-6) + (1/162)*(n-6)*(n-7)*(n-8)*[n>5]) (see Kadane).
E.g.f.: (x^4 - 18*x^3 + 72*x^2 - 108*x + 54)*x^5/((3^3)*(1-x)^4).
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EXAMPLE
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a(6) = 6!*(2*(6-4) + (1/3)*(6-5)*(6-6) + (1/162)*(6-6)*(6-7)*(6-8)*[6>5]) = 2880.
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MATHEMATICA
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Table[n!*(2*(n-4) + (1/3)*(n-5)*(n-6) + (1/162)*(n-6)*(n-7)*(n-8)*Boole[n>5]), {n, 5, 20}] (* Stefano Spezia, Sep 27 2022 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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