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A123903
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Total number of "Emperors" in all tournaments on n labeled nodes.
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10
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0, 1, 2, 6, 32, 320, 6144, 229376, 16777216, 2415919104, 687194767360, 387028092977152, 432345564227567616, 959230691832896684032, 4231240368651202111471616, 37138201178561408246973726720, 649037107316853453566312041152512, 22596875928343569839364720024765857792
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OFFSET
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0,3
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COMMENTS
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An "Emperor" is a player who beats everybody else.
a(n) is the number of isolated nodes in all simple labeled graphs on n nodes. - Geoffrey Critzer, Oct 19 2011
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LINKS
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FORMULA
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a(n) = n*2^((n-1)*(n-2)/2).
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MAPLE
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a:= n-> n*2^((n-1)*(n-2)/2):
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MATHEMATICA
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a=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, 20}];
Range[0, 20]!CoefficientList[Series[x a, {x, 0, 20}], x]
Table[n*2^Binomial[n-1, 2], {n, 0, 20}] (* G. C. Greubel, Aug 06 2019 *)
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PROG
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(PARI) vector(20, n, n--; n*2^binomial(n-1, 2)) \\ G. C. Greubel, Aug 06 2019
(Magma) [n*2^Binomial(n-1, 2): n in [0..20]]; // G. C. Greubel, Aug 06 2019
(Sage) [n*2^binomial(n-1, 2) for n in (0..20)] # G. C. Greubel, Aug 06 2019
(GAP) List([0..20], n-> n*2^Binomial(n-1, 2)); # G. C. Greubel, Aug 06 2019
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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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