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A123903
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Total number of "Emperors" in all tournamennts on n labeled nodes.
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2
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0, 1, 2, 6, 32, 320, 6144, 229376, 16777216, 2415919104, 687194767360, 387028092977152, 432345564227567616, 959230691832896684032, 4231240368651202111471616, 37138201178561408246973726720, 649037107316853453566312041152512, 22596875928343569839364720024765857792
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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, 0ct 19 2011.
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REFERENCES
| S. B. Maurer, The king chicken theorems, Math. Mag., 53 (1980), 67-80.
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FORMULA
| a(n) = n*2^((n-1)*(n-2)/2).
E.g.f.: x * Sum_{n>=0} 2^C(n,2) x^n/n!. - Geoffrey Critzer, 0ct 19 2011.
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MATHEMATICA
| a=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, 20}];
Range[0, 20]!CoefficientList[Series[x a, {x, 0, 20}], x]
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CROSSREFS
| Cf. A123553, A125031.
Sequence in context: A191691 A191712 A005736 * A172401 A005742 A055612
Adjacent sequences: A123900 A123901 A123902 * A123904 A123905 A123906
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 20 2006
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