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A004121
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Generalized weak orders on n points.
(Formerly M2095)
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3
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2, 16, 208, 3968, 109568, 4793344, 410662912, 82657083392, 38274970222592, 37590755515826176, 75458309991776124928, 305873605165090925969408, 2491832958314452159507202048, 40704585435508852018947014262784
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
C. G. Wagner, Enumeration of generalized weak orders. Arch. Math. (Basel) 39 (1982), no. 2, 147-152.
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FORMULA
| E.g.f.: 1/(1-Sum_{i >= 1} 2^binomial(i+1, 2)*x^i/i!).
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MATHEMATICA
| max = 14; f[x_] := 1/(1 - Sum[(2^(i*(i+1)/2)*x^i)/i!, {i, 1, max}]); Drop[ CoefficientList[ Series[f[x], {x, 0, max}], x]*Range[0, max]!, 1] (* From Jean-François Alcover, Oct 21 2011, after g.f. *)
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CROSSREFS
| Cf. A004122, A004123, A000670 (asymmetric generalized weak orders on n points)
Sequence in context: A161568 A138429 A087923 * A188600 A206930 A206865
Adjacent sequences: A004118 A004119 A004120 * A004122 A004123 A004124
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Formula and more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 27 2001
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