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A004121 Generalized weak orders on n points.
(Formerly M2095)
4
2, 16, 208, 3968, 109568, 4793344, 410662912, 82657083392, 38274970222592, 37590755515826176, 75458309991776124928, 305873605165090925969408, 2491832958314452159507202048, 40704585435508852018947014262784 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..80

C. G. Wagner, Enumeration of generalized weak orders, Preprint, 1980. [Annotated scanned copy]

C. G. Wagner and N. J. A. Sloane, Correspondence, 1980

FORMULA

E.g.f.: 1/(1-Sum_{i >= 1} 2^binomial(i+1, 2)*x^i/i!).

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] (* Jean-Fran├žois Alcover, Oct 21 2011, after g.f. *)

CROSSREFS

Cf. A004122, A004123, A000670 (asymmetric generalized weak orders on n points).

Sequence in context: A138429 A087923 A222523 * A188600 A206930 A206865

Adjacent sequences:  A004118 A004119 A004120 * A004122 A004123 A004124

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Formula and more terms from Vladeta Jovovic, Mar 27 2001

STATUS

approved

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Last modified November 18 16:10 EST 2018. Contains 317323 sequences. (Running on oeis4.)