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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-François 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 EXTENSIONS Formula and more terms from Vladeta Jovovic, Mar 27 2001 STATUS approved

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Last modified January 22 19:45 EST 2022. Contains 350504 sequences. (Running on oeis4.)