A004121 Generalized weak orders on n points.

2, 16, 208, 3968, 109568, 4793344, 410662912, 82657083392, 38274970222592, 37590755515826176, 75458309991776124928, 305873605165090925969408, 2491832958314452159507202048, 40704585435508852018947014262784

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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

Crossrefs

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

Programs

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. *)

Formula

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

Extensions

Formula and more terms from Vladeta Jovovic, Mar 27 2001