A004121 Generalized weak orders on n points. (Formerly M2095)

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

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

N. J. A. Sloane

Extensions

Formula and more terms from Vladeta Jovovic, Mar 27 2001

Status

approved