A004122 Generalized weak orders on n points.

2, 13, 123, 1546, 24283, 457699, 10064848, 252945467, 7151532895, 224661610888, 7763387794649, 292659248485051, 11951855446598278, 525645673381008537, 24769319755329986599, 1244984053628241578058, 66487872534167725541751

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

• T. D. Noe, Table of n, a(n) for n = 1..100
• 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. A004121, A004123, A000670.

Programs

Mathematica

With[{nn=20},Rest[CoefficientList[Series[1/(2-Exp[x]Exp[Exp[x]-1]),{x,0,nn}], x] Range[0,nn]!]] (* Harvey P. Dale, Nov 05 2011 *)

Formula

E.g.f. : 1/(2-exp(x)*exp(exp(x)-1)).

Extensions

Formula and more terms from Vladeta Jovovic, Mar 27 2001