A018241 Number of simple allowable sequences on 1..n.

1, 1, 2, 32, 4608, 7028736, 132089118720, 34998332896051200, 147462169661142781132800, 11008782516353752266715850342400, 16061608070479103314001351327405309952000, 500842967990688435516159987675099451681186775040000

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

References

• J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.
• G. Kreweras, Sur un problème de scrutin à plus de deux candidats, Publications de l'Institut de Statistique de l'Université de Paris, 26 (1981), 69-87.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..40
• G. Kreweras, Sur un problème de scrutin à plus de deux candidats, Publications de l'Institut de Statistique de l'Université de Paris, 26 (1981), 69-87. [Annotated scanned copy]
• R. P. Stanley, On the number of reduced decompositions of elements of Coxeter groups, European J. Combin., 5 (1984), 359-372.

Crossrefs

Cf. A003121, A005118, A074962.

Programs

Maple

A018241 := proc(n) local i; (n-2)!*binomial(n,2)!/product( (2*i+1)^(n-i-1), i=0..n-2 ); end;

Mathematica

a[n_] := (n*(n-1)/2)!*(n-2)! / Product[ (2i+1)^(n-i-1), {i, 0, n-2}]; a[1] = 1; Table[ a[n], {n, 1, 11}] (* Jean-François Alcover, Jan 25 2012 *)

Formula

a(n) = (n-2)!*C(n,2)! / (1^{n-1} * 3^{n-2} * ... * (2n-3)^1).

a(n) ~ Pi * exp(n^2/4 - 3*n/2 + 7/24) * n^(n^2/2 + n/2 - 13/24) / (A^(1/2) * 2^(n^2 - n/2 - 19/24)), where A = 1.2824271291... is the Glaisher-Kinkelin constant (see A074962). - Vaclav Kotesovec, Nov 13 2014