A055533 Number of labeled order relations on n nodes in which longest chain has n-1 nodes.

1, 12, 108, 960, 9000, 90720, 987840, 11612160, 146966400, 1995840000, 28979596800, 448345497600, 7366565606400, 128152088064000, 2353813862400000, 45527990796288000, 925143000477696000

Offset: 2

Author

N. J. A. Sloane, Jul 10 2000

Keywords

• nonn

Comments

Also number of labeled acyclic digraphs with n nodes and binomial(n,2)-1 arcs, cf. A081064. - Vladeta Jovovic, Jul 14 2008

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 60.

Crossrefs

A column or diagonal of triangle in A342587.

Programs

PARI

a(n)=if(n<2,0,n!/2*(n-1)^2) /* Michael Somos, Mar 06 2004 */

Formula

E.g.f.: (x^2/2)(1+x)/(1-x)^3. a(n)=n!(n-1)^2/2, if n>1. - Vladeta Jovovic, Dec 01 2002

D-finite with recurrence (n-2)^2*a(n) -n*(n-1)^2*a(n-1)=0. - R. J. Mathar, Mar 08 2021

Extensions

More terms from Vladeta Jovovic, Dec 01 2002