A055533 - OEIS

%I #17 Mar 16 2021 08:31:09

%S 1,12,108,960,9000,90720,987840,11612160,146966400,1995840000,

%T 28979596800,448345497600,7366565606400,128152088064000,

%U 2353813862400000,45527990796288000,925143000477696000

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

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

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 60.

%F 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

%F D-finite with recurrence (n-2)^2*a(n) -n*(n-1)^2*a(n-1)=0. - _R. J. Mathar_, Mar 08 2021

%o (PARI) a(n)=if(n<2,0,n!/2*(n-1)^2) /* _Michael Somos_, Mar 06 2004 */

%Y A column or diagonal of triangle in A342587.

%K nonn

%O 2,2

%A _N. J. A. Sloane_, Jul 10 2000

%E More terms from _Vladeta Jovovic_, Dec 01 2002