A052747 a(0) = a(1) = a(2) = 0; a(n) = n!/(n-2) for n > 2.

0, 0, 0, 6, 12, 40, 180, 1008, 6720, 51840, 453600, 4435200, 47900160, 566092800, 7264857600, 100590336000, 1494484992000, 23712495206400, 400148356608000, 7155594141696000, 135161222676480000, 2688996956405760000, 56200036388880384000, 1231048416137379840000

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

A simple grammar.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..450
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 703.

Crossrefs

Equals the square root of the second right hand column of A162990 for n=>3. [Johannes W. Meijer, Jul 21 2009]

Programs

Maple

spec := [S,{B=Cycle(Z),S=Prod(Z,Z,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Mathematica

a[n_] := If[n < 3, 0, n!/(n-2)]; Array[a, 20, 0] (* Amiram Eldar, Oct 07 2020 *)

PARI

a(n)=if(n>2,n!/(n-2),0) \\ Charles R Greathouse IV, Nov 20 2011

Formula

E.g.f.: log(-1/(-1+x))*x^2

Recurrence: {a(0)=0, a(1)=0, a(2)=0, a(3)=6, (n+2-n^2)*a(n)+(n-1)*a(n+1)}

Sum_{n>=3} 1/a(n) = 3 - e. - Amiram Eldar, Oct 07 2020

Sum_{n>=3} (-1)^(n+1)/a(n) = 3/e - 1. - Amiram Eldar, Aug 20 2022

Extensions

Better description from Olivier Gérard, Jun 13 2001