A052759 E.g.f.: x^3*log(1/(1-x)).

0, 0, 0, 0, 24, 60, 240, 1260, 8064, 60480, 518400, 4989600, 53222400, 622702080, 7925299200, 108972864000, 1609445376000, 25406244864000, 426824913715200, 7602818775552000, 143111882833920000, 2838385676206080000, 59157933040926720000, 1292600836944248832000

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

Previous name was: A simple grammar.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..450
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 716.

Programs

Magma

[n le 3 select 0 else Factorial(n)/(n-3): n in [0..30]]; // Vincenzo Librandi, Jul 08 2015

Maple

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

Mathematica

Join[{0, 0, 0, 0}, Table[n!/(n - 3), {n, 4, 30}]] (* Vincenzo Librandi, Jul 08 2015 *)

PARI

a(n) = if (n <= 3, 0, n!/(n-3)); \\ Michel Marcus, Jul 08 2015

Formula

E.g.f.: x^3*log(-1/(-1+x)).

Recurrence: a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=24, (-n^2+2*n+3)*a(n)+(-2+n)*a(n+1) = 0.

a(n) = n! / (n-3) (n > 3). - Olivier Gérard, Jun 13 2001

Sum_{n>=4} 1/a(n) = 11/2 - 2*e. - Amiram Eldar, Oct 07 2020

Sum_{n>=4} (-1)^n/a(n) = 3/2 - 4/e. - Amiram Eldar, Aug 20 2022