A052794 E.g.f.: -x^5*log(1-x).
0, 0, 0, 0, 0, 0, 720, 2520, 13440, 90720, 725760, 6652800, 68428800, 778377600, 9686476800, 130767436800, 1902071808000, 29640619008000, 492490285056000, 8688935743488000, 162193467211776000, 3193183885731840000, 66117689869271040000, 1436223152160276480000
Offset: 0
Links
- Amiram Eldar, Table of n, a(n) for n = 0..450
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 751.
Programs
-
Maple
spec := [S,{B=Cycle(Z),S=Prod(Z,Z,Z,Z,Z,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20); -
Mathematica
a[n_] := If[n < 6, 0, n!/(n - 5)]; Array[a, 20, 0] (* Amiram Eldar, Oct 07 2020 *)
Formula
E.g.f.: x^5*log(-1/(-1+x)).
Recurrence: a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (-n^2+4*n+5)*a(n) + (-4+n)*a(n+1)=0.
From Amiram Eldar, Oct 07 2020: (Start)
a(n) = n! / (n-5) for n > 5.
Sum_{n>=6} 1/a(n) = 87/8 - 4*e. (End)
Sum_{n>=6} (-1)^n/a(n) = 53/24 - 6/e. - Amiram Eldar, Aug 20 2022