A052794 - OEIS

%I #21 Aug 20 2022 06:37:14

%S 0,0,0,0,0,0,720,2520,13440,90720,725760,6652800,68428800,778377600,

%T 9686476800,130767436800,1902071808000,29640619008000,492490285056000,

%U 8688935743488000,162193467211776000,3193183885731840000,66117689869271040000,1436223152160276480000

%N E.g.f.: -x^5*log(1-x).

%H Amiram Eldar, <a href="/A052794/b052794.txt">Table of n, a(n) for n = 0..450</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=751">Encyclopedia of Combinatorial Structures 751</a>.

%F E.g.f.: x^5*log(-1/(-1+x)).

%F 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.

%F From _Amiram Eldar_, Oct 07 2020: (Start)

%F a(n) = n! / (n-5) for n > 5.

%F Sum_{n>=6} 1/a(n) = 87/8 - 4*e. (End)

%F Sum_{n>=6} (-1)^n/a(n) = 53/24 - 6/e. - _Amiram Eldar_, Aug 20 2022

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

%t a[n_] := If[n < 6, 0, n!/(n - 5)]; Array[a, 20, 0] (* _Amiram Eldar_, Oct 07 2020 *)

%Y Cf. A052747, A052759, A052778.

%K easy,nonn

%O 0,7

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