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

0,7

Links

Amiram Eldar, Table of n, a(n) for n = 0..450

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 751.

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

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 *)

Crossrefs

Cf. A052747, A052759, A052778.

Sequence in context: A112530 A052800 A321842 * A226885 A096933 A061299

Adjacent sequences: A052791 A052792 A052793 * A052795 A052796 A052797

Keyword

easy,nonn

Author

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

Status

approved