A052578 a(0) = 0, a(n) = 4*n! for n > 0.

0, 4, 8, 24, 96, 480, 2880, 20160, 161280, 1451520, 14515200, 159667200, 1916006400, 24908083200, 348713164800, 5230697472000, 83691159552000, 1422749712384000, 25609494822912000, 486580401635328000, 9731608032706560000, 204363768686837760000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..447
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 522

Crossrefs

Cf. A000142, A052849 (k=2), A052560 (k=3).

Programs

Magma

[0] cat [4*Factorial(n): n in [1..25]]; // Vincenzo Librandi, Feb 13 2018

Maple

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

Mathematica

Join[{0},4Range[25]!]  (* Harvey P. Dale, Mar 12 2011 *)

PARI

a(n)=if(n,4*n!,0) \\ Charles R Greathouse IV, Nov 20 2011

Formula

E.g.f.: -4*x/(-1+x)

Recurrence: {a(0)=0, (-1-n)*a(n)+a(n+1), a(1)=4}