A052560 a(n) = 3*n!.

3, 3, 6, 18, 72, 360, 2160, 15120, 120960, 1088640, 10886400, 119750400, 1437004800, 18681062400, 261534873600, 3923023104000, 62768369664000, 1067062284288000, 19207121117184000, 364935301226496000, 7298706024529920000, 153272826515128320000

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

a(n) is the size of the centralizer of a 3-cycle in the symmetric group S_(n+3). - Ahmed Fares (ahmedfares(AT)my-deja.com), May 12 2001

3 times factorial numbers. - Omar E. Pol, Jan 17 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 502
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv:1406.3081 [math.CO], 2014.
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A000142, A129380.

Row 13 of A276955 (from term a(3)=18 onward).

Programs

Magma

[3*Factorial(n): n in [0..25]]; // Vincenzo Librandi, Jun 13 2011

Maple

spec := [S,{S=Union(Sequence(Z),Sequence(Z),Sequence(Z))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
a:=n->sum(n!, k=1..n):seq(a(n)-sum(n!, k=4..n), n=0..19); # Zerinvary Lajos, Dec 22 2008

Mathematica

3*Range[0, 25]! (* Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *)

PARI

a(n)=3*n! \\ Charles R Greathouse IV, Nov 20 2011

Sage

[3*factorial(n) for n in range(25)] # G. C. Greubel, May 05 2019

Formula

E.g.f.: 3/(1-x).

a(n) = n*a(n-1), with a(0) = 3.

For n>0: a(n) = Sum_{k=1..n+1} A083746(k). - Reinhard Zumkeller, Apr 14 2007