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%I #40 Sep 08 2022 08:44:59
%S 3,3,6,18,72,360,2160,15120,120960,1088640,10886400,119750400,
%T 1437004800,18681062400,261534873600,3923023104000,62768369664000,
%U 1067062284288000,19207121117184000,364935301226496000,7298706024529920000,153272826515128320000
%N a(n) = 3*n!.
%C 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
%C 3 times factorial numbers. - _Omar E. Pol_, Jan 17 2009
%H Vincenzo Librandi, <a href="/A052560/b052560.txt">Table of n, a(n) for n = 0..200</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=502">Encyclopedia of Combinatorial Structures 502</a>
%H Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv:1406.3081 [math.CO], 2014.
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F E.g.f.: 3/(1-x).
%F a(n) = n*a(n-1), with a(0) = 3.
%F For n>0: a(n) = Sum_{k=1..n+1} A083746(k). - _Reinhard Zumkeller_, Apr 14 2007
%p spec := [S,{S=Union(Sequence(Z),Sequence(Z),Sequence(Z))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p a:=n->sum(n!, k=1..n):seq(a(n)-sum(n!, k=4..n), n=0..19); # _Zerinvary Lajos_, Dec 22 2008
%t 3*Range[0, 25]! (* _Vladimir Joseph Stephan Orlovsky_, Jun 12 2011 *)
%o (Magma) [3*Factorial(n): n in [0..25]]; // _Vincenzo Librandi_, Jun 13 2011
%o (PARI) a(n)=3*n! \\ _Charles R Greathouse IV_, Nov 20 2011
%o (Sage) [3*factorial(n) for n in range(25)] # _G. C. Greubel_, May 05 2019
%Y Cf. A000142, A129380.
%Y Row 13 of A276955 (from term a(3)=18 onward).
%K easy,nonn
%O 0,1
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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