%I #27 Jun 20 2022 05:47:11
%S 0,3,12,54,288,1800,12960,105840,967680,9797760,108864000,1317254400,
%T 17244057600,242853811200,3661488230400,58845346560000,
%U 1004293914624000,18140058832896000,345728180109312000
%N a(n) = 3*n*n!.
%H G. C. Greubel, <a href="/A052673/b052673.txt">Table of n, a(n) for n = 0..350</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=621">Encyclopedia of Combinatorial Structures 621</a>
%H Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
%F E.g.f.: 3*x/(1-x)^2.
%F Recurrence: a(0)=0, a(1)=3, (n-1)*a(n) = n^2*a(n-1).
%F a(n) = A122972(n+2) - A122972(n) for n > 0. - _Reinhard Zumkeller_, Sep 21 2006
%F For n>0: a(n) = A083746(n+2). - _Reinhard Zumkeller_, Apr 14 2007
%F G.f.: 3*Hypergeometric2F0([2,2], [], x). - _G. C. Greubel_, Jun 12 2022
%p spec := [S,{S=Prod(Sequence(Z),Sequence(Z),Union(Z,Z,Z))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t Table[3 n n!,{n,0,20}] (* _Harvey P. Dale_, Feb 12 2017 *)
%o (Magma) [3*(Factorial(n+1)-Factorial(n)): n in [0..30]]; // _G. C. Greubel_, Jun 12 2022
%o (SageMath) [3*n*factorial(n) for n in (0..30)] # _G. C. Greubel_, Jun 12 2022
%Y Cf. A083746, A122972.
%Y Cf. A000142, A008585.
%K easy,nonn
%O 0,2
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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