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(1+3^n)*n!.
0

%I #16 Jun 03 2022 18:59:50

%S 2,4,20,168,1968,29280,525600,11027520,264579840,7142929920,

%T 214280640000,7071181286400,254561568307200,9927888709939200,

%U 416971151460864000,18763699200390144000,900657519773147136000

%N (1+3^n)*n!.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=516">Encyclopedia of Combinatorial Structures 516</a>

%F E.g.f.: -2*(-1+2*x)/(-1+x)/(-1+3*x)

%F D-finite Recurrence: {a(1)=4, a(0)=2, (3*n^2+9*n+6)*a(n)+(-4*n-8)*a(n+1)+a(n+2)=0}

%F (1+3^n)*n!

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

%t With[{nn=20},CoefficientList[Series[-2(-1+2x)/(-1+x)/(-1+3x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 04 2021 *)

%K easy,nonn

%O 0,1

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