%I #20 Oct 19 2022 15:34:53

%S 0,1,4,36,432,6480,116640,2449440,58786560,1587237120,47617113600,

%T 1571364748800,56569130956800,2206196107315200,92660236507238400,

%U 4169710642825728000,200146110855634944000,10207451653637382144000

%N Expansion of e.g.f. x*(1-x)/(1-3*x).

%H G. C. Greubel, <a href="/A052700/b052700.txt">Table of n, a(n) for n = 0..375</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=650">Encyclopedia of Combinatorial Structures 650</a>

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

%F D-finite recurrence: a(1)=1, a(0)=0, a(2)=4, a(n) = 3*n*a(n-1).

%F a(n) = 2*3^(n-2)*n! = 2*A153647(n-2), n>1.

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

%t Table[2*3^(n-2)*n! -2*Boole[n==0]/9 + Boole[n==1]/3, {n,0,30}] (* _G. C. Greubel_, May 31 2022 *)

%t With[{nn=30},CoefficientList[Series[x (1-x)/(1-3x),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 19 2022 *)

%o (SageMath) [0,1]+[2*3^(n-2)*factorial(n) for n in (2..30)] # _G. C. Greubel_, May 31 2022

%Y Cf. A153647.

%K easy,nonn

%O 0,3

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