%I #20 May 09 2024 13:26:19
%S 1,1,6,42,408,4920,71280,1204560,23264640,505491840,12203654400,
%T 324084499200,9388910361600,294668851276800,9959509521561600,
%U 360665744414976000,13931586106454016000,571775010100310016000
%N E.g.f. (1-x)/(1-2x-x^2).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=553">Encyclopedia of Combinatorial Structures 553</a>
%F E.g.f.: (-1+x)/(-1+2*x+x^2)
%F Recurrence: {a(1)=1, a(0)=1, (-2-n^2-3*n)*a(n) +(-4-2*n)*a(n+1) +a(n+2)=0}
%F Sum(1/2*_alpha^(-n), _alpha=RootOf(-1+2*_Z+_Z^2))*n!
%F a(n) = n!*A001333(n). - _R. J. Mathar_, Jun 03 2022
%p spec := [S,{S=Sequence(Prod(Sequence(Z),Union(Z,Prod(Z,Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t Table[LucasL[n, 2]*n!/2, {n, 0, 17}] (* _Zerinvary Lajos_, Jul 09 2009 *)
%t With[{nn=20},CoefficientList[Series[(1-x)/(1-2x-x^2),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Jul 01 2017 *)
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000