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%I #20 Dec 14 2023 11:40:22
%S 1,1,6,48,504,6600,103680,1900080,39795840,937681920,24548832000,
%T 706966444800,22210346188800,755916735974400,27706219904563200,
%U 1088037381150720000,45576301518139392000,2028445209752113152000,95589693062063456256000,4754884242802394308608000
%N E.g.f.: (1-x)^2/(1-3*x+x^2).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=509">Encyclopedia of Combinatorial Structures 509</a>
%F E.g.f.: (-1+x)^2/(1-3*x+x^2).
%F Recurrence: {a(1)=1, a(0)=1, a(2)=6, (n^2+3*n+2)*a(n)+(-6-3*n)*a(n+1)+a(n+2)=0}
%F Sum(-1/5*(3*_alpha-2)*_alpha^(-1-n), _alpha=RootOf(_Z^2-3*_Z+1))*n!
%F a(n) = n! * Fibonacci(2*n) for n > 0. - _Ilya Gutkovskiy_, Jul 17 2021
%p spec := [S,{S=Sequence(Prod(Z,Sequence(Z),Sequence(Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=20},CoefficientList[Series[(1-x)^2/(1-3x+x^2),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 06 2021 *)
%Y Cf. A000142, A001906, A005443, A088305.
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000