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E.g.f.: log((1-x)/(1-3*x+x^2)).
1

%I #23 Jun 06 2019 12:02:43

%S 0,2,6,34,276,2928,38520,606240,11118240,232928640,5488922880,

%T 143707737600,4138613740800,130021152307200,4425207423436800,

%U 162194949242726400,6369480464675328000,266808295408951296000,11874724735152254976000,559591803705456377856000

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

%C Previous name was: A simple grammar.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=849">Encyclopedia of Combinatorial Structures 849</a>

%F Recurrence: {a(1)=2, a(2)=6, a(3)=34, (-n^3-2*n-3*n^2)*a(n)+(4*n^2+12*n+8)*a(n+1)+(-4*n-8)*a(n+2)+a(n+3)}

%F For n > 0, a(n) = (n-1)! * (phi^(2*n) + 1/phi^(2*n) - 1), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Jun 06 2019

%p spec := [S,{B=Sequence(Z,1 <= card),C=Union(Z,B),S=Cycle(C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20); # end of program

%p with(combinat):

%p 0, seq( (fibonacci(2*n+1)+fibonacci(2*n-1)-1) * (n-1)!, n=1..20); # _Mark van Hoeij_, May 29 2013

%o (PARI) x='x+O('x^66); concat([0],Vec(serlaplace(log(-(-1+x)/(1-3*x+x^2))))) \\ _Joerg Arndt_, May 29 2013

%K easy,nonn

%O 0,2

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

%E New name using e.g.f., _Vaclav Kotesovec_, Jun 06 2019