cp's OEIS Frontend

A052878 E.g.f.: log((1-x)/(1-3*x+x^2)).

%I A052878 #23 Jun 06 2019 12:02:43
%S A052878 0,2,6,34,276,2928,38520,606240,11118240,232928640,5488922880,
%T A052878 143707737600,4138613740800,130021152307200,4425207423436800,
%U A052878 162194949242726400,6369480464675328000,266808295408951296000,11874724735152254976000,559591803705456377856000
%N A052878 E.g.f.: log((1-x)/(1-3*x+x^2)).
%C A052878 Previous name was: A simple grammar.
%H A052878 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=849">Encyclopedia of Combinatorial Structures 849</a>
%F A052878 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 A052878 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 A052878 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 A052878 with(combinat):
%p A052878 0, seq( (fibonacci(2*n+1)+fibonacci(2*n-1)-1) * (n-1)!, n=1..20);  # _Mark van Hoeij_, May 29 2013
%o A052878 (PARI)  x='x+O('x^66); concat([0],Vec(serlaplace(log(-(-1+x)/(1-3*x+x^2))))) \\ _Joerg Arndt_, May 29 2013
%K A052878 easy,nonn
%O A052878 0,2
%A A052878 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052878 New name using e.g.f., _Vaclav Kotesovec_, Jun 06 2019