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A052832 Expansion of e.g.f. log((-1+x)/(-1+x+x^2)).

%I A052832 #19 Jan 20 2025 06:29:43
%S A052832 0,0,2,6,36,240,2040,20160,231840,3024000,44271360,718502400,
%T A052832 12813292800,249080832000,5243151513600,118824010905600,
%U A052832 2884729655808000,74694359900160000,2054806272110592000,59849389401145344000,1840003788783992832000,59545276650123264000000
%N A052832 Expansion of e.g.f. log((-1+x)/(-1+x+x^2)).
%C A052832 Old name was: A simple grammar.
%H A052832 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=797">Encyclopedia of Combinatorial Structures 797</a>
%F A052832 Recurrence: {a(1)=0, a(3)=6, a(2)=2, (n^3+3*n^2+2*n)*a(n)+(-4-2*n)*a(n+2)+a(n+3)}.
%F A052832 (RootOf(_Z^2-_Z-1)^n*RootOf(_Z^2-_Z-1)+(1-RootOf(_Z^2-_Z-1))^(n+1)-1)*GAMMA(n+1)/RootOf(_Z^2-_Z-1)/(-1+RootOf(_Z^2-_Z-1)).
%F A052832 D-finite with recurrence a(n) +2*(-n+1)*a(n-1) +(n-1)*(n-2)*(n-3)*a(n-3)=0. - _R. J. Mathar_, Jan 13 2025
%p A052832 spec := [S,{B=Prod(Z,C),C=Sequence(Z,1 <= card),S= Cycle(B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p A052832 # alternative
%p A052832 A052832 := proc(n)
%p A052832     log((-1+x)/(-1+x+x^2));
%p A052832     coeftayl(%,x=0,n)*n! ;
%p A052832 end proc:
%p A052832 seq(A052832(n),n=0..20) ; # _R. J. Mathar_, Jan 20 2025
%K A052832 easy,nonn
%O A052832 0,3
%A A052832 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052832 More terms from _Alois P. Heinz_, Mar 16 2016