%I #24 Apr 18 2017 07:04:11

%S 0,2,5,20,114,864,8280,96480,1325520,20966400,374855040,7468070400,

%T 163938297600,3929729126400,102104460057600,2857878742118400,

%U 85719362496768000,2742726680838144000,93247371837075456000,3356802948155424768000,127556444063199191040000

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

%C Previous name was: A simple grammar.

%H Alois P. Heinz, <a href="/A052850/b052850.txt">Table of n, a(n) for n = 0..200</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=818">Encyclopedia of Combinatorial Structures 818</a>

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

%F Recurrence: {a(1)=2, a(2)=5, a(3)=20, a(4)=114, (2*n^3-2*n)*a(n)+(-3*n^2+2*n+5)*a(n+1)+(-2+n)*a(n+2)}.

%F For n>0, a(n) = (n-1)! * (2^n+n-1). - _Vaclav Kotesovec_, Oct 01 2013

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

%p a:= n-> `if`(n=0, 0, (2^n+n-1)*(n-1)!): seq(a(n), n=0..25); # _Alois P. Heinz_, Nov 09 2011

%t CoefficientList[Series[x/(1-x)+Log[(1-x)/(1-2*x)], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Oct 01 2013 *)

%Y Bisection of A199660. - _Alois P. Heinz_, Nov 09 2011

%K easy,nonn

%O 0,2

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

%E New name using e.g.f., _Vaclav Kotesovec_, Oct 01 2013