A052850 E.g.f.: x/(1-x)+log((1-x)/(1-2*x)).

0, 2, 5, 20, 114, 864, 8280, 96480, 1325520, 20966400, 374855040, 7468070400, 163938297600, 3929729126400, 102104460057600, 2857878742118400, 85719362496768000, 2742726680838144000, 93247371837075456000, 3356802948155424768000, 127556444063199191040000

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Previous name was: A simple grammar.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 818

Crossrefs

Bisection of A199660. - Alois P. Heinz, Nov 09 2011

Programs

Maple

spec := [S,{B=Sequence(Z,1 <= card),C=Cycle(B),S=Union(B,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
a:= n-> `if`(n=0, 0, (2^n+n-1)*(n-1)!): seq(a(n), n=0..25); # Alois P. Heinz, Nov 09 2011

Mathematica

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

Formula

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

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)}.

For n>0, a(n) = (n-1)! * (2^n+n-1). - Vaclav Kotesovec, Oct 01 2013

Extensions

New name using e.g.f., Vaclav Kotesovec, Oct 01 2013