A052808 E.g.f.: -log(1-x+log(1-x)).

0, 2, 5, 24, 169, 1572, 18208, 252676, 4088138, 75571648, 1571427096, 36304942704, 922615912656, 25577663099232, 768176940800592, 24845381066244288, 860979848497650768, 31825036424306681088, 1249895536243141292544, 51975908060575367916288

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Previous name was: A simple grammar.

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 770

Programs

Maple

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

Mathematica

With[{nn=30},CoefficientList[Series[-Log[1-x+Log[1-x]],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Mar 27 2013 *)

PARI

a(n)=if(n<0,0,n!*polcoeff(-log(1-x+log(1-x+x*O(x^n))),n))

Formula

E.g.f.: -log(1-x+log(1-x)). - Michael Somos, Sep 21 2002

a(n) ~ (n-1)! / (1-LambertW(1))^n. - Vaclav Kotesovec, Oct 01 2013

Extensions

More terms from Harvey P. Dale, Mar 27 2013

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