A052756 E.g.f.: (-1/3)*LambertW(-3*x).

0, 1, 6, 81, 1728, 50625, 1889568, 85766121, 4586471424, 282429536481, 19683000000000, 1531578985264449, 131621703842267136, 12381557655576425121, 1265437718438866624512, 139628860198736572265625, 16543163447903718821855232, 2094704750199298376445300801

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Previous name was: A simple grammar.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..330
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 712

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[-1/3 LambertW[-3x],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jun 01 2013 *)

PARI

x='x+O('x^50); concat([0], Vec(serlaplace((-1/3)*lambertw(-3*x)))) \\ G. C. Greubel, Nov 05 2017

Formula

E.g.f.: (-1/3)*LambertW(-3*x).

For n>0, a(n) = (3*n)^(n-1). - Vaclav Kotesovec, Sep 30 2013

a(n) = [x^n] x/(1 - 3*n*x). - Ilya Gutkovskiy, Oct 12 2017

Extensions

New name using e.g.f. by Vaclav Kotesovec, Sep 30 2013