A052756 - OEIS

%I #23 Nov 05 2017 23:06:23

%S 0,1,6,81,1728,50625,1889568,85766121,4586471424,282429536481,

%T 19683000000000,1531578985264449,131621703842267136,

%U 12381557655576425121,1265437718438866624512,139628860198736572265625,16543163447903718821855232,2094704750199298376445300801

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

%C Previous name was: A simple grammar.

%H G. C. Greubel, <a href="/A052756/b052756.txt">Table of n, a(n) for n = 0..330</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=712">Encyclopedia of Combinatorial Structures 712</a>

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

%F For n>0, a(n) = (3*n)^(n-1). - _Vaclav Kotesovec_, Sep 30 2013

%F a(n) = [x^n] x/(1 - 3*n*x). - _Ilya Gutkovskiy_, Oct 12 2017

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

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

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

%K easy,nonn

%O 0,3

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

%E New name using e.g.f. by _Vaclav Kotesovec_, Sep 30 2013