A052764 E.g.f.: -1/4*LambertW(-4*x).

0, 1, 8, 144, 4096, 160000, 7962624, 481890304, 34359738368, 2821109907456, 262144000000000, 27197360938418176, 3116402981210161152, 390877006486250192896, 53265296773103187132416, 7836416409600000000000000, 1237940039285380274899124224, 208998227690370098316628197376

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..320
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 721

Programs

Maple

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

Mathematica

CoefficientList[Series[-1/4*LambertW[-4*x], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)

PARI

x='x+O('x^50); concat([0], Vec(serlaplace((-1/4)*lambertw(-4*x)))) \\ G. C. Greubel, Nov 07 2017

Formula

E.g.f.: -1/4*LambertW(-4*x).

For n>0, a(n) = 2^(2*n-2)*n^(n-1). - Vaclav Kotesovec, Sep 30 2013

a(n) = [x^n] x/(1 - 4*n*x). - Ilya Gutkovskiy, Oct 12 2017

Extensions

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