A052789 Expansion of e.g.f. -(1/5)*LambertW(-5*x).

0, 1, 10, 225, 8000, 390625, 24300000, 1838265625, 163840000000, 16815125390625, 1953125000000000, 253295162119140625, 36279705600000000000, 5688009063105712890625, 968890104070000000000000, 178179480135440826416015625, 35184372088832000000000000000

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..313
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 746

Crossrefs

Cf. A052756, A052764.

Programs

Maple

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

Mathematica

CoefficientList[Series[-1/5*LambertW[-5*x], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *)

PARI

x='x+O('x^50); concat([0], Vec(serlaplace(- lambertw(-5*x)/5))) \\ G. C. Greubel, Nov 08 2017

Formula

E.g.f.: -(1/5)*LambertW(-5*x).

For n > 0, a(n) = (5*n)^(n-1). - Vaclav Kotesovec, Sep 30 2013

a(n) = [x^n] x/(1 - 5*n*x). - Ilya Gutkovskiy, Oct 12 2017

Extensions

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