%I #29 Nov 10 2017 09:56:16
%S 0,1,10,225,8000,390625,24300000,1838265625,163840000000,
%T 16815125390625,1953125000000000,253295162119140625,
%U 36279705600000000000,5688009063105712890625,968890104070000000000000,178179480135440826416015625,35184372088832000000000000000
%N Expansion of e.g.f. -(1/5)*LambertW(-5*x).
%C Previous name was: A simple grammar.
%H G. C. Greubel, <a href="/A052789/b052789.txt">Table of n, a(n) for n = 0..313</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=746">Encyclopedia of Combinatorial Structures 746</a>
%F E.g.f.: -(1/5)*LambertW(-5*x).
%F For n > 0, a(n) = (5*n)^(n-1). - _Vaclav Kotesovec_, Sep 30 2013
%F a(n) = [x^n] x/(1 - 5*n*x). - _Ilya Gutkovskiy_, Oct 12 2017
%p spec := [S,{B=Set(S),S=Prod(Z,B,B,B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t CoefficientList[Series[-1/5*LambertW[-5*x], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 30 2013 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(- lambertw(-5*x)/5))) \\ _G. C. Greubel_, Nov 08 2017
%Y Cf. A052756, A052764.
%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