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%I #22 Nov 08 2017 11:33:49
%S 0,1,8,144,4096,160000,7962624,481890304,34359738368,2821109907456,
%T 262144000000000,27197360938418176,3116402981210161152,
%U 390877006486250192896,53265296773103187132416,7836416409600000000000000,1237940039285380274899124224,208998227690370098316628197376
%N E.g.f.: -1/4*LambertW(-4*x).
%C Previous name was: A simple grammar.
%H G. C. Greubel, <a href="/A052764/b052764.txt">Table of n, a(n) for n = 0..320</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=721">Encyclopedia of Combinatorial Structures 721</a>
%F E.g.f.: -1/4*LambertW(-4*x).
%F For n>0, a(n) = 2^(2*n-2)*n^(n-1). - _Vaclav Kotesovec_, Sep 30 2013
%F a(n) = [x^n] x/(1 - 4*n*x). - _Ilya Gutkovskiy_, Oct 12 2017
%p spec := [S,{B=Set(S),S=Prod(Z,B,B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t CoefficientList[Series[-1/4*LambertW[-4*x], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 30 2013 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace((-1/4)*lambertw(-4*x)))) \\ _G. C. Greubel_, Nov 07 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
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