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%I #22 Nov 09 2017 21:20:32
%S 0,1,4,27,268,3585,60846,1255471,30535912,855688833,27148954330,
%T 962037575631,37659124454700,1613921425656865,75156944627712598,
%U 3778932799275876495,204039148080188427856,11774630933193827543553
%N E.g.f.: -LambertW(x/(-1+x)).
%C Previous name was: A simple grammar.
%H G. C. Greubel, <a href="/A052871/b052871.txt">Table of n, a(n) for n = 0..369</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=842">Encyclopedia of Combinatorial Structures 842</a>
%F E.g.f.: -LambertW(x/(-1+x))
%F a(n) = Sum_{k=1..n} (n!/k!)*binomial(n-1, k-1)*k^(k-1). - _Vladeta Jovovic_, Sep 17 2003
%F a(n) ~ (1+exp(-1))^(n+1/2)*n^(n-1). - _Vaclav Kotesovec_, Sep 30 2013
%p spec := [S,{C=Sequence(Z,1 <= card),B=Set(S),S=Prod(B,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t CoefficientList[Series[-LambertW[x/(-1+x)], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 30 2013 *)
%o (Maxima) makelist(sum((n!/k!)*binomial(n-1, k-1)*k^(k-1), k, 1, n), n, 0, 17); /* _Bruno Berselli_, May 25 2011 */
%o (PARI) x='x+O('x^50); concat([0], Vec(serlaplace(- lambertw(x/(-1+x))) )) \\ _G. C. Greubel_, Nov 08 2017
%Y Cf. A008297, A060356.
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E New name using e.g.f., _Vaclav Kotesovec_, Sep 30 2013
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