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%I #18 Oct 07 2017 01:01:59
%S 0,0,1,7,81,1311,27273,693351,20830113,722035503,28364200569,
%T 1245313236663,60429110073489,3211572892464639,185523138537151977,
%U 11574425593731913479,775591270444009771137,55555665263291738684367,4236182199641241492147801
%N The sequence S defined in A058562.
%F E.g.f.: -(1/2)*LambertW(-2/3*exp(-2/3 + 1/3*x)) - 1/3 - x/3. - _Vladeta Jovovic_, Jun 25 2007
%F a(n) ~ sqrt(log(3/2)-1/3) * n^(n-1) / (2 * exp(n) * (log(27/8)-1)^n). - _Vaclav Kotesovec_, Jul 09 2013
%p spec := [ S, {N=Union(Z,S,P,Q), S=Set(Union(Z,P,Q),card>=2), P=Set(Union(Z,S,Q),card>=2), Q=Set(Union(Z,S,P),card>=2)}, labeled ]; [seq(combstruct[count](spec,size=n), n=0..40)]; # N=A058562, S=A058575
%p spec:=[S,{S=Set(Union(Z,S,S),card>=2)},labeled];[seq(combstruct[count](spec,size=n),n=0..20)]; # _Vladeta Jovovic_, Jun 25 2007
%t max = 18; se = Series[ -1/2*ProductLog[ -2/3*Exp[-2/3 + 1/3*x]] - 1/3 - x/3 , {x, 0, max}]; Join[{0, 0}, (CoefficientList[se, x] // DeleteCases[#, 0] &) ]* Range[0, max]! (* _Jean-François Alcover_, Jun 24 2013, after _Vladeta Jovovic_ *)
%Y Cf. A058562.
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Dec 26 2000
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