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A093377 Number of labeled n-vertex graphs without 2-components and without isolated vertices (1-components).

%I A093377 #15 Jan 05 2021 21:48:29
%S A093377 1,0,0,4,38,728,26864,1871576,251762204,66308767200,34497665550400,
%T A093377 35641856042561008,73354660691960203016,301272244237002052739424,
%U A093377 2471648864359822034978330304,40527681073171940835893232576032
%N A093377 Number of labeled n-vertex graphs without 2-components and without isolated vertices (1-components).
%C A093377 Also number of unlabeled n-block ordered r-bicoverings, cf. A060053. - _Vladeta Jovovic_, May 13 2004
%H A093377 Vincenzo Librandi, <a href="/A093377/b093377.txt">Table of n, a(n) for n = 0..65</a>
%F A093377 E.g.f.: exp(-x-x^2/2)*Sum_{n>=0} 2^binomial(n, 2)*x^n/n!.
%F A093377 Inverse binomial transform of A093352().
%t A093377 nn=20;g=Sum[2^Binomial[n,2]x^n/n!,{n,0,nn}];Range[0,nn]!CoefficientList[Series[Exp[ Log[g]-x-x^2/2!],{x,0,nn}],x]  (* _Geoffrey Critzer_, Apr 15 2013 *)
%o A093377 (PARI) N=66; x='x+O('x^N);
%o A093377 egf=exp(-x-x^2/2)*sum(i=0,N, 2^binomial(i, 2)*x^i/i!);
%o A093377 Vec(serlaplace(egf))
%o A093377 /* _Joerg Arndt_, Jul 06 2011 */
%Y A093377 Cf. A006129, A093351, A093352.
%K A093377 nonn
%O A093377 0,4
%A A093377 Goran Kilibarda, _Vladeta Jovovic_, Apr 28 2004