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

1, 0, 0, 4, 38, 728, 26864, 1871576, 251762204, 66308767200, 34497665550400, 35641856042561008, 73354660691960203016, 301272244237002052739424, 2471648864359822034978330304, 40527681073171940835893232576032

Offset: 0

Author

Goran Kilibarda, Vladeta Jovovic, Apr 28 2004

Keywords

• nonn

Comments

Also number of unlabeled n-block ordered r-bicoverings, cf. A060053. - Vladeta Jovovic, May 13 2004

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..65

Crossrefs

Cf. A006129, A093351, A093352.

Programs

Mathematica

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 *)

PARI

N=66; x='x+O('x^N);
egf=exp(-x-x^2/2)*sum(i=0,N, 2^binomial(i, 2)*x^i/i!);
Vec(serlaplace(egf))
/* Joerg Arndt, Jul 06 2011 */

Formula

E.g.f.: exp(-x-x^2/2)*Sum_{n>=0} 2^binomial(n, 2)*x^n/n!.

Inverse binomial transform of A093352().