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

0,4

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

Formula

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

Inverse binomial transform of A093352().

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 *)

Prog

(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 */

Crossrefs

Cf. A006129, A093351, A093352.

Sequence in context: A084285 A084286 A001187 * A178017 A131591 A030259

Adjacent sequences: A093374 A093375 A093376 * A093378 A093379 A093380

Keyword

nonn

Author

Goran Kilibarda, Vladeta Jovovic, Apr 28 2004

Status

approved