A093352 Number of labeled n-vertex graphs without a 2-component.

1, 1, 1, 5, 55, 959, 31883, 2076383, 267530657, 68644357201, 35172312944057, 36025019516955853, 73784654524456043287, 302228644804839247744495, 2475873364061564307502565395, 40564787473148108729970731074007, 1329227698679709317077126629247388161

Offset: 0

Author

Goran Kilibarda, Vladeta Jovovic, Apr 26 2004

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A093351, A006129.

Programs

Maple

A093352 := n -> n!*add((-1)^q/2^q/q!*2^binomial(n-2*q,2)/(n-2*q)!, q=0..floor(n/2)); # Marko Riedel, Apr 05 2022

Mathematica

nn = 15; g = Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}];
Range[0, nn]! CoefficientList[Series[g/Exp[x^2/2], {x, 0, nn}], x] (* Geoffrey Critzer, Aug 27 2013 *)

Formula

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

a(n) = n!*Sum_{q=0..floor(n/2)} ((-1)^q/(2^q*q!))*(2^C(n-2*q,2)/(n-2*q)!). - Marko Riedel, Apr 05 2022