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A093352 Number of labeled n-vertex graphs without a 2-component. 5
1, 1, 1, 5, 55, 959, 31883, 2076383, 267530657, 68644357201, 35172312944057, 36025019516955853, 73784654524456043287, 302228644804839247744495, 2475873364061564307502565395, 40564787473148108729970731074007, 1329227698679709317077126629247388161 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
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
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 *)
CROSSREFS
Sequence in context: A057130 A141357 A357394 * A293013 A195513 A172493
KEYWORD
nonn
AUTHOR
Goran Kilibarda, Vladeta Jovovic, Apr 26 2004
STATUS
approved

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Last modified June 18 04:26 EDT 2024. Contains 373468 sequences. (Running on oeis4.)