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A093377
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Number of labeled n-vertex graphs without 2-components and without isolated vertices (1-components).
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1
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1, 0, 0, 4, 38, 728, 26864, 1871576, 251762204, 66308767200, 34497665550400, 35641856042561008, 73354660691960203016, 301272244237002052739424, 2471648864359822034978330304, 40527681073171940835893232576032
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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E.g.f.: exp(-x-x^2/2)*Sum_{n>=0} 2^binomial(n, 2)*x^n/n!.
Inverse binomial transform of A093352().
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MATHEMATICA
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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 *)
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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