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A228596
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The number of simple labeled graphs on n nodes with no components of size 3.
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1
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1, 1, 2, 4, 48, 944, 32288, 2089312, 268215040, 68708556288, 35183367427072, 36028619925285888, 73786915826515503104, 302231414653310649337856, 2475880026112961032035266560, 40564819073011099018919903485952, 1329227995107917459000217502447435776
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: exp(-4*x^3/3!)*A(x) where A(x) is the e.g.f. for A006125.
Generally, the e.g.f. for the number of simple labeled graphs on n nodes with no size k components is exp( -A001187(k)*x^k/k! ) * A(x) with A(x) as above.
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MATHEMATICA
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nn = 15; g = Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}];
Range[0, nn]! CoefficientList[Series[Exp[-4 x^3/3!] g, {x, 0, nn}], x]
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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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