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A249672
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Number of simple labeled graphs of order n that have 3k connected components for some k.
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0
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1, 0, 0, 1, 6, 55, 826, 20839, 925470, 76332845, 12144225666, 3786386476697, 2323365229270526, 2810644438909846175, 6714880936575265290018, 31734660733696955320333111, 297106568811291486526250342118, 5516820501917771489801597101682245
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OFFSET
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0,5
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LINKS
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FORMULA
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E.g.f.: B(A(x) - 1) where B(x) is the e.g.f. for A079978 and A(x) is the e.g.f. for A001187.
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MATHEMATICA
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nn = 18; a[x_] := Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}];
c[x_] := Log[a[x]];
Range[0, nn]! CoefficientList[
Series[1/3 (E^x + 2 E^(-x/2) Cos[(Sqrt[3] x)/2]) /. x -> c[x], {x,
0, nn}], x] // Simplify
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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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