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A129585
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Number of labeled connected bi-point-determining graphs (see A129583).
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5
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1, 0, 0, 12, 252, 12312, 1061304, 170176656, 51134075424, 29204599254624, 32130964585236096, 68873851786953047040, 290164895151435531345024, 2417786648013402212500060416, 40014055814155246577685250570752
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| The calculation of connected bi-point-determining graphs is carried out by examining the connected components of bi-point-determining graphs. For more details, see reference.
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REFERENCES
| I. Gessel and J. Li, On Point-Determining Graphs, arXiv:0705.0042
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LINKS
| Ira Gessel, Ji Li, On Point-Determining Graphs, arXiv:0705.0042
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FORMULA
| E.g.f.: x+ln(Sum(2^binomial(n,2)*(2*ln(1+x)-x)^n/n!,n=0..infinity)/(1+x)). - Goran Kilibarda, Vladeta Jovovic (vladeta(AT)eunet.rs), May 09 2007
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MATHEMATICA
| max = 15; f[x_] := x + Log[ Sum[ 2^Binomial[n, 2]*((2*Log[1 + x] - x)^n/n!), {n, 0, max}]/(1 + x)]; A129585 = Drop[ CoefficientList[ Series[ f[x], {x, 0, max}], x]*Range[0, max]!, 1](* From Jean-François Alcover, Jan 13 2012, after e.g.f. *)
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CROSSREFS
| Cf. graphs: labeled A006125, unlabeled A000568; connected graphs: labeled A001187, unlabeled A001349; point-determining graphs: labeled A006024, unlabeled A004110; connected point-determining graphs: labeled A092430, unlabeled A004108; connected co-point-determining graphs: labeled A079306, unlabeled A004108; bi-point-determining graphs: labeled A129583, unlabeled A129584; connected bi-point-determining graphs: labeled A129585, unlabeled A129586; phylogenetic trees: labeled A000311, unlabeled A000669.
Sequence in context: A198475 A035013 A065583 * A034672 A133285 A113091
Adjacent sequences: A129582 A129583 A129584 * A129586 A129587 A129588
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KEYWORD
| nice,nonn
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AUTHOR
| Ji Li (vieplivee(AT)hotmail.com), May 07 2007
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EXTENSIONS
| More terms from Goran Kilibarda, Vladeta Jovovic (vladeta(AT)eunet.rs), May 09 2007
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