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A129585
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Number of labeled connected bi-point-determining graphs with n vertices (see A129583).
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5
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1, 1, 0, 0, 12, 252, 12312, 1061304, 170176656, 51134075424, 29204599254624, 32130964585236096, 68873851786953047040, 290164895151435531345024, 2417786648013402212500060416, 40014055814155246577685250570752, 1318911434129029730677931158374449664
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OFFSET
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0,5
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COMMENTS
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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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LINKS
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FORMULA
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E.g.f.: 1 + x + log((Sum_{n>=0} 2^binomial(n,2)*(2*log(1+x)-x)^n/n!)/(1+x)). - Goran Kilibarda, Vladeta Jovovic, May 09 2007
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MATHEMATICA
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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](* Jean-François Alcover, Jan 13 2012, after e.g.f. *)
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PROG
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(PARI) seq(n)={my(g=sum(k=0, n, 2^binomial(k, 2)*x^k/k!) + O(x*x^n)); Vec(serlaplace(1+x+log(subst(g, x, 2*log(1+x+O(x*x^n))-x)/(1+x))))} \\ Andrew Howroyd, May 06 2021
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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Ji Li (vieplivee(AT)hotmail.com), May 07 2007
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EXTENSIONS
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a(0)=1 prepended and terms a(16) and beyond from Andrew Howroyd, May 06 2021
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STATUS
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approved
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