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A013922
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Number of labeled connected graphs with n nodes and 0 cutpoints (blocks or nonseparable graphs).
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59
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0, 1, 1, 10, 238, 11368, 1014888, 166537616, 50680432112, 29107809374336, 32093527159296128, 68846607723033232640, 290126947098532533378816, 2417684612523425600721132544, 40013522702538780900803893881856
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OFFSET
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1,4
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COMMENTS
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Or, number of labeled 2-connected graphs with n nodes.
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REFERENCES
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Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p.402.
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 9.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.20(b), g(n).
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LINKS
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Thomas Lange, Biconnected reliability, Hochschule Mittweida (FH), Fakultät Mathematik/Naturwissenschaften/Informatik, Master's Thesis, 2015.
Andrés Santos, Density Expansion of the Equation of State, in A Concise Course on the Theory of Classical Liquids, Volume 923 of the series Lecture Notes in Physics, pp 33-96, 2016. DOI:10.1007/978-3-319-29668-5_3. See Reference 40.
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FORMULA
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Harary and Palmer give e.g.f. in Eqn. (1.3.3) on page 10.
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MATHEMATICA
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seq[n_] := CoefficientList[Log[x/InverseSeries[x*D[Log[Sum[2^Binomial[k, 2]*x^k/k!, {k, 0, n}] + O[x]^n], x]]], x]*Range[0, n-2]!;
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PROG
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(PARI) seq(n)={Vec(serlaplace(log(x/serreverse(x*deriv(log(sum(k=0, n, 2^binomial(k, 2) * x^k / k!) + O(x*x^n)))))), -n)} \\ Andrew Howroyd, Sep 26 2018
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Stanley Selkow (sms(AT)owl.WPI.EDU)
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STATUS
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approved
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