OFFSET
1,4
COMMENTS
Or, number of labeled 2-connected graphs with n nodes.
REFERENCES
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).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..50 (terms 1..25 from R. W. Robinson)
Huantian Cao, AutoGF: An Automated System to Calculate Coefficients of Generating Functions, thesis, 2002.
Huantian Cao, AutoGF: An Automated System to Calculate Coefficients of Generating Functions, thesis, 2002 [Local copy, with permission]
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.
S. Selkow, The enumeration of labeled graphs by number of cutpoints, Discr. Math. 185 (1998), 183-191.
FORMULA
Harary and Palmer give e.g.f. in Eqn. (1.3.3) on page 10.
MATHEMATICA
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]!;
seq[16] (* Jean-François Alcover, Aug 19 2019, after Andrew Howroyd *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
Stanley Selkow (sms(AT)owl.WPI.EDU)
STATUS
approved