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REFERENCES
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D. J. Broadhurst and D. Kreimer, Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop Pad-Borel resummation. Phys. Lett. B 475 (2000), 63-70.
Jonathan Burns, Assembly Graph Words - Single Transverse Component (Counts), http://shell.cas.usf.edu/~saito/DNAweb/SimpleAssemblyTable.txt.
Jonathan Burns, Egor Dolzhenko, Natasa Jonoska, Tilahun Muche and Masahico Saito, Four-Regular Graphs with Rigid Vertices Associated to DNA Recombination, May 23, 2011; http://jtburns.myweb.usf.edu/assembly/papers/Graphs_and_DNA_Recomb_2011.pdf.
Jonathan Burns and Tilahun Muche, Counting Irreducible Double Occurrence Words, Arxiv preprint arXiv:1105.2926, 2011.
M. Klazar, Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings, Advances in Appl. Math., Vol. 30 (2003), pp. 126-136.
M. Klazar, Counting even and odd partitions, Amer. Math. Monthly, 110 (No. 6, 2003), 527-532.
Nijenhuis, Albert and Wilf, Herbert S., The enumeration of connected graphs and linked diagrams, J. Combin. Theory Ser. A 27 (1979), no. 3, 356-359.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. R. Stein, On a class of linked diagrams, I. Enumeration, J. Combin. Theory, A 24 (1978), 357-366.
R. R. Stein and C. J. Everett, On a class of linked diagrams, II. Asymptotics, Discrete Math., 21 (1978), 309-318.
J. Touchard, Sur un proble`me de configurations et sur les fractions continues, Canad. J. Math., 4 (1952), 2-25.
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MATHEMATICA
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max = 18; f[x_] := Sum[c[k]*x^k, {k, 0, max}]; c[0] = 0; coes = CoefficientList[ Series[f[x] - (x+x^2*D[f[x]^2/x, x]), {x, 0, max}], x]; sol = Solve[ Thread[coes == 0]]; a[n_] := c[n] /. sol[[1]]; Table[a[n], {n, 1, max}](* From Jean-François Alcover, Apr 06 2012, after Paul D. Hanna *)
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