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Number of labeled connected digraphs on n nodes where every node has indegree 0 or outdegree 0 and no isolated nodes.
In- or outdegree zero implies loops are not admitted. Multi-arcs are not admitted. - R. J. Mathar, Nov 18 2023
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max terms = 1817; f[x_] :s = Log[Sum[ aExp[(2^n - 2)*x]*(x^n/n!), {n, 0, maxterms+2}]] + O[x]^(terms+2); coes = Drop[CoefficientList[ Series[ f[x] - Log[ Sum[ Exp[ (2^n-2)*s, x]*(x^n/n!), {n, 0, max}]], {x, Range[0, max}], x]; Table[a[nterms+1], {n, !, 2, 18}] /. First[ Solve[ Thread[ coes == 0]]] (* Jean-François Alcover, Nov 08 2011, after Vladeta Jovovic , updated Jan 12 2018 *)
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R. C. Read, RE. CM.; Wright, E. M., <a href="http://dx.doi.org/10.4153/CJM-1970-066-1">Colored graphs: A correction and extension</a>, Canad. J. Math. 22 1970 594-596.
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