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 A003514 Number of series-reduced labeled graphs with n nodes. (Formerly M1290) 18
 1, 1, 2, 4, 15, 102, 4166, 402631, 76374899, 27231987762, 18177070202320, 22801993267433275, 54212469444212172845, 246812697326518127351384, 2173787304796735262709419350, 37373588848096468764431235680525 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Cf. A003515. REFERENCES I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..80 D. M. Jackson and J. W. Reilly, The enumeration of homeomorphically irreducible labeled graphs, J. Combin. Theory, B 19 (1975), 272-286. FORMULA E.g.f.: (1 + x)^( - 1/2) * exp(x/2 - x^2/4) * Sum_{k=0..inf} (2 * exp( - x/(1 + x)))^binomial(k, 2) * (exp(x^2/2/(1 + x)))^k * x^k/k!. - Vladeta Jovovic, Mar 23 2001 MATHEMATICA max = 15; f[x_] := (1 + x)^(-1/2)*Exp[x/2-x^2/4]*Sum[(2*Exp[-x/(1+x)])^Binomial[k, 2]*Exp[x^2/2/(1+x)]^k*x^k/k!, {k, 0, max}]; CoefficientList[ Series[f[x], {x, 0, max}], x]*Range[0, max]!(* Jean-François Alcover, Nov 25 2011, after Vladeta Jovovic *) CROSSREFS Cf. A003515 (connected). Row sums of A307806. Sequence in context: A307085 A228934 A120490 * A065598 A264832 A100528 Adjacent sequences:  A003511 A003512 A003513 * A003515 A003516 A003517 KEYWORD nonn,nice,changed AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Mar 23 2001 STATUS approved

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Last modified January 24 16:47 EST 2020. Contains 331209 sequences. (Running on oeis4.)