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A003514
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Number of series-reduced labeled graphs with n nodes.
(Formerly M1290)
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14
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1, 1, 2, 4, 15, 102, 4166, 402631, 76374899, 27231987762, 18177070202320, 22801993267433275, 54212469444212172845, 246812697326518127351384, 2173787304796735262709419350, 37373588848096468764431235680525
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
D. M. Jackson and J. W. Reilly, The enumeration of homeomorphically irreducible labeled graphs, J. Combin. Theory, B 19 (1975), 272-286.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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!.
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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]!(* From Jean-François Alcover, Nov 25 2011, after Vladeta Jovovic *)
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CROSSREFS
| Sequence in context: A140836 A020134 A120490 * A065598 A100528 A132483
Adjacent sequences: A003511 A003512 A003513 * A003515 A003516 A003517
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| E.g.f. and more terms from Vladeta Jovovic (vladeta(AT)Eunet.u), Mar 23 2001
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