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A003514
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Number of series-reduced labeled graphs with n nodes.
(Formerly M1290)
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18
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1, 1, 2, 4, 15, 102, 4166, 402631, 76374899, 27231987762, 18177070202320, 22801993267433275, 54212469444212172845, 246812697326518127351384, 2173787304796735262709419350, 37373588848096468764431235680525, 1263513534110606141026676778422031561
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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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).
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) seq(n)={my(x='x+O('x^(n+1))); Vec(serlaplace((1 + x)^( - 1/2) * exp(x/2 - x^2/4) * sum(k=0, n, (2 * exp(-x/(1 + x)))^binomial(k, 2) * (exp(x^2/2/(1 + x)))^k * x^k/k!)))} \\ Andrew Howroyd, Feb 23 2024
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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