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A061540
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Number of connected labeled graphs with n nodes and n+1 edges.
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7
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0, 0, 0, 6, 205, 5700, 156555, 4483360, 136368414, 4432075200, 154060613850, 5720327205120, 226378594906035, 9523895202838016, 424814409531910125, 20037831121798963200, 996964614369038858060, 52198565072252054814720
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OFFSET
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1,4
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REFERENCES
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S. Janson, D. E. Knuth, T. Luczak and B. Pittel, The Birth of the Giant Component, Random Structures and Algorithms Vol. 4 (1993), 233-358.
E. M. Wright, The Number of Connected Sparsely Edged Graphs, Journal of Graph Theory Vol. 1 (1977), 317-330.
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LINKS
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Table of n, a(n) for n=1..18.
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FORMULA
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E.g.f.: W1(x) := T(x)^4/24 * (6-T(x))/(1-T(x))^3 where T(x) is the e.g.f. for rooted labeled trees (A000169), i.e. T(x)=-LambertW(-x) = x*exp(T(x)).
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MATHEMATICA
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max = 18; t[x_] := -ProductLog[-x]; w1[x_] := t[x]^4/24*(6-t[x])/(1-t[x])^3; Drop[ CoefficientList[ Series[ w1[x], {x, 0, max}], x]*Range[0, max]!, 1] (* From Jean-François Alcover, Apr 02 2012, after e.g.f. *)
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CROSSREFS
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Cf. A000169, A000272 A057500 A061541 A061542 A061543 A096117 A061544 A096150 and A096224.
Sequence in context: A082405 A183595 A054653 * A173370 A159307 A024083
Adjacent sequences: A061537 A061538 A061539 * A061541 A061542 A061543
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KEYWORD
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easy,nice,nonn
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AUTHOR
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RAVELOMANANA Vlady (vlad(AT)lri.fr), May 16 2001
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STATUS
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approved
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