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Search: id:A061541
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| A061541 |
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Number of connected labeled graphs with n nodes and n+2 edges. |
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+0
6
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| 0, 0, 0, 1, 120, 6165, 258125, 10230360, 405918324, 16530124800, 699126562530, 30884683104000, 1428626760992860, 69248819808744576, 3516693960681822375, 186964957159176734720, 10395215954531344335000
(list; graph; listen)
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OFFSET
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1,5
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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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FORMULA
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E.g.f.: W2(x) = 1/48*T(x)^4*(2 + 28*T(x) - 23*T(x)^2 + 9*T(x)^3 - T(x)^4)/(1 - T(x))^6, 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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CROSSREFS
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Cf. A000169, A000272, A057500, A061541, A061542, etc.
Sequence in context: A031145 A126245 A008661 this_sequence A003438 A092710 A055213
Adjacent sequences: A061538 A061539 A061540 this_sequence A061542 A061543 A061544
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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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