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A061543
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Number of connected labeled graphs with n nodes and n+4 edges.
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5
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0, 0, 0, 0, 10, 2997, 343140, 28044072, 1969994376, 128916045720, 8189607254829, 516895556463000, 32865110582830812, 2123144102136625568, 140115162250240202025, 9478591551140049252096, 658706750876277003711720
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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REFERENCES
| 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
| E.g.f.: W4(x) = - 1/11520*T(x)^5*( - 960 - 31632*T(x) - 54144*T(x)^2 + 100976*T(x)^3 - 117368*T(x)^4 + 79520*T(x)^5 - 35793*T(x)^6 + 10069*T(x)^7 - 1626*T(x)^8 + 108*T(x)^9)/(( - 1 + T(x))^12) 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
| Cf. A000169, A000272.
Sequence in context: A047945 A132675 A123377 * A133198 A001329 A007101
Adjacent sequences: A061540 A061541 A061542 * A061544 A061545 A061546
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KEYWORD
| easy,nice,nonn
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AUTHOR
| RAVELOMANANA Vlady (vlad(AT)lri.fr), May 16 2001
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