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Search: id:A061544
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| A061544 |
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Number of connected labeled graphs with n nodes and n+6 edges. |
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+0
7
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| 0, 0, 0, 0, 0, 455, 202755, 39183840, 5228627544, 573177986865, 56169415897650, 5157436533796140, 456501786661617840, 39667302684866008152, 3425100498297691978050, 296331952661358892037760
(list; graph; listen)
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OFFSET
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1,6
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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.: W6(x) = - 1/5806080*T(x)^6*( - 3669120 - 145514880*T(x) - 826813440*T(x)^2 - 160242624*T(x)^3 + 549065304*T(x)^4 - 1423242144*T(x)^5 + 1649073392*T(x)^6 - 1408032768*T(x)^7 + 881917344*T(x)^8 - 418233349*T(x)^9 + 147585749*T(x)^10 - 37755372*T(x)^11 + 6581528*T(x)^12 - 696620*T(x)^13 + 33000*T(x)^14)/(( - 1 + T(x))^18) 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.
Adjacent sequences: A061541 A061542 A061543 this_sequence A061545 A061546 A061547
Sequence in context: A092267 A123563 A043475 this_sequence A015276 A116331 A099650
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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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