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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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4
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0, 0, 0, 0, 10, 2997, 343140, 28044072, 1969994376, 128916045720, 8189607254829, 516895556463000, 32865110582830812, 2123144102136625568, 140115162250240202025, 9478591551140049252096, 658706750876277003711720
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OFFSET
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1,5
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LINKS
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FORMULA
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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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MATHEMATICA
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max=17; t[x_] := -ProductLog[-x]; 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; CoefficientList[ Series[w4[x], {x, 0, max}], x]*Range[0, max]! // Rest (* Jean-François Alcover, Sep 07 2012, from e.g.f. *)
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CROSSREFS
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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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