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A061543 Number of connected labeled graphs with n nodes and n+4 edges. 9
0, 0, 0, 0, 10, 2997, 343140, 28044072, 1969994376, 128916045720, 8189607254829, 516895556463000, 32865110582830812, 2123144102136625568, 140115162250240202025, 9478591551140049252096, 658706750876277003711720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..382

S. Janson, D. E. Knuth, T. Luczak and B. Pittel, The Birth of the Giant Component, arXiv:math/9310236 [math.PR], 1993.

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.

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)).

MATHEMATICA

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-Fran├žois Alcover, Sep 07 2012, from e.g.f. *)

CROSSREFS

Cf. A000169, A000272.

Sequence in context: A227223 A208185 A123377 * A305666 A320307 A225764

Adjacent sequences:  A061540 A061541 A061542 * A061544 A061545 A061546

KEYWORD

easy,nice,nonn

AUTHOR

Ravelomanana Vlady (vlad(AT)lri.fr), May 16 2001

STATUS

approved

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Last modified March 25 16:33 EDT 2019. Contains 321474 sequences. (Running on oeis4.)