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A061540 Number of connected labeled graphs with n nodes and n+1 edges. 7
0, 0, 0, 6, 205, 5700, 156555, 4483360, 136368414, 4432075200, 154060613850, 5720327205120, 226378594906035, 9523895202838016, 424814409531910125, 20037831121798963200, 996964614369038858060, 52198565072252054814720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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.

LINKS

Table of n, a(n) for n=1..18.

FORMULA

E.g.f.: W1(x) := T(x)^4/24 * (6-T(x))/(1-T(x))^3 where T(x) is the e.g.f. for rooted labeled trees (A000169), i.e. T(x)=-LambertW(-x) = x*exp(T(x)).

a(n) ~ 5*n^(n+1)/24 * (1 - 7/5*sqrt(2*Pi/n)). - Vaclav Kotesovec, Jul 09 2013

MATHEMATICA

max = 18; t[x_] := -ProductLog[-x]; w1[x_] := t[x]^4/24*(6-t[x])/(1-t[x])^3; Drop[ CoefficientList[ Series[ w1[x], {x, 0, max}], x]*Range[0, max]!, 1] (* Jean-Fran├žois Alcover, Apr 02 2012, after e.g.f. *)

CROSSREFS

Cf. A000169, A000272 A057500 A061541 A061542 A061543 A096117 A061544 A096150 and A096224.

Sequence in context: A082405 A183595 A054653 * A173370 A159307 A024083

Adjacent sequences:  A061537 A061538 A061539 * A061541 A061542 A061543

KEYWORD

easy,nice,nonn

AUTHOR

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

STATUS

approved

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Last modified December 18 07:26 EST 2014. Contains 252098 sequences.