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A121251
Number of labeled graphs without isolated vertices and with n edges.
15
1, 1, 6, 62, 900, 16824, 384668, 10398480, 324420840, 11472953760, 453518054216, 19815916826160, 948348447031440, 49334804947402800, 2771902062752597520, 167281797371598801136, 10791777047497882651296, 741135302021991803931360
OFFSET
0,3
COMMENTS
a(n) ~ C0*(C1*n)^n, where C0 = 1/2^(1+log(2)/4)/log(2) = 0.63970540489176946794... and C1 = 2/(log(2))^2/exp(1) = 1.5313857152078346894..., [Bender et al.]
REFERENCES
E. A. Bender, E. R. Canfield and B. D. McKay, The asymptotic number of labeled
LINKS
E. A. Bender and E. R. Canfield and B. D. McKay, The asymptotic number of labeled graphs with n vertices, q edges and no isolated vertices, preprint, 1996.
E. A. Bender, E. R. Canfield and B. D. McKay, The asymptotic number of labeled graphs with n vertices, q edges and no isolated vertices, J Combinatorial Theory, Series A, 80 (1997) 124-150.
A. N. Bhavale, B. N. Waphare, Basic retracts and counting of lattices, Australasian J. of Combinatorics (2020) Vol. 78, No. 1, 73-99.
FORMULA
a(n) = Sum_{m>=0} binomial(binomial(m,2),n)/2^(m+1). Column sums of A054548.
CROSSREFS
Cf. A006129.
Sequence in context: A144063 A186670 A190726 * A352071 A347016 A222079
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Aug 22 2006, Sep 19 2006
EXTENSIONS
More terms from Max Alekseyev, Aug 23 2006
STATUS
approved