A121251 Number of labeled graphs without isolated vertices and with n edges.

1, 1, 6, 62, 900, 16824, 384668, 10398480, 324420840, 11472953760, 453518054216, 19815916826160, 948348447031440, 49334804947402800, 2771902062752597520, 167281797371598801136, 10791777047497882651296, 741135302021991803931360, 53983717302568691555767360

Offset: 0

Author

Vladeta Jovovic, Aug 22 2006, Sep 19 2006

Keywords

• easy
• nonn

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.
• Kassahun H. Betre, Yan X. Zhang, and Carter Edmond, Pure Simplicial and Clique Complexes with a Fixed Number of Facets, arXiv:2411.12945 [math.CO], 2024. See p. 23.
• A. N. Bhavale, B. N. Waphare, Basic retracts and counting of lattices, Australasian J. of Combinatorics (2020) Vol. 78, No. 1, 73-99.

Crossrefs

Cf. A006129.

Formula

a(n) = Sum_{m>=0} binomial(binomial(m,2),n)/2^(m+1). Column sums of A054548.

Extensions

More terms from Max Alekseyev, Aug 23 2006