cp's OEIS Frontend

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

%I A121251 #21 Nov 23 2024 09:54:50
%S A121251 1,1,6,62,900,16824,384668,10398480,324420840,11472953760,
%T A121251 453518054216,19815916826160,948348447031440,49334804947402800,
%U A121251 2771902062752597520,167281797371598801136,10791777047497882651296,741135302021991803931360,53983717302568691555767360
%N A121251 Number of labeled graphs without isolated vertices and with n edges.
%C A121251 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.]
%D A121251 E. A. Bender, E. R. Canfield and B. D. McKay, The asymptotic number of labeled
%H A121251 E. A. Bender and E. R. Canfield and B. D. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/papers/nip3.pdf">The asymptotic number of labeled graphs with n vertices, q edges and no isolated vertices</a>, preprint, 1996.
%H A121251 E. A. Bender, E. R. Canfield and B. D. McKay, <a href="https://doi.org/10.1006/jcta.1997.2798">The asymptotic number of labeled graphs with n vertices, q edges and no isolated vertices</a>, J Combinatorial Theory, Series A, 80 (1997) 124-150.
%H A121251 Kassahun H. Betre, Yan X. Zhang, and Carter Edmond, <a href="https://arxiv.org/abs/2411.12945">Pure Simplicial and Clique Complexes with a Fixed Number of Facets</a>, arXiv:2411.12945 [math.CO], 2024. See p. 23.
%H A121251 A. N. Bhavale, B. N. Waphare, <a href="https://ajc.maths.uq.edu.au/pdf/78/ajc_v78_p073.pdf">Basic retracts and counting of lattices</a>, Australasian J. of Combinatorics (2020) Vol. 78, No. 1, 73-99.
%F A121251 a(n) = Sum_{m>=0} binomial(binomial(m,2),n)/2^(m+1). Column sums of A054548.
%Y A121251 Cf. A006129.
%K A121251 easy,nonn
%O A121251 0,3
%A A121251 _Vladeta Jovovic_, Aug 22 2006, Sep 19 2006
%E A121251 More terms from _Max Alekseyev_, Aug 23 2006