This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A086371 #5 Feb 16 2025 08:32:50
%S A086371 1,3,16,151,2750,97829,6803239
%N A086371 a(n) is the sum, over all labeled graphs G on n nodes, of the clique number w(G).
%C A086371 The expected clique number of G(n,1/2) is the rational value a(n)/b(n), where b(n) denotes the sequence A006125 (the number of graphs on n labeled nodes). For instance, the expected clique number of G(4,1/2) is a(4)/b(4) = 151/64. G(n,1/2) denotes the random graph on n labeled nodes obtained by choosing, randomly and independently, every pair of nodes {ij} to be an edge with probability 1/2 (Alon, Krivelevich and Sudakov p. 2)
%H A086371 N. Alon, M. Krivelevich and B. Sudakov, <a href="http://www.math.tau.ac.il/~nogaa/PDFS/clique3.pdf">Finding a large hidden clique in a random graph</a>, Proc. of the Ninth Annual ACM-SIAM SODA, ACM Press (1998), pp. 594-598. Also: Random Structures and Algorithms 13 (1998), pp. 457-466.
%H A086371 I.M. Bomze, M. Budinich, P.M. Pardalos and M. Pelillo, <a href="http://citeseer.nj.nec.com/bomze99maximum.html">The Maximum Clique Problem</a>, Handbook of Combinatorial Optimization (supplement vol. A), D.-Z. Du and P.M. Pardalos, eds. (1999), pp. 1-74.
%H A086371 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CliqueNumber.html">Clique Number</a>.
%e A086371 Consider the 8 different labeled graphs on 3 nodes: one of the graphs has clique number 1, six of the graphs have clique number 2 and one of the graphs has clique number 3. Hence a(3) = 1*1 + 6*2 + 1*3 = 16.
%Y A086371 Cf. A052450, A052451, A052452, A077392, A077393, A077394, A006125.
%K A086371 more,nice,nonn
%O A086371 1,2
%A A086371 Tim Paulden (timmy(AT)cantab.net), Sep 05 2003