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 A007080 M1989 #69 Mar 20 2025 04:17:39
%S A007080 1,2,10,152,7736,1375952,877901648,2046320373120,17658221702361472,
%T A007080 569773219836965265152,69280070663388783890248448,
%U A007080 31941407692847758201303724506112,56121720938871110502272391300032261120,377362438996731353329256282026362716827887616,9744754031799754169218003376206941877943086188308480,969342741943194323476512925742876053501022995325734477987840
%N A007080 Number of labeled Eulerian digraphs with n nodes.
%C A007080 Includes disconnected graphs. - _Felix A. Pahl_, Jul 15 2018
%C A007080 Loops and parallel edges are not allowed, but 2-cycles (in other words, edges A --> B and B --> A existing simultaneously) are allowed. - _Mikhail Lavrov_, Mar 04 2025
%D A007080 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007080 Matteo Beccaria, <a href="https://arxiv.org/abs/1709.01801">Thermal properties of a string bit model at large N</a>, arXiv:1709.01801 [hep-th], 2017.
%H A007080 Mohammad Behzad Kang and Andrew Salch, <a href="https://arxiv.org/abs/2410.24171">The mod p cohomology of the Morava stabilizer group at large primes</a>, arXiv:2410.24171 [math.AT], 2024. See p. 46.
%H A007080 Rüdiger Jehn, Kester Habermann, and Misha Lavrov, <a href="https://arxiv.org/abs/2503.14509">Number of ways that a football league can complete with all teams having the same number of points</a>, arXiv:2503.14509 [math.GM], 2025.
%H A007080 B. D. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/papers/LabelledEnumeration.pdf">Applications of a technique for labeled enumeration</a>, Congress. Numerantium, 40 (1983), 207-221.
%H A007080 B. D. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/papers/rt.pdf">The asymptotic numbers of regular tournaments, Eulerian digraphs and Eulerian oriented graphs</a>, Combinatorica 10 (1990), 367-377.
%F A007080 a(n) ~ e^(-1/4)*sqrt(n)(2^n/sqrt(Pi*n))^(n-1)*(1+O(1/sqrt(n))) [B. D. McKay, 1990]. - _Thomas Curtright_, Apr 11 2017
%e A007080 For n=3, the a(n) = 10 solutions are: (A . B . C), (A <--> B . C), (A <--> C . B), (B <--> C . A), (A --> B --> C --> A), (A --> C --> B --> A), (A <--> B <--> C), (A <--> C <--> B), (B <--> A <--> C), and (A <--> B <--> C <--> A). - _Mikhail Lavrov_, Mar 04 2025
%t A007080 a[n_]:=Coefficient[Expand[Product[Product[x[i]+x[j],{j, 1, n}],{i, 1,n}]],Product[x[k]^n,{k,1,n}]]/2^n (* practically unusable for n>7 *)
%t A007080 a[n_]:=N[(Sqrt[n]/E^(1/4))*(2^n/Sqrt[n*Pi])^(n-1)*(1+3/(16*n)+1/(7*n^2)+3/(20*n^3))]
%t A007080 (* four digit accuracy for n>7 *) (* _Thomas Curtright_, Apr 12 2017 *)
%Y A007080 Cf. A058338 (unlabeled), A229865 (loops allowed), A054957 (connected) - _Mikhail Lavrov_, Mar 04 2025
%K A007080 nonn,nice
%O A007080 1,2
%A A007080 _N. J. A. Sloane_, _Mira Bernstein_
%E A007080 Terms a(12) and beyond from McKay (1983), added by _Thomas Curtright_, Apr 12 2017