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%I M1989 #55 Dec 26 2018 16:56:06
%S 1,2,10,152,7736,1375952,877901648,2046320373120,17658221702361472,
%T 569773219836965265152,69280070663388783890248448,
%U 31941407692847758201303724506112,56121720938871110502272391300032261120,377362438996731353329256282026362716827887616,9744754031799754169218003376206941877943086188308480,969342741943194323476512925742876053501022995325734477987840
%N Number of labeled Eulerian digraphs with n nodes.
%C Includes disconnected graphs. - _Felix A. Pahl_, Jul 15 2018
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H 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 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 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 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
%t 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 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 (* four digit accuracy for n>7 *) (* _Thomas Curtright_, Apr 12 2017 *)
%K nonn,nice
%O 1,2
%A _N. J. A. Sloane_, _Mira Bernstein_
%E Terms a(12) and beyond from McKay (1983), added by _Thomas Curtright_, Apr 12 2017
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