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 A007080 Number of labeled Eulerian digraphs with n nodes. (Formerly M1989) 9
 1, 2, 10, 152, 7736, 1375952, 877901648, 2046320373120, 17658221702361472, 569773219836965265152, 69280070663388783890248448, 31941407692847758201303724506112, 56121720938871110502272391300032261120, 377362438996731353329256282026362716827887616, 9744754031799754169218003376206941877943086188308480, 969342741943194323476512925742876053501022995325734477987840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Includes disconnected graphs. - Felix A. Pahl, Jul 15 2018 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Table of n, a(n) for n=1..16. Matteo Beccaria, Thermal properties of a string bit model at large N, arXiv:1709.01801 [hep-th], 2017. B. D. McKay, Applications of a technique for labeled enumeration, Congress. Numerantium, 40 (1983), 207-221. B. D. McKay, The asymptotic numbers of regular tournaments, Eulerian digraphs and Eulerian oriented graphs, Combinatorica 10 (1990), 367-377. FORMULA 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 MATHEMATICA 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 *) 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))] (* four digit accuracy for n>7 *) (* Thomas Curtright, Apr 12 2017 *) CROSSREFS Sequence in context: A294373 A194026 A165940 * A231517 A134088 A076659 Adjacent sequences: A007077 A007078 A007079 * A007081 A007082 A007083 KEYWORD nonn,nice AUTHOR N. J. A. Sloane, Mira Bernstein EXTENSIONS Terms a(12) and beyond from McKay (1983), added by Thomas Curtright, Apr 12 2017 STATUS approved

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Last modified June 18 16:37 EDT 2024. Contains 373482 sequences. (Running on oeis4.)