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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
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.
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
KEYWORD
nonn,nice
AUTHOR
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.)