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A007080
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Number of labeled Eulerian digraphs with n nodes.
(Formerly M1989)
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9
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1, 2, 10, 152, 7736, 1375952, 877901648, 2046320373120, 17658221702361472, 569773219836965265152, 69280070663388783890248448, 31941407692847758201303724506112, 56121720938871110502272391300032261120, 377362438996731353329256282026362716827887616, 9744754031799754169218003376206941877943086188308480, 969342741943194323476512925742876053501022995325734477987840
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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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
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MATHEMATICA
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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))]
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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Terms a(12) and beyond from McKay (1983), added by Thomas Curtright, Apr 12 2017
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STATUS
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approved
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