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A102693
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a(n) = number of digraphs (not allowing loops) with vertices 1,2,...,n that have a unique Eulerian tour (up to cyclic shift).
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4
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1, 5, 42, 504, 7920, 154440, 3603600, 98017920, 3047466240, 106661318400, 4151586700800, 177925144320000, 8326896754176000, 422590010274432000, 23118159385601280000, 1356265350621941760000, 84945040381058457600000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| It appears that A102693 an be obtained from the permanent of (2,3,4,...,n+2) as in A203470. [From Clark Kimberling, Jan 02 2012]
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REFERENCES
| (unpublished work of the contributor)
R. P. Stanley, unpublished work.
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FORMULA
| a(n) = C_n(n-1)!/2 = (n+2)(n+3)...(2n-1), where C_n denotes a Catalan number
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EXAMPLE
| a(3) = 5. There are two such digraphs that are triangles and three that consist of two 2-cycles with a common vertex.
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MAPLE
| with(combstruct):ZL:=[T, {T=Union(Z, Prod(Epsilon, Z, T), Prod(T, Z, Epsilon), Prod(T, T, Z))}, labeled]:seq(count(ZL, size=i)/(2*i), i=2..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2007
> with(finance):seq(mul(cashflows([n, k, 1], 0), k=2..n), n=0..22); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
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CROSSREFS
| Equals (1/2) A065866(n-1).
Sequence in context: A024492 A005789 A151334 * A052654 A108398 A102244
Adjacent sequences: A102690 A102691 A102692 * A102694 A102695 A102696
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KEYWORD
| nonn
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AUTHOR
| R. P. Stanley (rstan(AT)math.mit.edu), Feb 04 2005
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