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Search: id:A102692
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| A102692 |
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a(n) = number of digraphs (allowing loops) with vertices 1,2,...,n that have a unique Eulerian tour (up to cyclic shift). |
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+0
1
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| 2, 4, 28, 336, 5808, 132000, 33731040, 126362880, 4993309440, 225677975040, 11487263961600, 650467886745600, 40565803419187200, 2763133948128153600, 204127536266119065600, 16257504491853520896000
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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R. P. Stanley, unpublished work.
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FORMULA
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a(n) = (n-1)!(a(n) + a(n+1)), where a(n) is a little Schroeder number (A001003).
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EXAMPLE
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a(3) = 2!(3+11) = 28. There are 16 such digraphs which are triangles with a possible loop at each vertex, and 12 which consist of two 2-cycles with a common vertex and a possible loop at the other two vertices.
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CROSSREFS
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Adjacent sequences: A102689 A102690 A102691 this_sequence A102693 A102694 A102695
Sequence in context: A117443 A095858 A062792 this_sequence A126580 A124687 A018291
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KEYWORD
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nonn
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AUTHOR
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R. P. Stanley (rstan(AT)math.mit.edu), Feb 04 2005
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