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A338104
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Number of spanning trees in the join of the disjoint union of two complete graphs each on n vertices with the empty graph on n+1 vertices.
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4
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1, 4, 1200, 2074464, 10883911680, 128615328600000, 2881502756476710912, 109416128865750000000000, 6508595325997684722663161856, 572150341080161420030586961966080, 71062412455566037275496151040000000000
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OFFSET
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0,2
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COMMENTS
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Equivalently, the graph can be described as the graph on 3*n + 1 vertices with labels 0..3*n and with i and j adjacent iff A011655(i + j) = 1.
These graphs are cographs.
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LINKS
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FORMULA
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a(n) = (n + 1)*(2*n)^n*(2*n + 1)^(2*(n - 1)).
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EXAMPLE
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The adjacency matrix of the graph associated with n = 2 is: (compare A204437)
[0, 1, 1, 0, 1, 1, 0]
[1, 0, 0, 1, 1, 0, 1]
[1, 0, 0, 1, 0, 1, 1]
[0, 1, 1, 0, 1, 1, 0]
[1, 1, 0, 1, 0, 0, 1]
[1, 0, 1, 1, 0, 0, 1]
[0, 1, 1, 0, 1, 1, 0]
a(2) = 1200 because the graph has 1200 spanning trees.
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MATHEMATICA
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Table[(n + 1)*(2 n)^n*(2 n + 1)^(2 (n - 1)), {n, 1, 10}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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