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A296190
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Numerators of Harary index for the n-permutation star graph.
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1
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0, 1, 10, 123, 2202, 59040, 2287680, 121394000, 92649740400, 105538103163360, 1034297134668000, 134399089883282400, 27076064087538702720, 5451799851068349018240, 19300076847195336557164800, 4599598343095846092562560000, 1682634821690958905899793664000
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OFFSET
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1,3
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COMMENTS
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The permutation star graph of order n is a vertex transitive graph with n! vertices and degree n-1. The graph can be constructed as the Cayley graph of the permutations of 1..n with the n-1 generators (1 2), (1 3)..(1 n) where (1 k) is the transposition of 1 and k. The number of nodes at distance k from a specified node is given by A007799(n,k). - Andrew Howroyd, Dec 09 2017
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LINKS
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FORMULA
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MATHEMATICA
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A007799[n_, i_] := Sum[Binomial[n - 1, k] Binomial[n - 1 - k, t] StirlingS1[k + 1, i - k + 1 - 2 t] (-1)^(i + 2 - t), {k, 0, Min[n - 1, i + 1]}, {t, Max[0, Ceiling[(i - 2 k)/2]], Min[n - 1 - k, Floor[(i + 1 - k)/2]]}];
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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