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A284039 Wiener index of the n-permutation star graph. 3
0, 1, 27, 744, 26520, 1239840, 74662560, 5663831040, 530098007040, 60105991680000, 8127440487936000, 1292894601191424000, 239129895342514176000, 50899158690744139776000, 12356174324714508288000000, 3393918280427832764006400000, 1047355019625604129593753600000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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, Sep 17 2017

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..50

Eric Weisstein's World of Mathematics, Permutation Star Graph

Eric Weisstein's World of Mathematics, Wiener Index

FORMULA

a(n) = n!/2 * Sum_{k=1..floor(3*(n-1)/2)} k*A007799(n, k). - Andrew Howroyd, Sep 17 2017

MATHEMATICA

a[n_, 0] = 1;

a[n_, 1] = n - 1;

a[n_, 2] = (n - 1) (n - 2);

a[n_, k_ /; k >= 2] := a[n, k] = (n - 1) a[n - 1, k - 1] + Sum[j a[j, k - 3], {j, 1, n - 2}];

Table[n!/2 Sum[k a[n, k], {k, Floor[3 (n - 1)/2]}], {n, 10}]

CROSSREFS

Cf. A007799, A192837.

Sequence in context: A046240 A042406 A279652 * A159668 A158645 A232951

Adjacent sequences:  A284036 A284037 A284038 * A284040 A284041 A284042

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Sep 13 2017

EXTENSIONS

Terms a(8) and beyond from Andrew Howroyd, Sep 17 2017

STATUS

approved

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Last modified April 9 23:09 EDT 2020. Contains 333382 sequences. (Running on oeis4.)