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A192837 Molecular topological indices of the permutation star graphs. 3
0, 4, 132, 4680, 214080, 12416400, 896132160, 79295610240, 8481591336960, 1081908144172800, 162548813750400000, 28443681284170521600, 5739117489117031219200, 1323378125974080765388800, 345972881092262536240128000, 101817548412839690547916800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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, May 13 2017

LINKS

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

Eric Weisstein's World of Mathematics, Molecular Topological Index

Eric Weisstein's World of Mathematics, Permutation Star Graph

FORMULA

a(n) = n!*(n-1) * (n-1 + Sum_{k=1..floor(3*(n-1)/2)} k*A007799(n, k)). - Andrew Howroyd, May 13 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, n - 2}];

Table[n! (n - 1) (n - 1 + Sum[k a[n, k], {k, Floor[3 (n - 1)/2]}]), {n, 20}]

(* Eric W. Weisstein, Sep 18 2017 *)

CROSSREFS

Cf. A007799.

Sequence in context: A064227 A204079 A252172 * A204077 A194537 A194538

Adjacent sequences:  A192834 A192835 A192836 * A192838 A192839 A192840

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jul 11 2011

EXTENSIONS

a(7)-a(16) from Andrew Howroyd, May 13 2017

STATUS

approved

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Last modified August 17 15:22 EDT 2018. Contains 313816 sequences. (Running on oeis4.)