A192837 Molecular topological indices of the permutation star graphs.

0, 4, 132, 4680, 214080, 12416400, 896132160, 79295610240, 8481591336960, 1081908144172800, 162548813750400000, 28443681284170521600, 5739117489117031219200, 1323378125974080765388800, 345972881092262536240128000, 101817548412839690547916800000

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: A353794 A204079 A252172 * A338040 A204077 A194537

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