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A192837 Molecular topological indices of the permutation star graphs.

%I A192837 #21 Feb 16 2025 08:33:15
%S A192837 0,4,132,4680,214080,12416400,896132160,79295610240,8481591336960,
%T A192837 1081908144172800,162548813750400000,28443681284170521600,
%U A192837 5739117489117031219200,1323378125974080765388800,345972881092262536240128000,101817548412839690547916800000
%N A192837 Molecular topological indices of the permutation star graphs.
%C A192837 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
%H A192837 Andrew Howroyd, <a href="/A192837/b192837.txt">Table of n, a(n) for n = 1..50</a>
%H A192837 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>
%H A192837 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PermutationStarGraph.html">Permutation Star Graph</a>
%F A192837 a(n) = n!*(n-1) * (n-1 + Sum_{k=1..floor(3*(n-1)/2)} k*A007799(n, k)). - _Andrew Howroyd_, May 13 2017
%t A192837 a[n_, 0] = 1; a[n_, 1] = n - 1; a[n_, 2] = (n - 1) (n - 2);
%t A192837 a[n_, k_ /; k >= 2] := a[n, k] = (n - 1) a[n - 1, k - 1] + Sum[j a[j, k - 3], {j, n - 2}];
%t A192837 Table[n! (n - 1) (n - 1 + Sum[k a[n, k], {k, Floor[3 (n - 1)/2]}]), {n, 20}]
%t A192837 (* _Eric W. Weisstein_, Sep 18 2017 *)
%Y A192837 Cf. A007799.
%K A192837 nonn
%O A192837 1,2
%A A192837 _Eric W. Weisstein_, Jul 11 2011
%E A192837 a(7)-a(16) from _Andrew Howroyd_, May 13 2017