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A284039 Wiener index of the n-permutation star graph.

%I A284039 #63 Feb 16 2025 08:33:43
%S A284039 0,1,27,744,26520,1239840,74662560,5663831040,530098007040,
%T A284039 60105991680000,8127440487936000,1292894601191424000,
%U A284039 239129895342514176000,50899158690744139776000,12356174324714508288000000,3393918280427832764006400000,1047355019625604129593753600000
%N A284039 Wiener index of the n-permutation star graph.
%C A284039 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
%H A284039 Andrew Howroyd, <a href="/A284039/b284039.txt">Table of n, a(n) for n = 1..50</a>
%H A284039 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PermutationStarGraph.html">Permutation Star Graph</a>
%H A284039 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WienerIndex.html">Wiener Index</a>
%F A284039 a(n) = n!/2 * Sum_{k=1..floor(3*(n-1)/2)} k*A007799(n, k). - _Andrew Howroyd_, Sep 17 2017
%t A284039 a[n_, 0] = 1;
%t A284039 a[n_, 1] = n - 1;
%t A284039 a[n_, 2] = (n - 1) (n - 2);
%t A284039 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}];
%t A284039 Table[n!/2 Sum[k a[n, k], {k, Floor[3 (n - 1)/2]}], {n, 10}]
%Y A284039 Cf. A007799, A192837.
%K A284039 nonn
%O A284039 1,3
%A A284039 _Eric W. Weisstein_, Sep 13 2017
%E A284039 Terms a(8) and beyond from _Andrew Howroyd_, Sep 17 2017