cp's OEIS Frontend

A296190 Numerators of Harary index for the n-permutation star graph.

%I A296190 #15 Feb 16 2025 08:33:52
%S A296190 0,1,10,123,2202,59040,2287680,121394000,92649740400,105538103163360,
%T A296190 1034297134668000,134399089883282400,27076064087538702720,
%U A296190 5451799851068349018240,19300076847195336557164800,4599598343095846092562560000,1682634821690958905899793664000
%N A296190 Numerators of Harary index for the n-permutation star graph.
%C A296190 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_, Dec 09 2017
%H A296190 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HararyIndex.html">Harary Index</a>
%H A296190 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PermutationStarGraph.html">Permutation Star Graph</a>
%F A296190 a(n)/A296057(n) = (n!/2) * Sum_{k=1..floor(3*(n-1)/2)} A007799(n, k)/k. - _Andrew Howroyd_, Dec 09 2017
%t A296190 A007799[n_, i_] := Sum[Binomial[n - 1, k] Binomial[n - 1 - k, t] StirlingS1[k + 1, i - k + 1 - 2 t] (-1)^(i + 2 - t), {k, 0, Min[n - 1, i + 1]}, {t, Max[0, Ceiling[(i - 2 k)/2]], Min[n - 1 - k, Floor[(i + 1 - k)/2]]}];
%t A296190 Table[n! Sum[A007799[n, k]/k, {k, Floor[3 (n - 1)/2]}]/2, {n, 20}] // Numerator (* _Eric W. Weisstein_, Dec 09 2017 *)
%Y A296190 Cf. A296057 (denominators), A007799, A284039.
%K A296190 nonn,frac
%O A296190 1,3
%A A296190 _Eric W. Weisstein_, Dec 07 2017
%E A296190 a(9)-a(17) from _Andrew Howroyd_, Dec 09 2017