|
%I #22 Dec 09 2017 20:19:49
%S 1,1,1,1,1,1,1,1,11,143,13,13,17,19,323,323,437,437,23,1,667,20677,
%T 899,31,899,33263,33263,33263,47027,2022161,65231,65231,3065857,
%U 3065857,3065857,3065857,4391633,4391633,4391633,4391633,6319667,385499687,8965109,8965109
%N Denominators of Harary index for the n-permutation star graph.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HararyIndex.html">Harary Index</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PermutationStarGraph.html">Permutation Star Graph</a>
%t 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 Table[n! Sum[A007799[n, k]/k, {k, Floor[3 (n - 1)/2]}]/2, {n, 20}] // Denominator (* _Eric W. Weisstein_, Dec 09 2017 *)
%Y Cf. A296190 (numerators), A007799, A284039.
%K nonn,frac
%O 1,9
%A _Andrew Howroyd_, Dec 09 2017
|
