A296785 - OEIS

%I #13 Dec 24 2017 10:35:39

%S 0,1,69,6216,846120,185976720,63980285040,32772128296320,

%T 23892198317930880,23892346459702828800,31800733054746203116800,

%U 54951669873436196523801600,120728819293576143371142220800,331279880265073822312384445491200

%N Detour index for the n-transposition graph.

%C Also, the maximum detour index of any bipartite graph on n! nodes. - _Andrew Howroyd_, Dec 21 2017

%H Andrew Howroyd, <a href="/A296785/b296785.txt">Table of n, a(n) for n = 1..100</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TranspositionGraph.html">Transposition Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DetourIndex.html">Detour Index</a>

%F a(n) = n!*(n!/2-1)^2 + (n!/2)^2*(n!-1) for n > 1. - _Andrew Howroyd_, Dec 20 2017

%F a(n) = A296819(n!). - _Andrew Howroyd_, Dec 23 2017

%t Table[If[n == 1, 0, n! (n! (2 n! - 5) + 4)/4], {n, 20}]

%o (PARI) a(n) = if(n==1, 0, n!*(n!/2-1)^2 + (n!/2)^2*(n!-1)) \\ _Andrew Howroyd_, Dec 20 2017

%Y Cf. A296782, A296819.

%K nonn

%O 1,3

%A _Eric W. Weisstein_, Dec 20 2017

%E Terms a(5) and beyond from _Andrew Howroyd_, Dec 20 2017