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%I #21 Mar 25 2018 04:38:07
%S 0,1,21,552,19560,920160,55974240,4293596160,406306575360,
%T 46556342784000,6357567896064000,1020650937901056000,
%U 190386526063878144000,40844355820490686464000,9987985777548364185600000,2762125829379285162393600000,857790151281459139077734400000
%N Wiener index of the n-transposition graph.
%H Andrew Howroyd, <a href="/A292062/b292062.txt">Table of n, a(n) for n = 1..50</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/WienerIndex.html">Wiener Index</a>
%F From _Andrew Howroyd_, Sep 08 2017: (Start)
%F a(n) = n! * A067318(n) / 2.
%F a(n) = n! * (n*n! - abs(Stirling1(n+1, 2))) / 2.
%F (End)
%F a(n) = (n!/2) * Sum_{k=1..n-1} abs(Stirling1(n, n-k))*k. - _Andrew Howroyd_, Dec 09 2017
%t Table[n! (n n! + (-1)^n StirlingS1[n + 1, 2])/2, {n, 20}]
%o (PARI)
%o a(n) = n! * (n*n! - abs(stirling(n+1, 2, 1))) / 2; \\ _Andrew Howroyd_, Sep 08 2017
%Y Cf. A067318, A296194.
%K nonn
%O 1,3
%A _Eric W. Weisstein_, Sep 08 2017
%E Terms a(9) and beyond from _Andrew Howroyd_, Sep 08 2017