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%I M5217 #48 Oct 04 2017 00:17:21
%S 1,30,30240,1816214400,10137091700736000,7561714896123855667200000,
%T 1025113885554181044609786839040000000,
%U 32964677266721834921175915315161407370035200000000,318071672921132854486459356650996997744817246158245068800000000000
%N a(n) = binomial(n,2)!/n!.
%C a(n) is also the number of distinct possible (n-1)-dimensional simplices if the (n-1)*n/2 1-faces are given (up to symmetry, rotation, reflection). - _Dan Dima_, Nov 03 2011
%C a(n) is also the number of edge labelings of the complete graph on n vertices. - _Nikos Apostolakis_, Jul 09 2013
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A006473/b006473.txt">Table of n, a(n) for n = 3..30</a>
%H O. Frank and K. Svensson, <a href="/A006472/a006472_1.pdf">On probability distributions of single-linkage dendrograms</a>, Journal of Statistical Computation and Simulation, 12 (1981), 121-131. (Annotated scanned copy)
%H C. L. Mallows, <a href="/A006472/a006472.pdf">Note to N. J. A. Sloane circa 1979</a>.
%e a(3)=1 since there is one possible triangle if the 3 edges are given and a(4)=30 since there are 30 distinct possible tetrahedra if the 6 edges are given. - _Dan Dima_, Nov 03 2011
%t Table[Binomial[n,2]!/n!,{n,3,20}] (* _Harvey P. Dale_, May 08 2013 *)
%K nonn
%O 3,2
%A _N. J. A. Sloane_
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