A006473 a(n) = binomial(n,2)!/n!.

1, 30, 30240, 1816214400, 10137091700736000, 7561714896123855667200000, 1025113885554181044609786839040000000, 32964677266721834921175915315161407370035200000000, 318071672921132854486459356650996997744817246158245068800000000000

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

a(n) is also the number of edge labelings of the complete graph on n vertices. - Nikos Apostolakis, Jul 09 2013

Examples

			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
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..30
• O. Frank and K. Svensson, On probability distributions of single-linkage dendrograms, Journal of Statistical Computation and Simulation, 12 (1981), 121-131. (Annotated scanned copy)
• C. L. Mallows, Note to N. J. A. Sloane circa 1979.

Programs

Mathematica

Table[Binomial[n,2]!/n!,{n,3,20}] (* Harvey P. Dale, May 08 2013 *)