A006473 a(n) = binomial(n,2)!/n!. (Formerly M5217)

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

Offset

3,2

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

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.

Example

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

Mathematica

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

Crossrefs

Sequence in context: A306917 A135349 A159373 * A115459 A135421 A028668

Adjacent sequences: A006470 A006471 A006472 * A006474 A006475 A006476

Keyword

nonn

Author

N. J. A. Sloane

Status

approved