OFFSET
1,2
COMMENTS
a(n) is the numerator of an upper bound of the number of vertices of the polytope of the n X n X n stochastic tensors, or equivalently, of the number of Latin squares of order n, or equivalently, of the number of n X n X n line-stochastic (0,1)-tensors (see Chang et al. and Zhang et al.).
LINKS
Haixia Chang, Vehbi Emrah Paksoy and Fuzhen Zhang, Polytopes of Stochastic Tensors, Ann. Funct. Anal. 7(3): 386-393 (August 2016). arXiv:1608.03203 [math.CO], 2016. See p. 6.
Fuzhen Zhang and Xiao-Dong Zhang, Comparison of the upper bounds for the extreme points of the polytopes of line-stochastic tensors, arXiv:2110.12337 [math.CO], 2021. See p. 3.
FORMULA
MATHEMATICA
a[n_]:=Numerator[Binomial[n^3+6n^2-6n+2, n^3-1]/n^3]; Array[a, 6]
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Stefano Spezia, Nov 20 2021
STATUS
approved