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A349508 a(n) is the numerator of binomial(n^3 + 6*n^2 - 6*n + 2, n^3 - 1)/n^3. 6
1, 21318, 111399602430962720, 219754881677312748254868619396977023490, 91574665590547903212939476569574243557076290573519342040406738188187312 (list; graph; refs; listen; history; text; internal format)
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
a(n)/A349509(n) <= A349510(n) < A349511(n) < A349512(n) (see Corollary 7 in Zhang et al., 2021).
a(n)/A349509(n) ~ 2^(-4 + 6*n - 6*n^2)*3^(-7/2 + 6*n - 6*n^2)*e^(-75 + 233/n + 18*n + 6*n^2)*n^(-1 - 6*n + 6*n^2)/sqrt(Pi).
MATHEMATICA
a[n_]:=Numerator[Binomial[n^3+6n^2-6n+2, n^3-1]/n^3]; Array[a, 6]
CROSSREFS
Cf. A349506, A349507, A349509 (denominators), A349510, A349511, A349512.
Sequence in context: A254385 A254392 A253980 * A250532 A234454 A319017
KEYWORD
nonn,frac
AUTHOR
Stefano Spezia, Nov 20 2021
STATUS
approved

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Last modified February 24 20:48 EST 2024. Contains 370307 sequences. (Running on oeis4.)