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%I #8 Aug 06 2018 10:59:52
%S 1,2,37,51264,14346274601,1435747717722810960,
%T 79118094349714452632485774477,
%U 3409699209687052091502059492845005192560640,154730604283618051465998344012575355916858352712971348277665,9576184829775011641104888042379740657096306109466956243538100418643876547244800
%N Number of singular vector tuples for a general n-dimensional {n}^n tensor.
%H Shalosh B. Ekhad and Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/svt.html">On the Number of Singular Vector Tuples of Hyper-Cubical Tensors</a>, 2016; also arXiv preprint arXiv:1605.00172, 2016.
%H Shmuel Friedland and Giorgio Ottaviani, <a href="http://dx.doi.org/10.1007/s10208-014-9194-z">The number of singular vector tuples and uniqueness of best rank-one approximation of tensors</a>, Found. Comput. Math. 14 (2014), no. 6, 1209-1242.
%H Bernd Sturmfels, <a href="http://www.ams.org/publications/journals/notices/201606/rnoti-p604.pdf">Tensors and Their Eigenvalues</a>, Notices AMS, 63 (No. 6, 2016), 606-606.
%t a[1] = 1;
%t a[n_] := Module[{Z, z, P},
%t Z[i_] := Sum[z[k], {k, 1, n}] - z[i];
%t P = Product[(Z[i]^n - z[i]^n)/(Z[i] - z[i]), {i, 1, n}] // Cancel;
%t SeriesCoefficient[P, Sequence @@ Table[{z[i], 0, n-1}, {i, 1, n}]]
%t ];
%t Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 5}] (* _Jean-François Alcover_, Aug 06 2018 *)
%Y Main diagonal of A284308.
%K nonn
%O 1,2
%A _Alois P. Heinz_, Mar 24 2017
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