A284309 Number of singular vector tuples for a general n-dimensional {n}^n tensor.

1, 2, 37, 51264, 14346274601, 1435747717722810960, 79118094349714452632485774477, 3409699209687052091502059492845005192560640, 154730604283618051465998344012575355916858352712971348277665, 9576184829775011641104888042379740657096306109466956243538100418643876547244800

Offset: 1

Author

Alois P. Heinz, Mar 24 2017

Keywords

• nonn

Links

• Shalosh B. Ekhad and Doron Zeilberger, On the Number of Singular Vector Tuples of Hyper-Cubical Tensors, 2016; also arXiv preprint arXiv:1605.00172, 2016.
• Shmuel Friedland and Giorgio Ottaviani, The number of singular vector tuples and uniqueness of best rank-one approximation of tensors, Found. Comput. Math. 14 (2014), no. 6, 1209-1242.
• Bernd Sturmfels, Tensors and Their Eigenvalues, Notices AMS, 63 (No. 6, 2016), 606-606.

Crossrefs

Main diagonal of A284308.

Programs

Mathematica

a[1] = 1;
a[n_] := Module[{Z, z, P},
  Z[i_] := Sum[z[k], {k, 1, n}] - z[i];
  P = Product[(Z[i]^n - z[i]^n)/(Z[i] - z[i]), {i, 1, n}] // Cancel;
  SeriesCoefficient[P, Sequence @@ Table[{z[i], 0, n-1}, {i, 1, n}]]
];
Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 5}] (* Jean-François Alcover, Aug 06 2018 *)