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A284309 Number of singular vector tuples for a general n-dimensional {n}^n tensor. 1
1, 2, 37, 51264, 14346274601, 1435747717722810960, 79118094349714452632485774477, 3409699209687052091502059492845005192560640, 154730604283618051465998344012575355916858352712971348277665, 9576184829775011641104888042379740657096306109466956243538100418643876547244800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..10.

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.

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-Fran├žois Alcover, Aug 06 2018 *)

CROSSREFS

Main diagonal of A284308.

Sequence in context: A110762 A277409 A201556 * A227468 A049487 A163792

Adjacent sequences:  A284306 A284307 A284308 * A284310 A284311 A284312

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 24 2017

STATUS

approved

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Last modified September 19 03:31 EDT 2021. Contains 347550 sequences. (Running on oeis4.)