A284308 Number A(n,k) of singular vector tuples for a general k-dimensional {n}^k tensor; square array A(n,k), n>=1, k>=1, read by antidiagonals.

1, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 24, 37, 4, 1, 1, 120, 997, 240, 5, 1, 1, 720, 44121, 51264, 1621, 6, 1, 1, 5040, 2882071, 23096640, 2940841, 11256, 7, 1, 1, 40320, 260415373, 18754813440, 14346274601, 180296088, 79717, 8, 1, 1, 362880, 31088448777, 24874143759360, 153480509680141, 9859397817600, 11559133741, 572928, 9, 1

Offset

1,5

Links

Alois P. Heinz, Antidiagonals n = 1..18, flattened

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.

Example

Square array A(n,k) begins:
  1, 1,     1,         1,             1,                   1, ...
  1, 2,     6,        24,           120,                 720, ...
  1, 3,    37,       997,         44121,             2882071, ...
  1, 4,   240,     51264,      23096640,         18754813440, ...
  1, 5,  1621,   2940841,   14346274601,     153480509680141, ...
  1, 6, 11256, 180296088, 9859397817600, 1435747717722810960, ...

Crossrefs

Columns k=1-9 give: A000012, A000027, A271905, A272551, A283829, A283830, A287083, A287084, A287085.

Rows n=1-3 give: A000012, A000142, A274308.

Main diagonal gives A284309.

Sequence in context: A144351 A213936 A142589 * A369435 A172400 A226691

Adjacent sequences: A284305 A284306 A284307 * A284309 A284310 A284311

Keyword

nonn,tabl

Author

Alois P. Heinz, Mar 24 2017

Status

approved