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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.
10
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
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
Rows n=1-3 give: A000012, A000142, A274308.
Main diagonal gives A284309.
Sequence in context: A144351 A213936 A142589 * A369435 A172400 A226691
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Mar 24 2017
STATUS
approved