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%I #39 Mar 29 2019 09:58:59
%S 1,2,5,16,58,231,1016,4782,23653,121727,648611,3541871,19713695
%N Number of monomials in expansion of determinant of an n X n Hankel matrix [ t(i+j) ] in terms of its entries.
%H Benjamin Basso and Lance J. Dixon, <a href="https://arxiv.org/abs/1705.03545">Gluing Ladders into Fishnets</a>, arXiv:1705.03545 [hep-th], 2017. See p. 5.
%p with(linalg): A019448 := proc(n) local i, j, m; m := array(1..n, 1..n); for i from 1 to n do for j from 1 to n do m[i, j] := a[i+j] od od; nops([coeffs(det(m))]); end; # _Jeffrey Shallit_, Jun 08 2000
%p with(LinearAlgebra): f:=n->nops([coeffs(Determinant(Matrix(n, (i, j) -> a[i+j] )))]): [seq(f(n), n=1..10)]; # _Vaclav Kotesovec_, Mar 29 2019
%t f[n_] := Length@ Expand@ Det@ Table[t[i + j], {i, n}, {j, n}]; Do[ Print@ f@n, {n, 11}] (* _Robert G. Wilson v_, Sep 17 2006 *)
%Y Cf. A019447, A019589, A086647.
%K nonn,hard,more
%O 1,2
%A Herbert S. Wilf
%E a(8)-a(9) from _Jeffrey Shallit_, Jun 08 2000
%E a(10)-a(11) from _Robert G. Wilson v_, Sep 17 2006
%E a(12) from _Roman Pearce_, Aug 30 2014
%E a(13) from _Vaclav Kotesovec_, Mar 20 2019
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