A019448 Number of monomials in expansion of determinant of an n X n Hankel matrix [ t(i+j) ] in terms of its entries.
1, 1, 2, 5, 16, 58, 231, 1016, 4782, 23653, 121727, 648611, 3541871, 19713695
Offset: 0
Links
- Benjamin Basso and Lance J. Dixon, Gluing Ladders into Fishnets, arXiv:1705.03545 [hep-th], 2017. See p. 5.
Programs
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Maple
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 with(LinearAlgebra): f:=n->nops([coeffs(Determinant(Matrix(n, (i, j) -> a[i+j] )))]): [seq(f(n), n=0..10)]; # Vaclav Kotesovec, Mar 29 2019
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Mathematica
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 *)
Extensions
a(8)-a(9) from Jeffrey Shallit, Jun 08 2000
a(10)-a(11) from Robert G. Wilson v, Sep 17 2006
a(12) from Roman Pearce, Aug 30 2014
a(13) from Vaclav Kotesovec, Mar 20 2019
a(0)=1 prepended by Alois P. Heinz, Jan 08 2025