A019448 Number of monomials in expansion of determinant of an n X n Hankel matrix [ t(i+j) ] in terms of its entries.

1, 2, 5, 16, 58, 231, 1016, 4782, 23653, 121727, 648611, 3541871, 19713695

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Benjamin Basso and Lance J. Dixon, Gluing Ladders into Fishnets, arXiv:1705.03545 [hep-th], 2017. See p. 5.

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=1..10)]; # Vaclav Kotesovec, Mar 29 2019

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 *)

Crossrefs

Cf. A019447, A019589, A086647.

Sequence in context: A262441 A328296 A300042 * A243326 A185143 A280760

Adjacent sequences: A019445 A019446 A019447 * A019449 A019450 A019451

Keyword

nonn,hard,more

Author

Herbert S. Wilf

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

Status

approved