A019447 Number of monomials in expansion of determinant of an n X n Toeplitz matrix [ t(|i-j|) ] in terms of its entries.
1, 1, 2, 4, 12, 35, 120, 427, 1628, 6090, 23797, 90296, 350726, 1338076, 5165957, 19732508
Offset: 0
Programs
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Maple
with(LinearAlgebra): f:=n->nops([coeffs(Determinant(Matrix(n, (i,j) -> a[abs(i-j)])))]): [seq(f(n),n=0..12)];
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Mathematica
f[n_] := Length[ Expand[ Det[ Table[ t[ Abs[ i - j]], {i, 1, n}, {j, 1, n}]]]]; Table[ f[n], {n, 1, 11}]
Extensions
Terms a(12) and a(13) from Thotsaporn Thanatipanonda, Jan 26-28 2012
Terms a(14) and a(15) from Roman Pearce, Aug 30 2014
a(0)=1 prepended by Alois P. Heinz, Feb 25 2024