%I #6 Mar 13 2024 19:24:36
%S 1,-1,-1,3920,588,1,-8100814848000,-39479417600,-2979480,-1,
%T 1611539173017517109941370880000,61936836322916982325248000,
%U 39909735720699801600,163294580720,1,-6618882426924155530592746398747608414335176303936798720000
%N A triangle of coefficients from the transorthogonal ( or simplex code) matrix characteristic polynomial: h(i,j)=-1/(2^(i+j)-1);i,j<=n; m(i,j)=2^n^2)*Inverse(h(i,j))/6;.
%C The name contains an unmatched parenthesis. - Editors, Mar 13 2024
%C Row sums are:
%C {1, -2, 4509, -8140297245081, 1611601109893749762807690510321,
%C -6618882924928306991992730326130237124487220310559174099681}
%D http://www.ee.cityu.edu.hk/~eekwwong/ee40214/chapter3.pdf [broken link]
%F h(i,j)=-1/(2^(i+j)-1);i,j<=n; m(i,j)=2^n^2)*Inverse(h(i,j))/6;
%e {1},
%e {-1, -1},
%e {3920, 588, 1},
%e {-8100814848000, -39479417600, -2979480, -1},
%e {1611539173017517109941370880000, 61936836322916982325248000,39909735720699801600, 163294580720, 1},
%e {-6618882426924155530592746398747608414335176303936798720000,-498004150819770968302750426840905467826794397696000, -641629015618830186439905263755182106214400,
%e -5802015429341199319726979481600,-113104918891987680, -1}
%t M[w_] := Table[Table[ -1/(2^(n + m) - 1), {n, 1, w}], {m, 1, w}]; IM[w_] := Inverse[M[w]]; Join[{1}, Table[CharacteristicPolynomial[2^(n^2)*IM[n]/6, x], {n, 1, 5}]]; a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[2^(n^2)*IM[n]/6, x], x], {n, 1, 5}]]; Flatten[a] Join[{1}, Table[Apply[Plus, CoefficientList[CharacteristicPolynomial[2^(n^2)*IM[n]/6, x], x]], {n, 1, 5}]];
%K uned,tabl,sign
%O 1,4
%A _Roger L. Bagula_, Mar 20 2008