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%I #2 Mar 30 2012 17:34:35
%S 1,2,2,1,-1,24,24,24,24,12,-12,12,-12,4,-4,-4,4,1,1,-1,-1,40320,40320,
%T 40320,40320,40320,40320,40320,40320,20160,-20160,-20160,-20160,20160,
%U 20160,-20160,20160,6720,6720,-6720,-6720,-6720,-6720,6720,6720,1680
%N A triangle sequence of permutation Hadamard {1,-1) matrix polynomials: M(d)=Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}]; m(n)=M(2^n)*Hadamard(2^n)
%C Row sums are:
%C {0, -4, -25078, -6495526469206231383391390,
%C 286062680268501848545408513842882834075841335269461890307160415945609971775008
%C 5331640349522681828065666242531221092072696301456782016,...}.
%C Example matrix:
%C m(2^2)={{24, 24, 24, 24},
%C {12, -12, 12, -12},
%C {4, -4, -4, 4},
%C {1, 1, -1, -1}}.
%F M(d)=Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}];
%F m(n)=M(2^n)*Hadamard(2^n);
%F out_(n,m)=coefficients(characteristicpolynomial(m(n),x),x)
%e {1, -1},
%e {-4, -1, 1},
%e {-18432, -5952, -688, -7, 1},
%t Needs["Hadamard`"];
%t M[d_] := Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}];
%t a = Join[{{{1}}}, Table[M[2^n].If[Hadamard[2^n] == {} && 2^n >= 3, 0, If[2^n == 2, Hadamard[2], Hadamard[2^n][[1]]]], {n, 1, 4}]];
%t Table[CoefficientList[CharacteristicPolynomial[a[[n]], x], x], {n, 1, Length[ a]}];
%t Flatten[a]
%t Table[Apply[Plus, CoefficientList[CharacteristicPolynomial[a[[n]], x], x]], {n, 1, Length[a]}];
%K sign,tabl,uned
%O 0,2
%A _Roger L. Bagula_, Mar 19 2009
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