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 A158452 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) 0
 1, 2, 2, 1, -1, 24, 24, 24, 24, 12, -12, 12, -12, 4, -4, -4, 4, 1, 1, -1, -1, 40320, 40320, 40320, 40320, 40320, 40320, 40320, 40320, 20160, -20160, -20160, -20160, 20160, 20160, -20160, 20160, 6720, 6720, -6720, -6720, -6720, -6720, 6720, 6720, 1680 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are: {0, -4, -25078, -6495526469206231383391390, 286062680268501848545408513842882834075841335269461890307160415945609971775008 5331640349522681828065666242531221092072696301456782016,...}. Example matrix: m(2^2)={{24, 24, 24, 24}, {12, -12, 12, -12}, {4, -4, -4, 4}, {1, 1, -1, -1}}. LINKS FORMULA M(d)=Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}]; m(n)=M(2^n)*Hadamard(2^n); out_(n,m)=coefficients(characteristicpolynomial(m(n),x),x) EXAMPLE {1, -1}, {-4, -1, 1}, {-18432, -5952, -688, -7, 1}, MATHEMATICA Needs["Hadamard`"]; M[d_] := Table[If[ m == n, d!/n!, 0], {n, d}, {m, d}]; 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}]]; Table[CoefficientList[CharacteristicPolynomial[a[[n]], x], x], {n, 1, Length[ a]}]; Flatten[a] Table[Apply[Plus, CoefficientList[CharacteristicPolynomial[a[[n]], x], x]], {n, 1, Length[a]}]; CROSSREFS Sequence in context: A174120 A240939 A016739 * A208929 A039965 A300481 Adjacent sequences:  A158449 A158450 A158451 * A158453 A158454 A158455 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Mar 19 2009 STATUS approved

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Last modified September 30 11:32 EDT 2020. Contains 337439 sequences. (Running on oeis4.)