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 A136481 Symmetric polynomial matrices that give multivariate determinants as Coefficients of characteristic polynomials: h(n,m)=If[m == 1, n, If[n - m + 1 == 0, 1, If[n - m == 0, 1, If[n - m > 0, 1, 0]]]],n,m<=d. 1
 1, 1, -1, -1, -2, 1, 1, 0, 3, -1, -1, 0, 2, -4, 1, 1, 0, 0, -5, 5, -1, -1, 0, 0, -2, 9, -6, 1, 1, 0, 0, 0, 7, -14, 7, -1, -1, 0, 0, 0, 2, -16, 20, -8, 1, 1, 0, 0, 0, 0, -9, 30, -27, 9, -1, -1, 0, 0, 0, 0, -2, 25, -50, 35, -10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are: {1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2} REFERENCES Terr, David and Weisstein, Eric W. "Symmetric Polynomial." http : // mathworld.wolfram.com/SymmetricPolynomial.html LINKS FORMULA h(n,m)=If[m == 1, n, If[n - m + 1 == 0, 1, If[n - m == 0, 1, If[n - m > 0, 1, 0]]]],n,m<=d EXAMPLE {1}, {1, -1}, {-1, -2, 1}, {1, 0, 3, -1}, {-1, 0, 2, -4, 1}, {1, 0, 0, -5, 5, -1}, {-1, 0, 0, -2, 9, -6, 1}, {1, 0, 0, 0, 7, -14, 7, -1}, {-1,0, 0, 0, 2, -16, 20, -8, 1}, {1, 0, 0, 0, 0, -9, 30, -27,9, -1}, {-1, 0, 0, 0, 0, -2, 25, -50, 35, -10, 1} MATHEMATICA f[n_, m_] := If[m == 1, n, If[n - m + 1 == 0, 1, If[n - m == 0, 1, If[n - m > 0, 1, 0]]]]; M[d_] := Table[Table[f[n, m], {n, 1, d}], {m, 1, d}]; a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[M[n], x], x], {n, 1, 10}]]; Flatten[a] CROSSREFS Cf. A100218, A098599. Sequence in context: A130162 A175595 A175417 * A100218 A098599 A129334 Adjacent sequences:  A136478 A136479 A136480 * A136482 A136483 A136484 KEYWORD uned,tabl,sign AUTHOR Roger L. Bagula, Mar 20 2008 STATUS approved

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Last modified October 21 06:18 EDT 2019. Contains 328292 sequences. (Running on oeis4.)