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A136481
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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.
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0
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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; internal format)
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OFFSET
| 1,5
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COMMENTS
| Row sums are:
{1, 0, -2, 3, -2, 0, 1, 0, -2, 3, -2}
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REFERENCES
| Terr, David and Weisstein, Eric W. "Symmetric Polynomial." http : // mathworld.wolfram.com/SymmetricPolynomial.html
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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
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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}
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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]
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CROSSREFS
| Cf. A100218, A098599.
Sequence in context: A130162 A175595 A175417 * A100218 A098599 A129334
Adjacent sequences: A136478 A136479 A136480 * A136482 A136483 A136484
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KEYWORD
| uned,tabl,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 20 2008
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