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Search: id:A136459
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| A136459 |
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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;. |
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+0
1
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| 1, -1, -1, 3920, 588, 1, -8100814848000, -39479417600, -2979480, -1, 1611539173017517109941370880000, 61936836322916982325248000, 39909735720699801600, 163294580720, 1, -6618882426924155530592746398747608414335176303936798720000
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row sums are:
{1, -2, 4509, -8140297245081, 1611601109893749762807690510321,
-6618882924928306991992730326130237124487220310559174099681}
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REFERENCES
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http://www.ee.cityu.edu.hk/~eekwwong/ee40214/chapter3.pdf
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FORMULA
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h(i,j)=-1/(2^(i+j)-1);i,j<=n; m(i,j)=2^n^2)*Inverse(h(i,j))/6;
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EXAMPLE
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{1},
{-1, -1},
{3920, 588, 1},
{-8100814848000, -39479417600, -2979480, -1},
{1611539173017517109941370880000, 61936836322916982325248000,39909735720699801600, 163294580720, 1},
{-6618882426924155530592746398747608414335176303936798720000,-498004150819770968302750426840905467826794397696000, -641629015618830186439905263755182106214400,
-5802015429341199319726979481600,-113104918891987680, -1}
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MATHEMATICA
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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}]];
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CROSSREFS
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Adjacent sequences: A136456 A136457 A136458 this_sequence A136460 A136461 A136462
Sequence in context: A068240 A022212 A131409 this_sequence A034283 A014887 A031822
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 20 2008
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