A136459 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;.

1, -1, -1, 3920, 588, 1, -8100814848000, -39479417600, -2979480, -1, 1611539173017517109941370880000, 61936836322916982325248000, 39909735720699801600, 163294580720, 1, -6618882426924155530592746398747608414335176303936798720000

Offset

1,4

Comments

Row sums are:

{1, -2, 4509, -8140297245081, 1611601109893749762807690510321,

-6618882924928306991992730326130237124487220310559174099681}

References

http://www.ee.cityu.edu.hk/~eekwwong/ee40214/chapter3.pdf

Links

Table of n, a(n) for n=1..16.

Formula

h(i,j)=-1/(2^(i+j)-1);i,j<=n; m(i,j)=2^n^2)*Inverse(h(i,j))/6;

Example

{1},
{-1, -1},
{3920, 588, 1},
{-8100814848000, -39479417600, -2979480, -1},
{1611539173017517109941370880000, 61936836322916982325248000,39909735720699801600, 163294580720, 1},
{-6618882426924155530592746398747608414335176303936798720000,-498004150819770968302750426840905467826794397696000, -641629015618830186439905263755182106214400,
-5802015429341199319726979481600,-113104918891987680, -1}

Mathematica

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}]];

Crossrefs

Sequence in context: A131409 A209732 A221239 * A235315 A229642 A266060

Adjacent sequences: A136456 A136457 A136458 * A136460 A136461 A136462

Keyword

uned,tabl,sign

Author

Roger L. Bagula, Mar 20 2008

Status

approved