login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A136449 Expansions of the characteristic polynomials of certain matrices, see Mathematica code. 0

%I #12 Sep 16 2022 09:42:43

%S 1,1,-1,-4,-1,1,-27,10,4,-1,256,43,-42,-4,1,3125,-686,-398,72,9,-1,

%T -46656,-5885,5774,542,-180,-9,1,-823543,127282,86112,-11640,-2460,

%U 264,16,-1,16777216,1692439,-1666738,-138336,51576,3100,-520,-16,1,387420489,-46044262,-33920458,3633796,967479,-88890

%N Expansions of the characteristic polynomials of certain matrices, see Mathematica code.

%H C. Brezinski, <a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.12.857">Biorthogonal Polynomials And The Bordering Method For Linear Systems</a>, (1993):http://citeseer.ist.psu.edu/brezinski93biorthogonal.html

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HankelMatrix.html">Hankel Matrix</a>.

%e {1},

%e {1, -1},

%e {-4, -1, 1},

%e {-27, 10,4, -1},

%e {256, 43, -42, -4, 1},

%e {3125, -686, -398, 72, 9, -1},

%e {-46656, -5885, 5774, 542, -180, -9, 1},

%e {-823543, 127282, 86112, -11640, -2460, 264, 16, -1},

%e {16777216, 1692439, -1666738, -138336, 51576, 3100, -520, -16, 1},

%e {387420489, -46044262, -33920458, 3633796, 967479, -88890, -9850, 700, 25, -1},

%e {-10000000000, -840097729, 829514502, 60334298, -23981636, -1413279, 283290, 11850, -1200, -25, 1}

%t H[n_] := Table[Table[If[i + j - 1 > n, 0, i + j - 1], {i, 1, n}], {j, 1, n}];

%t a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[H[n], x], x], {n, 1, 10}]];

%t Flatten[a]

%Y Cf. A000312.

%K uned,tabl,sign

%O 1,4

%A _Roger L. Bagula_, Mar 19 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)