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A136449 Expansions of the characteristic polynomials of certain matrices, see Mathematica code. 0
1, 1, -1, -4, -1, 1, -27, 10, 4, -1, 256, 43, -42, -4, 1, 3125, -686, -398, 72, 9, -1, -46656, -5885, 5774, 542, -180, -9, 1, -823543, 127282, 86112, -11640, -2460, 264, 16, -1, 16777216, 1692439, -1666738, -138336, 51576, 3100, -520, -16, 1, 387420489, -46044262, -33920458, 3633796, 967479, -88890 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
C. Brezinski, Biorthogonal Polynomials And The Bordering Method For Linear Systems, (1993):http://citeseer.ist.psu.edu/brezinski93biorthogonal.html
Eric Weisstein's World of Mathematics, Hankel Matrix.
EXAMPLE
{1},
{1, -1},
{-4, -1, 1},
{-27, 10,4, -1},
{256, 43, -42, -4, 1},
{3125, -686, -398, 72, 9, -1},
{-46656, -5885, 5774, 542, -180, -9, 1},
{-823543, 127282, 86112, -11640, -2460, 264, 16, -1},
{16777216, 1692439, -1666738, -138336, 51576, 3100, -520, -16, 1},
{387420489, -46044262, -33920458, 3633796, 967479, -88890, -9850, 700, 25, -1},
{-10000000000, -840097729, 829514502, 60334298, -23981636, -1413279, 283290, 11850, -1200, -25, 1}
MATHEMATICA
H[n_] := Table[Table[If[i + j - 1 > n, 0, i + j - 1], {i, 1, n}], {j, 1, n}];
a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[H[n], x], x], {n, 1, 10}]];
Flatten[a]
CROSSREFS
Cf. A000312.
Sequence in context: A169654 A357744 A088158 * A209427 A140805 A113370
KEYWORD
uned,tabl,sign
AUTHOR
Roger L. Bagula, Mar 19 2008
STATUS
approved

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Last modified July 20 01:41 EDT 2024. Contains 374441 sequences. (Running on oeis4.)