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A136449 Hankel matrices are antidiagonals with decreasing n from the middle antidiagonal: here the characteristic polynomials of the matrices are made into a triangle of coefficients. 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

COMMENTS

Row sums are:

1, 0, -4, -14, 254, 2121, -46413, -623970, 16718722, 311959028, -9975349928

REFERENCES

C. Brezinski, Biorthogonal Polynomials And The Bordering Method For Linear Systems (1993):http://citeseer.ist.psu.edu/brezinski93biorthogonal.html

Weisstein, Eric W. "Hankel Matrix." http://mathworld.wolfram.com/HankelMatrix.html

LINKS

Table of n, a(n) for n=1..51.

FORMULA

Matrices are h(i,j) = If[i + j - 1 > n, 0, i + j - 1] for i,j < =n.

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: A220652 A169654 A088158 * A209427 A140805 A113370

Adjacent sequences:  A136446 A136447 A136448 * A136450 A136451 A136452

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Mar 19 2008

STATUS

approved

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Last modified May 17 12:43 EDT 2021. Contains 343971 sequences. (Running on oeis4.)