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A134448 a(n) = discriminant of Brioschi quintic polynomial x^5 - 10*n*x^3 + 45*n^2*x - n^2. 1
9320403125, 9549620000000, 550785472903125, 9781641420800000, 91103907470703125, 564113147623200000, 2635397242528203125, 10017850209075200000, 32531698595851003125, 93301200312500000000, 242001831271659903125, 577707584762880000000, 1286270633097318903125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..13.

Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics 36(2), 2007, pp. 251-257. MR2312537.  Zbl 1133.11012.

Matthew Moore, Theorems and Algorithms Associated with Solving the General Quintic [Appears to give incorrect formula for the Brioschi quintic]

Eric Weisstein's World of Mathematics, Brioschi Quintic Form

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

FORMULA

The discriminant is 5^5*n^8*(-1+1728n)^2. - Klaus Brockhaus, Oct 28 2007

G.f.: -3125*x*(2989441*x^9 +3026533493*x^8 +142898228696*x^7 +1359450487664*x^6 +3912930922946*x^5 +3912461211074*x^4 +1358941584752*x^3 +142800728024*x^2 +3023070581*x +2982529) / (x -1)^11. - Colin Barker, Sep 02 2013

MATHEMATICA

Discriminant[p_?PolynomialQ, x_] := With[{n = Exponent[p, x], k = Exponent[D[p, x], x]}, Cancel[((-1)^(n(n - 1)/2)Resultant[ p, D[p, x], x]) Coefficient[p, x, n]^(n - k - 2)]] ; Table[Discriminant[x^5 - 10p x^3 + 45p^2 x - p^2, x], {p, 1, 20}]

CROSSREFS

Cf. A134450.

Sequence in context: A140501 A216014 A178558 * A048053 A130429 A130430

Adjacent sequences:  A134445 A134446 A134447 * A134449 A134450 A134451

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Oct 26 2007, Oct 28 2007

EXTENSIONS

Corrected by Klaus Brockhaus, Oct 28 2007

More terms from Colin Barker, Sep 02 2013

STATUS

approved

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Last modified September 18 05:51 EDT 2021. Contains 347509 sequences. (Running on oeis4.)