A134448 a(n) = discriminant of Brioschi quintic polynomial x^5 - 10*n*x^3 + 45*n^2*x - n^2.

9320403125, 9549620000000, 550785472903125, 9781641420800000, 91103907470703125, 564113147623200000, 2635397242528203125, 10017850209075200000, 32531698595851003125, 93301200312500000000, 242001831271659903125, 577707584762880000000, 1286270633097318903125

Offset

1,1

Links

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

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}]

Prog

(PARI) a(n) = poldisc(x^5 - 10*n*x^3 + 45*n^2*x - n^2); \\ Michel Marcus, Mar 02 2023

Crossrefs

Cf. A134450.

Sequence in context: A216014 A375862 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