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!)
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
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: A140501 A216014 A178558 * A048053 A130429 A130430
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

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 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)