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%I #33 Mar 02 2023 04:39:13
%S 9320403125,9549620000000,550785472903125,9781641420800000,
%T 91103907470703125,564113147623200000,2635397242528203125,
%U 10017850209075200000,32531698595851003125,93301200312500000000,242001831271659903125,577707584762880000000,1286270633097318903125
%N a(n) = discriminant of Brioschi quintic polynomial x^5 - 10*n*x^3 + 45*n^2*x - n^2.
%H Matthew Moore, <a href="https://web.archive.org/web/20211016014955/https://www.math.arizona.edu/~ura-reports/053/Moore.Matthew/Final.pdf">Theorems and Algorithms Associated with Solving the General Quintic</a> [Appears to give incorrect formula for the Brioschi quintic]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BrioschiQuinticForm.html">Brioschi Quintic Form</a>.
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F The discriminant is 5^5*n^8*(-1+1728n)^2. - _Klaus Brockhaus_, Oct 28 2007
%F 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
%t 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}]
%o (PARI) a(n) = poldisc(x^5 - 10*n*x^3 + 45*n^2*x - n^2); \\ _Michel Marcus_, Mar 02 2023
%Y Cf. A134450.
%K nonn,easy
%O 1,1
%A _Artur Jasinski_, Oct 26 2007, Oct 28 2007
%E Corrected by _Klaus Brockhaus_, Oct 28 2007
%E More terms from _Colin Barker_, Sep 02 2013
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