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A134448
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a(n) = discriminant of Brioschi quintic polynomial x^5 - 10*n*x^3 + 45*n^2*x - n^2.
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1
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9320403125, 9549620000000, 550785472903125, 9781641420800000, 91103907470703125, 564113147623200000, 2635397242528203125, 10017850209075200000, 32531698595851003125, 93301200312500000000, 242001831271659903125, 577707584762880000000, 1286270633097318903125
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OFFSET
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1,1
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
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FORMULA
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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
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MATHEMATICA
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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}]
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PROG
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(PARI) a(n) = poldisc(x^5 - 10*n*x^3 + 45*n^2*x - n^2); \\ Michel Marcus, Mar 02 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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