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Search: id:A114876
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| A114876 |
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Numerator of the discriminant of the n-th Legendre polynomial. |
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+0
2
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| 1, 4, 108, 442368, 51200000, 52428800000, 43177371238400000, 60766747818779941065981952, 23542283154891408151173909109014528, 60268244876522004867005207319077191680000000000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The denominator is A114877. It appears that every prime <= 2n-1 is a factor of the numerator or denominator of the discriminant d(n).
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LINKS
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Eric Weisstein's World of Mathematics, MathWorld: Polynomial Discriminant
Eric Weisstein's World of Mathematics, MathWorld: Legendre Polynomial
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FORMULA
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Let d(1)=1 and d(n) = d(n-1) n^(2n-2) (2n-1)^(3-2n). Then a(n)=numer(d(n)).
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EXAMPLE
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1, 4/3, 108/125, 442368/2100875, 51200000/2977309629, 52428800000/118890080527911,... = A114876/A114877
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CROSSREFS
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Cf. A114877.
Adjacent sequences: A114873 A114874 A114875 this_sequence A114877 A114878 A114879
Sequence in context: A107048 A002109 A076265 this_sequence A037980 A015100 A061454
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KEYWORD
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easy,frac,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jan 03 2006
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