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Search: id:A075733
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| A075733 |
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Array of coefficients in Zagier's polynomials P_(n,0)(x). |
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3
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| 1, -2, 1, -8, 8, 1, -18, 48, -32, 1, -32, 160, -256, 128, 1, -50, 400, -1120, 1280, -512, 1, -72, 840, -3584, 6912, -6144, 2048, 1, -98, 1568, -9408, 26880, -39424, 28672, -8192, 1, -128, 2688, -21504, 84480, -180224, 212992, -131072, 32768, 1, -162, 4320, -44352, 228096, -658944, 1118208
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Zagier's polynomial P_{n,m} (m<=n and m>=0) are used under pari-gp (for algorithmic acceleration of alternating or positive series)
Up to signs, coefficients of Chebyshev's T-polynomials for even index. See A127674.
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FORMULA
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P_(n, 0)(x) = (-1)^n*2^(2*n-1)*prod(i=1, n, x-cos(Pi*(2*i-1)/4/n)^2)
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CROSSREFS
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Cf. A000332.
Sequence in context: A015152 A021461 A127674 this_sequence A123516 A016446 A086657
Adjacent sequences: A075730 A075731 A075732 this_sequence A075734 A075735 A075736
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KEYWORD
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sign,tabl
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 18 2002
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