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A075733 Array of coefficients in Zagier's polynomials P_(n,0)(x). 2
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..51.

FORMULA

P_(n, 0)(x) = (-1)^n*2^(2*n-1)*prod(i=1, n, x-cos(Pi*(2*i-1)/4/n)^2)

CROSSREFS

Cf. A000332.

Sequence in context: A015152 A021461 * A127674 A271316 A145901 A286724

Adjacent sequences:  A075730 A075731 A075732 * A075734 A075735 A075736

KEYWORD

sign,tabl

AUTHOR

Benoit Cloitre, Oct 18 2002

STATUS

approved

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Last modified October 16 11:06 EDT 2018. Contains 316263 sequences. (Running on oeis4.)