A075733 Array of coefficients in Zagier's polynomials P_(n,0)(x).

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

Offset: 1

Author

Benoit Cloitre, Oct 18 2002

Keywords

• sign
• tabl

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.

Crossrefs

Cf. A000332.

Formula

P_(n, 0)(x) = (-1)^n*2^(2*n-1)*Product_{i=1..n} (x - cos(Pi*(2*i-1)/(4*n))^2).