A075613 Triangular array read by rows, giving coefficients of P(n,X) = Product_{i=1..2n+1} (X - 1/cos(Pi*k/(2n+1))), a polynomial with integer coefficients.

1, 1, -4, -4, 1, 1, -12, -12, 16, 16, 1, 1, -24, -24, 80, 80, -64, -64, 1, 1, -40, -40, 240, 240, -448, -448, 256, 256, 1, 1, -60, -60, 560, 560, -1792, -1792, 2304, 2304, -1024, -1024, 1, 1, -84, -84, 1120, 1120, -5376, -5376, 11520, 11520, -11264, -11264, 4096, 4096, 1, 1, -112, -112, 2016, 2016, -13440

Offset

1,3

Comments

Also, coefficients of U(2n,x) repeated (A008312, Chebyshev polynomials of second kind). - Ralf Stephan, Sep 06 2004

Links

Table of n, a(n) for n=1..61.

Example

P(3,X) = X^7 + X^6 - 24*X^5 - 24*X^4 + 80*X^3 + 80*X^2 - 64*X - 64.
Array begins:
  1, 1,  -4,  -4;
  1, 1, -12, -12, 16, 16;
  1, 1, -24, -24, 80, 80, -64, -64;
  ...

Crossrefs

Cf. A008312, A075581.

Sequence in context: A108428 A373431 A174126 * A221837 A189150 A155194

Adjacent sequences: A075610 A075611 A075612 * A075614 A075615 A075616

Keyword

easy,sign,tabf

Author

Benoit Cloitre, Oct 11 2002

Status

approved