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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.
0
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
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
Sequence in context: A108428 A373431 A174126 * A221837 A189150 A155194
KEYWORD
easy,sign,tabf
AUTHOR
Benoit Cloitre, Oct 11 2002
STATUS
approved