A075615 - OEIS

%I #16 Nov 22 2016 16:16:09

%S 1,0,-2,1,0,-8,0,8,1,0,-18,0,48,0,-32,1,0,-32,0,160,0,-256,0,128,1,0,

%T -50,0,400,0,-1120,0,1280,0,-512,1,0,-72,0,840,0,-3584,0,6912,0,-6144,

%U 0,2048,1,0,-98,0,1568,0,-9408,0,26880,0,-39424,0,28672,0,-8192,1,0,-128,0,2688,0,-21504,0,84480,0,-180224,0

%N Let P(k,X) = Product_{i=1..2*k} (X-1/cos(Pi*(2*i-1)/(4*k)) ) which is a polynomial with integer coefficients. Sequence gives array of coefficients for P(k,X).

%C Included in A053120.

%e Array begins:

%e 1, 0,  -2;

%e 1, 0,  -8, 0,   8;

%e 1, 0, -18, 0,  48, 0,   -32;

%e 1, 0, -32, 0, 160, 0,  -256, 0,  128;

%e 1, 0, -50, 0, 400, 0, -1120, 0, 1280, 0, -512;

%e ...

%t rows = 8; P[k_] := Product[x-1/Cos[Pi*((2*i-1)/(4*k))], {i, 1, 2*k}]; Table[CoefficientList[P[k], x] // Round // Reverse, {k, 1, rows}] // Flatten (* _Jean-François Alcover_, Nov 22 2016 *)

%K easy,sign,tabf

%O 1,3

%A _Benoit Cloitre_, Oct 11 2002