A075615 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).

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

Offset

1,3

Comments

Included in A053120.

Links

Table of n, a(n) for n=1..75.

Example

Array begins:
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, -50, 0, 400, 0, -1120, 0, 1280, 0, -512;
...

Mathematica

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 *)

Crossrefs

Sequence in context: A188835 A217735 A369585 * A195284 A351263 A076341

Adjacent sequences: A075612 A075613 A075614 * A075616 A075617 A075618

Keyword

easy,sign,tabf

Author

Benoit Cloitre, Oct 11 2002

Status

approved