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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). 0
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 (list; graph; refs; listen; history; text; internal format)
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: A021896 A188835 A217735 * A195284 A351263 A076341

Adjacent sequences: A075612 A075613 A075614 * A075616 A075617 A075618

KEYWORD

easy,sign,tabf

AUTHOR

Benoit Cloitre, Oct 11 2002

STATUS

approved

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Last modified January 28 20:13 EST 2023. Contains 359905 sequences. (Running on oeis4.)