A076626 Array of coefficients of polynomials p(n,x) = 2^(n-1)*Product_{i=0..n} (x - cos(i*Pi/n)) of degree (n+1) with P(-1,x) = 1, P(0,x) = 0.

1, 0, 0, -1, 0, 1, 0, -2, 0, 2, 1, 0, -5, 0, 4, 0, 4, 0, -12, 0, 8, -1, 0, 13, 0, -28, 0, 16, 0, -6, 0, 38, 0, -64, 0, 32, 1, 0, -25, 0, 104, 0, -144, 0, 64, 0, 8, 0, -88, 0, 272, 0, -320, 0, 128, -1, 0, 41, 0, -280, 0, 688, 0, -704, 0, 256, 0, -10, 0, 170, 0, -832, 0, 1696, 0, -1536, 0, 512, 1, 0, -61, 0, 620, 0, -2352, 0, 4096, 0, -3328, 0, 1024

Offset

0,8

Comments

Mirror image of triangle in A201863. - Philippe Deléham, Dec 07 2011

Links

Table of n, a(n) for n=0..90.

Formula

T(n,k) = 2*T(n-1,k-1) - T(n-2,k). - Philippe Deléham, Dec 07 2011

Example

p(4,x) = 8*x^5 - 12*x^3 + 4*x hence 0,4,0,-12,0,8 are terms in the sequence.
From Philippe Deléham, Dec 07 2011: (Start)
Triangle begins:
   1;
   0,    0;
  -1,    0,    1;
   0,   -2,    0,    2;
   1,    0,   -5,    0,    4;
   0,    4,    0,  -12,    0,    8;
  -1,    0,   13,    0,  -28,    0,   16;
   0,   -6,    0,   38,    0,  -64,    0,   32;
   1,    0,  -25,    0,  104,    0, -144,    0,   64; (End)

Crossrefs

Cf. A201863, A201509.

Sequence in context: A362615 A362614 A336167 * A182886 A108731 A235168

Adjacent sequences: A076623 A076624 A076625 * A076627 A076628 A076629

Keyword

sign,tabl

Author

Benoit Cloitre, Oct 22 2002

Extensions

Definition corrected by Philippe Deléham, Dec 07 2011

Status

approved