OFFSET
1,7
COMMENTS
T(n,k)=cos(n,k)*cos(pi*k/2) begins {1}, {1,0}, {1,0,-1}, {1,0,-3,0},... - Paul Barry, May 21 2006
LINKS
Clark Kimberling, Polynomials associated with reciprocation, JIS 12 (2009) 09.3.4, section 5.
EXAMPLE
The trigonometric expansion of Cos(4x) = Cos[x]^4 - 6*Cos[x]^2*Sin[x]^2 + Sin[x]^4, therefore the fourth row is 1, 0, -6, 0, 1.
The trigonometric expansion of Cos(5x) = Cos[x]^5 - 10*Cos[x]^3*Sin[x]^2 + 5*Cos[x]*Sin[x]^4, therefore the fifth row of the triangle is 1, 0, -10, 0, 5
The table begins:
1
1 0 -1
1 0 -3
1 0 -6 0 1
1 0 -10 0 5
1 0 -15 0 15 0 -1
1 0 -21 0 35 0 -7
1 0 -28 0 70 0 -28 0 1
MATHEMATICA
Flatten[Table[ Plus @@ CoefficientList[ TrigExpand[ Cos[n*x]], { Cos[x], Sin[x]}], {n, 13}]]
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Robert G. Wilson v, Jul 07 2004
STATUS
approved