A164658 Numerators of coefficients of integrated Chebyshev polynomials T(n,x) (in increasing order of powers of x).

1, 0, 1, -1, 0, 2, 0, -3, 0, 1, 1, 0, -8, 0, 8, 0, 5, 0, -5, 0, 8, -1, 0, 6, 0, -48, 0, 32, 0, -7, 0, 14, 0, -56, 0, 8, 1, 0, -32, 0, 32, 0, -256, 0, 128, 0, 9, 0, -30, 0, 72, 0, -72, 0, 128, -1, 0, 50, 0, -80, 0, 160, 0, -1280, 0, 512, 0, -11, 0, 55, 0, -616, 0, 352, 0, -1408, 0, 256, 1, 0, -24, 0, 168, 0, -512, 0, 768

Offset: 0

Author

Wolfdieter Lang, Oct 16 2009

Keywords

• sign
• frac
• tabl
• easy

Comments

The denominators are given in A164659.

The column m of the rational triangle A164658/A164659 when multiplied by m/2^(m-2) becomes (with shifted offset) the column no. m-1 divided by 2^(m-1) of the Chebyshev T-triangle A053120 for m=1,2,3,...

Examples

			Rationals a(n,m)/A164659(n,m) = [1], [0, 1/2], [-1, 0, 2/3], [0, -3/2, 0, 1], [1, 0, -8/3, 0, 8/5],...
		

Links

• Wolfdieter Lang, First eleven rows of the rational coefficients.
• Index entries for sequences related to Chebyshev polynomials.

Crossrefs

Row sums of triangle give A164662.

A053120: coefficients of T-polynomials.

Row sums of rational triangle A164658/A164659 are given by A164660/A164661.

Programs

Mathematica

row[n_] := CoefficientList[Integrate[ChebyshevT[n, x], x], x] // Rest // Numerator; Table[row[n], {n, 0, 12}] // Flatten (* Jean-François Alcover, Oct 06 2016 *)

Formula

a(n,m) = numerator(b(n,m)), with int(T(n,x))= sum(b(n,m)*x^m,m=1..n+1), n>=0, where T(n,x) are Chebyshevs polynomials of the first kind.