A164659 Denominators of coefficients of integrated Chebyshev polynomials T(n,x) (in increasing order of powers of x).

1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 1, 3, 1, 5, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 5, 1, 7, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 7, 1, 9, 1, 2, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 3, 1, 1, 1, 1, 1, 9, 1, 11, 1, 2, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 13, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1

Offset: 0

Author

Wolfdieter Lang, Oct 16 2009

Keywords

• nonn
• frac
• tabl
• easy

Comments

The numerators are given in A164658.

See the W. Lang link in A164658 for this table and the rational table A164658/A164659.

Examples

			Rational table A164658(n,m)/a(n,m) = [1], [0, 1/2], [-1, 0, 2/3], [0, -3/2, 0, 1], [1, 0, -8/3, 0, 8/5],...
		

Links

• Index entries for sequences related to Chebyshev polynomials.

Crossrefs

Row sums of this triangle give A164663.

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

Programs

Mathematica

row[n_] := CoefficientList[Integrate[ChebyshevT[n, x], x], x] // Rest // Denominator; Table[row[n], {n, 0, 13}] // Flatten (* Jean-François Alcover, Oct 06 2016 *)

Formula

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