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

0,3

Comments

The numerators are given in A164658.

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

Links

Table of n, a(n) for n=0..103.

Index entries for sequences related to Chebyshev polynomials.

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.

Example

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],...

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 *)

Crossrefs

Row sums of this triangle give A164663.

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

Sequence in context: A357943 A194086 A342723 * A057898 A094293 A338156

Adjacent sequences: A164656 A164657 A164658 * A164660 A164661 A164662

Keyword

nonn,frac,tabl,easy

Author

Wolfdieter Lang, Oct 16 2009

Status

approved