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

0,6

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 nr. m-1 divided by 2^(m-1) of the Chebyshev T-triangle A053120 for m=1,2,3,...

Links

Table of n, a(n) for n=0..86.

Wolfdieter Lang, First eleven rows of the rational coefficients.

Index entries for sequences related to Chebyshev polynomials.

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.

Example

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],...

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 *)

Crossrefs

Row sums of triangle give A164662.

A053120: coefficients of T-polynomials.

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

Sequence in context: A194663 A135685 A349447 * A079067 A356676 A160271

Adjacent sequences: A164655 A164656 A164657 * A164659 A164660 A164661

Keyword

sign,frac,tabl,easy

Author

Wolfdieter Lang, Oct 16 2009

Status

approved