cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Wolfdieter Lang, Oct 16 2009

Keywords

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],...
		

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.

A164662 Row sums of triangle A164658 (numerators of coefficients from Integral_{x} T(n,x), with T(n,x) Chebyshev polynomials of the first kind).

Original entry on oeis.org

1, 1, 1, -2, 1, 8, -11, -41, -127, 107, -639, -1372, -3695, 514, -25983, -26339, -70655, -46299, -430955, -484134, -2808479, 93148, -5032895, -17319181, -72165695, 43371103, -171203135, -378398576, -148383647, -2605023034, -3368133419, 11479942073, -11902375935, 2021161097, -708801692671
Offset: 0

Views

Author

Wolfdieter Lang, Oct 16 2009

Keywords

Comments

The row sums of the rational triangle A164658/A164659 give A164660/A164661.

Crossrefs

Row sums of denominator triangle A164659 gives A164663.

Formula

a(n) = Sum_{m=1..n+1} A164658(n,m), n>=0.
Showing 1-2 of 2 results.