A164662 -id:A164662 - cp's OEIS frontend

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

Wolfdieter Lang, Oct 16 2009

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,...

			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],...

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

Row sums of triangle give A164662.
A053120: coefficients of T-polynomials.
Row sums of rational triangle A164658/A164659 are given by A164660/A164661.

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

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.

A164663 Row sums of triangle A164659 (denominators of coefficients from int(T(n,x),x), with T(n,x) Chebyshev polynomials of the first kind).

Original entry on oeis.org

1, 3, 5, 5, 11, 9, 17, 11, 25, 15, 31, 21, 35, 25, 49, 23, 55, 29, 53, 39, 71, 41, 77, 43, 79, 47, 97, 53, 95, 73, 89, 63, 115, 51, 165, 73, 131, 77, 135, 71, 141, 103, 125, 105, 163, 89, 169, 81, 161, 101, 193, 109, 181, 119, 197, 121, 261, 111, 203, 139, 179, 143, 239, 95

Offset: 0

Wolfdieter Lang, Oct 16 2009

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

Index entries for sequences related to Chebyshev polynomials.

Row sums of numerator triangle A164658 gives A164662.

a(n) = Sum_{m=1..n+1} A164659(n,m), n>=0.

cp's OEIS Frontend

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

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