

A164658


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


6



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
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OFFSET

0,6


COMMENTS

The denominators are given in A164659.
The column nr. m of the rational triangle A164658/A164659 when multiplied by m/2^(m2) becomes (with shifted offset) the column nr. m1 divided by 2^(m1) of the Chebyshev Ttriangle A053120 for m=1,2,3,...


LINKS

Table of n, a(n) for n=0..86.
W. 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 (* JeanFrançois Alcover, Oct 06 2016 *)


CROSSREFS

Row sums of triangle give A164662.
A053120: coefficients of Tpolynomials.
Row sums of rational triangle A164658/A164659 are given by A164660/A164661.
Sequence in context: A135523 A194663 A135685 * A079067 A160271 A274912
Adjacent sequences: A164655 A164656 A164657 * A164659 A164660 A164661


KEYWORD

sign,frac,tabl,easy


AUTHOR

Wolfdieter Lang, Oct 16 2009


STATUS

approved



