A164659 - OEIS

%I #10 Oct 06 2016 09:14:22

%S 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,

%T 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,

%U 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

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

%C The numerators are given in A164658.

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

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

%F 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.

%e 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],...

%t row[n_] := CoefficientList[Integrate[ChebyshevT[n, x], x], x] // Rest // Denominator; Table[row[n], {n, 0, 13}] // Flatten (* _Jean-François Alcover_, Oct 06 2016 *)

%Y Row sums of this triangle give A164663.

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

%K nonn,frac,tabl,easy

%O 0,3

%A _Wolfdieter Lang_, Oct 16 2009