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

%I A164658 #21 Apr 08 2025 08:45:49
%S A164658 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,
%T A164658 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,
%U A164658 -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
%N A164658 Numerators of coefficients of integrated Chebyshev polynomials T(n,x) (in increasing order of powers of x).
%C A164658 The denominators are given in A164659.
%C A164658 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,...
%H A164658 Wolfdieter Lang, <a href="/A164658/a164658.txt">First eleven rows of the rational coefficients</a>.
%H A164658 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials</a>.
%F A164658 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.
%e A164658 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],...
%t A164658 row[n_] := CoefficientList[Integrate[ChebyshevT[n, x], x], x] // Rest // Numerator; Table[row[n], {n, 0, 12}] // Flatten (* _Jean-François Alcover_, Oct 06 2016 *)
%Y A164658 Row sums of triangle give A164662.
%Y A164658 A053120: coefficients of T-polynomials.
%Y A164658 Row sums of rational triangle A164658/A164659 are given by A164660/A164661.
%K A164658 sign,frac,tabl,easy
%O A164658 0,6
%A A164658 _Wolfdieter Lang_, Oct 16 2009