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%I #10 Aug 29 2019 08:53:12
%S 1,1,4,1,8,1,64,1,128,1,512,1,1024,1,16384,1,32768,1,131072,1,262144,
%T 1,2097152,1,4194304,1,16777216,1,33554432,1,1073741824,1,2147483648,
%U 1,8589934592,1,17179869184,1,137438953472,1,274877906944,1,1099511627776
%N Denominator of moments of Chebyshev U- (or S-) polynomials.
%C The numerators are given in A134828.
%C The weight function for Chebyshev's U-polynomials is w(x) = sqrt(1-x^2)*2/Pi for x in [-1,+1]. For the S-polynomials S(n,x) = U(n,x/2) on [-2,+2] it is sqrt(1-x^2)/Pi. For the coefficient of the S-polynomials see A049310.
%H W. Lang, <a href="/A134828/a134828.txt">Rationals and more</a>.
%F a(n) = denominator(r(n)) with r(n) = Integral_{x=-1..+1} (2/Pi)*sqrt(1-x^2)*x^n dx, n >= 0.
%F a(n)=1 if n is odd, a(n) = denominator(C(n/2)/2^n) if n is even, with the Catalan numbers C(n):=A000108(n).
%e Rationals: [1, 0, 1/4, 0, 1/8, 0, 5/64, 0, 7/128, 0, 21/512, 0, 33/1024, 0, ...].
%Y Cf. A120777 (coincides with denominators for even n).
%K nonn,easy,frac
%O 0,3
%A _Wolfdieter Lang_, Jan 21 2008
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