The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A134829 Denominator of moments of Chebyshev U- (or S-) polynomials. 1
 1, 1, 4, 1, 8, 1, 64, 1, 128, 1, 512, 1, 1024, 1, 16384, 1, 32768, 1, 131072, 1, 262144, 1, 2097152, 1, 4194304, 1, 16777216, 1, 33554432, 1, 1073741824, 1, 2147483648, 1, 8589934592, 1, 17179869184, 1, 137438953472, 1, 274877906944, 1, 1099511627776 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The numerators are given in A134828. 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. LINKS W. Lang, Rationals and more. FORMULA a(n) = denominator(r(n)) with r(n) = Integral_{x=-1..+1} (2/Pi)*sqrt(1-x^2)*x^n dx, n >= 0. 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). EXAMPLE Rationals: [1, 0, 1/4, 0, 1/8, 0, 5/64, 0, 7/128, 0, 21/512, 0, 33/1024, 0, ...]. CROSSREFS Cf. A120777 (coincides with denominators for even n). Sequence in context: A295786 A080102 A106475 * A245966 A130297 A271478 Adjacent sequences:  A134826 A134827 A134828 * A134830 A134831 A134832 KEYWORD nonn,easy,frac AUTHOR Wolfdieter Lang, Jan 21 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 20 13:25 EDT 2021. Contains 348108 sequences. (Running on oeis4.)