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A134828 Numerator of moments of Chebyshev U- (or S-) polynomials. 2
1, 0, 1, 0, 1, 0, 5, 0, 7, 0, 21, 0, 33, 0, 429, 0, 715, 0, 2431, 0, 4199, 0, 29393, 0, 52003, 0, 185725, 0, 334305, 0, 9694845, 0, 17678835, 0, 64822395, 0, 119409675, 0, 883631595, 0, 1641030105, 0, 6116566755, 0, 11435320455, 0, 171529806825, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
COMMENTS
The denominators are given in A134829.
Essentially the absolute values of numerators in expansion of sqrt(1+x^2). - Arkadiusz Wesolowski, Jan 17 2013
LINKS
FORMULA
a(n) = numerator(r(n)) with r(n) = Integral_{x=-1..+1} (2/Pi)*sqrt(1-x^2)*x^n dx, n >= 0.
a(n)=0 if n is odd, a(n) = numerator(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, ...].
MATHEMATICA
f[n_] := Numerator[CatalanNumber[n]/2^n]; Riffle[Array[f, 24, 0], 0] (* Arkadiusz Wesolowski, Jan 17 2013 *)
CROSSREFS
Cf. A098597 (coincides with numerators for even n).
Sequence in context: A201334 A323643 A325966 * A292899 A199062 A328900
KEYWORD
nonn,easy,frac
AUTHOR
Wolfdieter Lang, Jan 21 2008
STATUS
approved

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Last modified July 12 11:28 EDT 2024. Contains 374245 sequences. (Running on oeis4.)