A134828 - OEIS

%I #14 Aug 30 2019 04:03:06

%S 1,0,1,0,1,0,5,0,7,0,21,0,33,0,429,0,715,0,2431,0,4199,0,29393,0,

%T 52003,0,185725,0,334305,0,9694845,0,17678835,0,64822395,0,119409675,

%U 0,883631595,0,1641030105,0,6116566755,0,11435320455,0,171529806825,0

%N Numerator of moments of Chebyshev U- (or S-) polynomials.

%C The denominators are given in A134829.

%C Essentially the absolute values of numerators in expansion of sqrt(1+x^2). - _Arkadiusz Wesolowski_, Jan 17 2013

%H W. Lang, <a href="/A134828/a134828.txt">Rationals and more</a>.

%F a(n) = numerator(r(n)) with r(n) = Integral_{x=-1..+1} (2/Pi)*sqrt(1-x^2)*x^n dx, n >= 0.

%F 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).

%e Rationals: [1, 0, 1/4, 0, 1/8, 0, 5/64, 0, 7/128, 0, 21/512, 0, 33/1024, 0, ...].

%t f[n_] := Numerator[CatalanNumber[n]/2^n]; Riffle[Array[f, 24, 0], 0] (* _Arkadiusz Wesolowski_, Jan 17 2013 *)

%Y Cf. A098597 (coincides with numerators for even n).

%K nonn,easy,frac

%O 0,7

%A _Wolfdieter Lang_, Jan 21 2008