|
|
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).
|
|
KEYWORD
|
nonn,easy,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|