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
KEYWORD
nonn,easy,frac
AUTHOR
Wolfdieter Lang, Jan 21 2008
STATUS
approved