%I A120778
%S A120778 1,5,11,93,193,793,1619,26333,53381,215955,436109,3518265,7088533,
%T A120778 28539857,57414019,1846943453,3711565741,14911085359,29941580393,
%U A120778 240416274739,482473579583,1936010885087,3883457090629
%N A120778 Numerators of partial sums of Catalan numbers scaled by powers of 1/4.
%C A120778 For denominators see A120777.
%C A120778 From the expansion of 0 = sqrt(1-1) = 1-(1/2)*sum(C(k)/4^k,k=0..infinity) 
               one has r:=limit(r(n),n to infinity)=2, with the partial sums r(n) 
               defined below.
%H A120778 W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A120778.text">
               Rationals r(n) and limit 2.</a>
%F A120778 a(n)=numerator(r(n)), with the rationals r(n):=sum(C(k)/4^k,k=0..n) with 
               C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest 
               terms.
%e A120778 Rationals r(n): [1, 5/4, 11/8, 93/64, 193/128, 793/512, 1619/1024, 26333/
               16384,...].
%Y A120778 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%Y A120778 Factor of A160481.
%Y A120778 (End)
%Y A120778 Sequence in context: A057726 A057727 A128454 this_sequence A042761 A123025 
               A053778
%Y A120778 Adjacent sequences: A120775 A120776 A120777 this_sequence A120779 A120780 
               A120781
%K A120778 nonn,easy,frac
%O A120778 0,2
%A A120778 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 
               2006