Search: id:A123749
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%I A123749
%S A123749 1,11,35,965,8755,8783,237449,2138185,6415985,519743405,4677875401,
%T A123749 14033861347,378916960525,3410263045325,3410267502725,30692424759805,
%U A123749 276231889624955,828695755304725,67124359204727825,604119244624305025
%N A123749 Numerators of partial sums of a series for 3/sqrt(5)=(3/5)*sqrt(5).
%C A123749 Denominators are given by A124396.
%C A123749 The sums over central binomial coefficients scaled by powers of 9, r(n):=sum(binomial(2*k,
               k)/9^k,k=0..n) have the limit s:=lim(r(n),n->infinity) = 3/sqrt(5). 
               From the expansion of 1/sqrt(1-x) for x=4/9.
%H A123749 W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A123749.text">
               Rationals and more.</a>
%F A123749 a(n)=numerator(r(n)) with the rationals r(n):=sum(binomial(2*k,k)/9^k,
               k=0..n) in lowest terms.
%F A123749 r(n)=sum(((2*k-1)!!/((2*k)!!)*(4/9)^k,k=0..n),n>=0, with the double factorials 
               A001147 and A000165.
%e A123749 a(3)=965 because r(3)=1+2/9+2/27+20/729 = 965/729 = a(3)/A124396(3).
%Y A123749 Cf. A123747/A123748 partial sums for a series for sqrt(5).
%Y A123749 Sequence in context: A103115 A003777 A098116 this_sequence A159493 A012644 
               A138893
%Y A123749 Adjacent sequences: A123746 A123747 A123748 this_sequence A123750 A123751 
               A123752
%K A123749 nonn,frac,easy
%O A123749 0,2
%A A123749 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Nov 10 2006

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