Search: id:A123748
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%I A123748
%S A123748 1,5,25,5,125,3125,15625,78125,78125,390625,9765625,48828125,244140625,
%T A123748 244140625,78125,6103515625,30517578125,152587890625,152587890625,
%U A123748 762939453125,19073486328125,95367431640625,476837158203125
%N A123748 Denominators of partial sums of a series for sqrt(5).
%C A123748 Denominators of sums over central binomial coefficients scaled by powers 
               of 5.
%C A123748 Numerators are given by A123747.
%C A123748 For the rationals r(n) see the W. Lang link under A123747.
%F A123748 a(n)=denominator(r(n)) with the rationals r(n):=sum(binomial(2*k,k)/5^k,
               k=0..n) in lowest terms.
%F A123748 r(n)=sum(((2*k-1)!!/((2*k)!!)*(4/5)^k,k=0..n),n>=0, with the double factorials 
               A001147 and A000165.
%e A123748 a(3)=5 because r(3)= 1+2/5+6/25+4/25 = 9/5 = A123747(3)/a(3).
%Y A123748 Sequence in context: A156310 A142725 A070387 this_sequence A050108 A070386 
               A050084
%Y A123748 Adjacent sequences: A123745 A123746 A123747 this_sequence A123749 A123750 
               A123751
%K A123748 nonn,frac,easy
%O A123748 0,2
%A A123748 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Nov 10 2006

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