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%I #5 May 01 2013 12:21:32
%S 1,2,14,938,5274374,199225484935778,329478051871899046990657602014,
%T 1022767669188735114815831063606918316150663428260080434555738
%N Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 3/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal.
%C Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165421(n+2), hence s(n) = sum(A165421(i+1)/A225156(i),i=1..n) = product(A165421(i+1)/A225156(i),i=1..n) = A165421(n+2)/a(n) = A011764(n-1)/a(n).
%H Paul Yiu, <a href="http://math.fau.edu/yiu/RecreationalMathematics2003.pdf">Recreational Mathematics</a>, Department of Mathematics, Florida Atlantic University, 2003, Chapter 5.4, p. 207 (Project).
%F a(n) = 3^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/3.
%e f(n) = 3, 3/2, 9/7, 81/67, ...
%e 3 + 3/2 = 3 * 3/2 = 9/2; 3 + 3/2 + 9/7 = 3 * 3/2 * 9/7 = 81/14; ...
%e s(n) = 1/b(n) = 3, 9/2, 81/14, ...
%p b:=proc(n) option remember; b(n-1)-b(n-1)^2; end:
%p b(1):=1/3;
%p a:=n->3^(2^(n-1))*b(n);
%p seq(a(i),i=1..9);
%Y Cf. A011764, A076628, A165421, A225156.
%K nonn
%O 1,2
%A _Martin Renner_, Apr 30 2013
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