This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A225163 #5 May 01 2013 12:21:32 %S A225163 1,2,14,938,5274374,199225484935778,329478051871899046990657602014, %T A225163 1022767669188735114815831063606918316150663428260080434555738 %N A225163 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 A225163 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 A225163 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 A225163 a(n) = 3^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/3. %e A225163 f(n) = 3, 3/2, 9/7, 81/67, ... %e A225163 3 + 3/2 = 3 * 3/2 = 9/2; 3 + 3/2 + 9/7 = 3 * 3/2 * 9/7 = 81/14; ... %e A225163 s(n) = 1/b(n) = 3, 9/2, 81/14, ... %p A225163 b:=proc(n) option remember; b(n-1)-b(n-1)^2; end: %p A225163 b(1):=1/3; %p A225163 a:=n->3^(2^(n-1))*b(n); %p A225163 seq(a(i),i=1..9); %Y A225163 Cf. A011764, A076628, A165421, A225156. %K A225163 nonn %O A225163 1,2 %A A225163 _Martin Renner_, Apr 30 2013