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 A225169 #4 May 01 2013 12:24:43 %S A225169 1,9,819,7519239,695384944860879,6470289227069622272847335347359, %T A225169 605164280025029017271801950447677089988237937249820002811725119 %N A225169 Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 10/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal. %C A225169 Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165428(n+2), hence sum(A165428(i+1)/A225162(i),i=1..n) = product(A165428(i+1)/A225162(i),i=1..n) = A165428(n+2)/a(n) = A220812(n-1)/a(n). %F A225169 a(n) = 10^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/10. %e A225169 f(n) = 10, 10/9, 100/91, 10000/9181, ... %e A225169 10 + 10/9 = 10 * 10/9 = 100/9; 10 + 10/9 + 100/91 = 10 * 10/9 * 100/91 = 10000/819; ... %e A225169 s(n) = 1/b(n) = 10, 100/9, 10000/819, ... %p A225169 b:=proc(n) option remember; b(n-1)-b(n-1)^2; end: %p A225169 b(1):=1/10; %p A225169 a:=n->10^(2^(n-1))*b(n); %p A225169 seq(a(i),i=1..7); %Y A225169 Cf. A076628, A165428, A220812, A225162. %K A225169 nonn %O A225169 1,2 %A A225169 _Martin Renner_, Apr 30 2013