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 A225165 #5 May 01 2013 12:22:43 %S A225165 1,5,155,176855,265770796655,679134511201261085170655, %T A225165 4943777738415359153962876938905400001585992709055 %N A225165 Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 6/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal. %C A225165 Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165424(n+2), hence sum(A165424(i+1)/A225158(i),i=1..n) = product(A165424(i+1)/A225158(i),i=1..n) = A165424(n+2)/a(n) = A173501(n+2)/a(n). %F A225165 a(n) = 6^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/6. %e A225165 f(n) = 6, 6/5, 36/31, 1296/1141, ... %e A225165 6 + 6/5 = 6 * 6/5 = 36/5; 6 + 6/5 + 36/31 = 6 * 6/5 * 36/31 = 1296/155; ... %e A225165 s(n) = 1/b(n) = 6, 36/5, 1296/155, ... %p A225165 b:=proc(n) option remember; b(n-1)-b(n-1)^2; end: %p A225165 b(1):=1/6; %p A225165 a:=n->6^(2^(n-1))*b(n); %p A225165 seq(a(i),i=1..8); %Y A225165 Cf. A076628, A165424, A173501, A225158. %K A225165 nonn %O A225165 1,2 %A A225165 _Martin Renner_, Apr 30 2013