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 A225166 #5 May 01 2013 12:23:28 %S A225166 1,6,258,552894,2881632108858,87461276190009420415561494, %T A225166 88945179016152188483365571645414219233310820789054258 %N A225166 Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 7/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal. %C A225166 Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165425(n+2), hence sum(A165425(i+1)/A225159(i),i=1..n) = product(A165425(i+1)/A225159(i),i=1..n) = A165425(n+2)/a(n). %F A225166 a(n) = 7^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/7. %e A225166 f(n) = 7, 7/6, 49/43, 2401/2143, ... %e A225166 7 + 7/6 = 7 * 7/6 = 49/6; 7 + 7/6 + 49/43 = 7 * 7/6 * 49/43 = 2401/258; ... %e A225166 s(n) = 1/b(n) = 7, 49/6, 2401/258, ... %p A225166 b:=proc(n) option remember; b(n-1)-b(n-1)^2; end: %p A225166 b(1):=1/7; %p A225166 a:=n->7^(2^(n-1))*b(n); %p A225166 seq(a(i),i=1..8); %Y A225166 Cf. A076628, A165425, A225159. %K A225166 nonn %O A225166 1,2 %A A225166 _Martin Renner_, Apr 30 2013