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 A225167 #5 May 01 2013 12:23:54 %S A225167 1,7,399,1475103,22572192792639,5844003553148435725257076863, %T A225167 428857285713570950220841681681938481172663051541516755199 %N A225167 Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 8/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal. %C A225167 Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165426(n+2), hence sum(A165426(i+1)/A225160(i),i=1..n) = product(A165426(i+1)/A225160(i),i=1..n) = A165426(n+2)/a(n) = A167182(n+2)/a(n). %F A225167 a(n) = 8^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/8. %e A225167 f(n) = 8, 8/7, 64/57, 4096/3697, ... %e A225167 8 + 8/7 = 8 * 8/7 = 64/7; 8 + 8/7 + 64/57 = 8 * 8/7 * 64/57 = 4096/399; ... %e A225167 s(n) = 1/b(n) = 8, 64/7, 4096/399, ... %p A225167 b:=proc(n) option remember; b(n-1)-b(n-1)^2; end: %p A225167 b(1):=1/8; %p A225167 a:=n->8^(2^(n-1))*b(n); %p A225167 seq(a(i),i=1..8); %Y A225167 Cf. A076628, A165426, A167182, A225160. %K A225167 nonn %O A225167 1,2 %A A225167 _Martin Renner_, Apr 30 2013