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 A225164 #5 May 01 2013 12:22:17 %S A225164 1,4,84,45444,15686405364,2147492192737717340004, %T A225164 45388476229808808857318702720533556450342484 %N A225164 Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 5/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal. %C A225164 Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165423(n+2), hence s(n) = sum(A165423(i+1)/A225157(i),i=1..n) = product(A165423(i+1)/A225157(i),i=1..n) = A165423(n+2)/a(n) = A176594(n-1)/a(n). %F A225164 a(n) = 5^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/5. %e A225164 f(n) = 5, 5/4, 25/21, 625/541, ... %e A225164 5 + 5/4 = 5 * 5/4 = 25/4; 5 + 5/4 + 25/21 = 5 * 5/4 * 25/21 = 625/84; ... %e A225164 s(n) = 1/b(n) = 5, 25/4, 625/84, ... %p A225164 b:=proc(n) option remember; b(n-1)-b(n-1)^2; end: %p A225164 b(1):=1/5; %p A225164 a:=n->5^(2^(n-1))*b(n); %p A225164 seq(a(i),i=1..8); %Y A225164 Cf. A076628, A165423, A176594, A225157. %K A225164 nonn %O A225164 1,2 %A A225164 _Martin Renner_, Apr 30 2013