%I #4 May 01 2013 12:24:43
%S 1,9,819,7519239,695384944860879,6470289227069622272847335347359,
%T 605164280025029017271801950447677089988237937249820002811725119
%N 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 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 a(n) = 10^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/10.
%e f(n) = 10, 10/9, 100/91, 10000/9181, ...
%e 10 + 10/9 = 10 * 10/9 = 100/9; 10 + 10/9 + 100/91 = 10 * 10/9 * 100/91 = 10000/819; ...
%e s(n) = 1/b(n) = 10, 100/9, 10000/819, ...
%p b:=proc(n) option remember; b(n-1)-b(n-1)^2; end:
%p b(1):=1/10;
%p a:=n->10^(2^(n-1))*b(n);
%p seq(a(i),i=1..7);
%Y Cf. A076628, A165428, A220812, A225162.
%K nonn
%O 1,2
%A _Martin Renner_, Apr 30 2013