From the expansion of sqrt(1+1/5) = 1+(1/10)*sum(C(k)/(-20)^k,k=0..infinity) one has, with the partial sums r(n) are defined below, r:=limit(r(n),n to infinity)= (2*(sqrt(30)-5)) = 0.954451150....
a(n)=numerator(r(n)), with the rationals r(n):=sum(((-1)^k)*C(k)/20^k,k=0..n) with C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest terms.
