a(1) = 1; a(n+1) = sum of terms in continued fraction for sum of continued fractions, [a(n); a(n-1), a(n-2),...,a(1)] and [0; a(n), a(n-1), a(n-2),...,a(1)].

A058083

a(1) = 1; a(n+1) = sum of terms in continued fraction for sum of continued fractions, [a(n); a(n-1), a(n-2),...,a(1)] and [0; a(n), a(n-1), a(n-2),...,a(1)].