The Euler-Minding series for branched continued fractions (Q1822441)

For suitable x(k) (k\(\geq 1)\) and y(k) (k\(\geq 0)\) denote the continued fraction \(y(0)+x(1)/y(1)+...x(j)/y(j)\) by \(K\{\) x(k),y(k);j\(\}\). With twin sequences a(i,k) (k\(\geq 1)\) and b(i,k) (k\(\geq 0)\) prescribed for \(i\geq 0\), let \(C(i,j)=K\{a(i,k),b(i,k);j\}\). The convergent \(K\{\) x(k),C(k;n-k);n\(\}\) is expressed as a series resembling the Euler-Minding series for the convergent of a simple continued fraction.