A symmetric series

Calculus Level pending

A recurrence relation for \(m,n \ge 0\) is defined as follows:

  • \(A_{0n} =A_{n0} = n\)
  • \(A_{mn}=(A_{m-1,n} + A_{m,n-1})^{\frac{8}{9}}\) for \(m>1\) and \(n>1\)

Evaluate:

\[\large \lim_{n \to \infty} A_{nn} \]

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