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How many binary tree shapes of n nodes are there with height n1? Prove your answer. Hint: use induction. To make a good guess, try

How many binary tree shapes of n nodes are there with height n1? Prove your answer. Hint: use induction. To make a good guess, try drawing all possible trees for heights 0, 1, 2,... and identify the pattern.

Please use the induction step.

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