You are a helpful assistant that can solve the given question step by step with the help of the wikipedia search tool and python interpreter tool. Given a question, you need to first think about the reasoning process in the mind and then provide the answer. During thinking, you can invoke the wikipedia search tool to search and python interpreter tool to calculate the math problem for fact information about specific topics if needed. The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags respectively, and the search query and result are enclosed within <search> </search> and <result> </result> tags respectively. For example, <think> This is the reasoning process. </think> <search> search query here </search> <result> search result here </result> <think> This is the reasoning process. </think> <python> python code here </python> <result> python interpreter result here </result> <think> This is the reasoning process. </think> <answer> The final answer is \[ oxed{answer here} \] </answer>. In the last part of the answer, the final exact answer is enclosed within oxed{} with latex format.
system

The trunk of the sky-high tree branches into two at a height of one foot. We consider a branch to be the section between two consecutive nodes where no further branching occurs. Each branch in the sky-high tree is straight and ends one foot higher than the lower end. We refer to the branches emerging from the higher end of a branch as its children, and these branches are also referred to as each other's siblings.

Every branch in the sky-high tree has at least two children, and if it doesn't have exactly two children, then it has a sibling with exactly two children. Siblings always have different numbers of children. If a branch has more than two children, then it has a sibling with exactly one fewer child than itself. 

How many branches emerge from the nodes that are $n$ feet high?
user
\binom{2n+2}{n+1} - \binom{2n+2}{n}
rule

The trunk of the sky-high tree branches into two at a height of one foot. We consider a branch to be the section between two consecutive nodes where no further branching occurs. Each branch in the sky-high tree is straight and ends one foot higher than the lower end. We refer to the branches emerging from the higher end of a branch as its children, and these branches are also referred to as each other's siblings.

Every branch in the sky-high tree has at least two children, and if it doesn't have exactly two children, then it has a sibling with exactly two children. Siblings always have different numbers of children. If a branch has more than two children, then it has a sibling with exactly one fewer child than itself. 

How many branches emerge from the nodes that are $n$ feet high?
train