A binary tree is full if all of its vertices have either zero or two children. Let B_n denote the number of full binary trees with n vertices. Implement a function to find B_n.

Sure , I can help you with that ! Here ' s a Python function that uses dynamic programming to calculate the number of full binary trees with n vertices : \n `` ` python \n def full _ binary _ tre es ( n ): \n if n == 0 : \n return 1 \n elif n == 1 : \n return 0 \n else : \n return ( full _ binary _ tre es ( n - 1 ) + full _ binary _ tre es ( n - 2 )) * 2 \n `` ` \n This function uses recurs ion to calculate the number of full binary trees with n vertices . The base cases are when n is 0 or 1 , in which case there is only one possible full binary tree ( an empty tree ). For n 1 , the function calcul ates the number of full binary trees with n - 1 vertices and n - 2 vertices , and then multi plies the results by 2 to account for the two possible ways to split a node with n children ( into two children with n - 1 children each , or into one child with n children and another child with 0 children ). \n I hope this helps ! Let me know if you have any questions . </s>