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Enjoy this problem!
Your huffman codes with essential indifference are binary trees (each node has 0 or 2 children) with isomorphism.
Let f(n) be the number of trees with n leaves.
Here's the first 26 numbers of such trees:
[1,1,1,2,3,6,11,23,46,98,207,451,983,2179,4850,10905, 24631,56011,127912,293547,676157,1563372,3626149,8436379,19680277]