About this episode
An introduction to A000220, counting asymmetric (identity) trees with n nodes. We unpack what symmetry means for trees, why the first nonzero term appears at n = 7, and how the sequence connects to the broader family of tree counts via generating functions. We explore the role of the rooted-tree generating function A004111, the subtraction of symmetry contributions, and the resulting asymptotic growth a(n) ~ c d^n / n^52 with d ≈ 2.5175 and c ≈ 0.3. We also examine practical Maple/Mathematica snippets, and place A000220 in context with related sequences A000005, A000055, A000081, and A000411, along with key references for deeper study.
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