OEIS A000311: Schroeder’s Fourth Problem and the Web of Combinatorics

In this episode we explore OEIS A000311—Schroeder’s fourth problem—counting labeled series-reduced rooted trees with N leaves. We unpack what ‘series-reduced’ means, see how the same numbers pop up in total partitions of N, series-parallel networks with N-labeled edges, and singleton-reduced phylogenetic trees, and glimpse how generating functions reveal a shared structure behind biology, networks, and number theory. Along the way we glimpse the rapid growth and the unity of seemingly different counting problems.

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