OEIS A000300: Fourth power of rooted tree enumeration

We dive into A000300, the fourth power of the rooted-tree enumerator. Its generating function is B(x)^4, where B(x) is the rooted-tree generating function (A000081); geometrically, it counts linear forests of four rooted trees. The early terms are 1, 4, 14, 44, and the OEIS entry provides Maple and Mathematica code to generate terms. This sequence sits at the heart of combinatorial counting, linking ideas from Sloan’s work on the OEIS and Riordan’s Introduction to Combinatorial Analysis, and it offers a concrete model for understanding the growth of complex structures and their connections to other areas of math and CS.

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