OEIS A00142: Factorial numbers

We dive into A00142, the factorial numbers. From the curious fact that 0! = 1 to the evolution of factorial notation, we trace history and notation. Then we explore surprising properties and connections: Legendre's formula for prime factors and trailing zeros, Wilson's theorem, and the explosive growth of factorials alongside Stirling's approximation. We also survey related ideas—double and falling factorials, primorials, subfactorials (derangements), superfactorials—and the gamma function that extends factorials to non-integer and complex values. All framed with a touch of history and cross-cultural roots.

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