Gasarch on what counts as "closed form" and what does not, using the Ordered Bell numbers as an example: https://blog.computationalcomplexity.org/2024/05/what-is-closed-form-horse-numbers-are.html

He asks, in the form of a Platonic dialogue: is \(\tbinom{n}{i}\) or \(\tfrac{n!}{i!(n-i)!}\) closed form? What, if anything, makes that sort of formula different from the formula \(H(n)\), denoting the \(n\)th ordered Bell number?