Recursion in an async fn requires boxing. For example, this will not compile:

async fn foo(n: usize) {
    if n > 0 {
        foo(n - 1).await;
    }
}

To achieve async recursion, the async fn needs to be desugared such that the Future is explicit in the return type:

use std::future::Future;
fn foo_desugared(n: usize) -> impl Future<Output = ()> {
    async move {
        if n > 0 {
            foo_desugared(n - 1).await;
        }
    }
}

Finally, the future is wrapped in a pinned box:

use std::future::Future;
use std::pin::Pin;
fn foo_recursive(n: usize) -> Pin<Box<dyn Future<Output = ()>>> {
    Box::pin(async move {
        if n > 0 {
            foo_recursive(n - 1).await;
        }
    })
}

The Box<...> ensures that the result is of known size, and the pin is required to keep it in the same place in memory.