Rust solution:

fn completer(bracket: char) -> char {
    match bracket {
        '[' => ']',
        '{' => '}',
        '(' => ')',
        ')' => '(',
        '}' => '{',
        ']' => '[',
        _ => unreachable!(),
    }
}

fn rec(v: &mut Vec, stack: &mut Vec, depth: usize) {
    // If we have more characters in the stack to complete
    // than the space avaiable, bail!
    if stack.len() > depth {
        return;
    }

    if depth == 0 {
        let output: String = v.iter().collect();
        println!("{}", output);
        return;
    }

    for b in &['[', '{', '('] {
        v.push(*b);
        stack.push(*b);
        rec(v, stack, depth - 1);
        stack.pop();
        v.pop();
    }

    if let Some(c) = stack.pop() {
        v.push(completer(c));
        rec(v, stack, depth - 1);
        stack.push(c);
        v.pop();
    }
}

fn main() {
    let depth: usize = std::env::args().nth(1).unwrap().parse().unwrap();
    let mut v = Vec::with_capacity(depth);
    let mut s = Vec::with_capacity(depth / 2);
    rec(&mut v, &mut s, depth);
}

Hope you enjoy this!

Edit: Lemmy makes the usize in angle brackets disappear after parse::. Idk what to do.

Edit: I kinda fixed it by assigning the type as a part of the variable definition.

Note to self: the angle bracket problem persists nonetheless.