Generating Catalan numbers.

Enumerate all binary trees with N nodes, C++20 way:   

#include <memory>
#include <string>
#include <cassert>
#include <iostream>
#include <coroutine>
#include <cppcoro/generator.hpp>

struct tnode;
using tree = std::shared_ptr<tnode>;
struct tnode {
	tree left;
	tree right;
	tnode() {};
	tnode(tree l, tree r) : left(l), right(r) {}
};

auto print(tree t) -> std::string {
	return  t ? (std::string{"["} + print(t->left) + " "
		     + print(t->right) + "]") : "*";
}

cppcoro::generator<tree> gen(int n) {
	if (n == 0) {
		co_yield nullptr;
	} else {
		for (int i = 0; i < n; ++i) {
			for (auto left : gen(i)) {
				for (auto right : gen(n - i - 1)) {
					co_yield tree(new tnode(left, right));
				}
			}
		}
	}
}

int main(int argc, char **argv) {
	for (auto t : gen(std::atoi(argv[1]))) {
		std::cout << print(t) << std::endl;
	}
}

Source: gen.cpp. 

To generate Catalan numbers, do:

$ for i in $(seq 0 1000000) ;do ./gen $i | wc -l ;done
       1
       1
       2
       5
      14
      42
     132
     429
    1430
    4862
   16796
   58786
  208012
  742900