Finding all combinations of well-formed brackets

Question

This came up while talking to a friend and I thought I\'d ask here since it\'s an interesting problem and would like to see other people\'s solutions.

The task is to

Answer 1

In javascript / nodejs.

The program was originally meant to answer the Ultimate Question, but it is just perfect to enumerate the valid brackets combinations.

function* life(universe){
    if( !universe ) yield '';
    for( let everything = 1 ; everything <= universe ; ++everything )
        for( let meaning of life(everything - 1) )
            for( let question of life(universe - everything) )    
                yield question + '(' + meaning + ')';
}
let love = 5;
let answer = [...life(love)].length;
console.log(answer);

function brackets(n){
    for( k = 1 ; k <= n ; k++ ){
        console.log(...life(k));
    }
}

brackets(5);