Finding all possible combinations of parentheses and verify result's right using Catalan Number

findAllParensCombinations.js

function findAllCombinations(numParens) {
  var totalCombs = 0;
  if(numParens > 0) {
    totalCombs = attachParen('', numParens, numParens, totalCombs);
  }
  return totalCombs;
}

function attachParen(str, open, close, total) {
  if(open > 0) {
    total = attachParen(str + '(', open - 1, close, total);
  }

  if(close > 0 && close > open) {
    total = attachParen(str + ')', open, close - 1, total);
  }

  // show only full combinations
  // we could show all the combinations just by
  // changing this condition to an "else"
  if(open === 0 && close === 0) {
    console.log(str);
    ++total;
  }

  return total;
}

function checkNumCombinations(numParens, result) {
  // Using Catalan Numbers to mathematically verify number of combinations
  // http://en.wikipedia.org/wiki/Catalan_number
  var expected = (function catalanNumber(numParens) {
    var total = 1;

    for(var i = 2; i <= numParens; i++) {
      total *= (numParens + i) / i;
    }

    return Math.round(total);
  })(numParens);

  console.log('Total combinations: ' + result + '. Expected: ' + expected);
  return expected === result;
}

// Testing it out
var combinations = 5;
if(checkNumCombinations(combinations, findAllCombinations(combinations))) {
  console.log('OK');
} else {
  console.log('Error');
}