The following JavaScript class enables you to get the expanded coefficients of a binomial raised to a particular power. Pass in the power and it will return an array of coefficients. For example, passing in a power of 6 returns {1, 6, 15, 20, 15, 6, 1}. This is also a row in Pascal's Triangle. It's using the following formula to calculate the coefficients, where n is the the power the binomial is raised to and k is the term position (0 to n).

Here is the class (PascalsTriangle.js):

function PascalsTriangle()
{
    this.GetExpandedBinomialCoefficients = function(power)
    {
        var coefficients = new Array(power);

        for (var index = 0; index <= power; index++)
        {
            coefficients[index] = this.GetExpandedBinomialCoefficient(power, index);
        }

        return coefficients;
    }

    this.GetExpandedBinomialCoefficient = function(power, term)
    {
        return this.GetFactorial(power) / (this.GetFactorial(term) * this.GetFactorial(power - term));
    }

    this.GetFactorial = function(value)
    {
        if (value <= 1)
            return 1;
        else
            return value * this.GetFactorial(value - 1);
    }
}

The class can be used as follows:

var pascalsTriangle = new PascalsTriangle();
var coefficients = pascalsTriangle.GetExpandedBinomialCoefficients(6);
alert(coefficients.join(' '));

This video covers Pascal's Triangle...