Create a lower triangular n × n matrix filled with the first n rows of Pascal’s triangle.

Pascal.jl

module Pascal

export pascal

function factorial(n)
    if n==0; return(1); end
    result = n * factorial(n-1)
    return(result)
end

function choose(n, r)
    result = factorial(n) / (factorial(r) * factorial(n-r))
    return(result)
end

function pascal_element(i, j)
    if i <= j; return(choose(j,i)); end
    return(0.0)
end

function pascal(n)
    return([pascal_element(i,j) for j in [0:(n-1)], i in [0:(n-1)]])
end

end