Pascal's Triangle calculated using a recursive function in Lua.

PascalTriangle.lua

--Recursive function to create the mathemeatical series
function pascal(col,row)
	if(col == 0) or (col == row) then return 1
		else return pascal(col-1,row-1) + pascal(col,row-1)
	end
end

--Prints Pascal's Triangle to the 'n'th row 
function PascalTriangle(num)
	if (num <= 0) then print("Number must be greater than zero") return end
	for r = 0,num,1 do
		for c = 0,r,1 do
			io.write(pascal(c,r).." ")
		end
		print()
	end
end

--Test Section
PascalTriangle(10)
--[[
Output:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
1 10 45 120 210 252 210 120 45 10 1

]]

PascalTriangle(0) -- returns 'Number must be greater than zero'