I need to calculate all the numbers in a certain row of Pascal's triangle. Obviously, this is easy to do with combinatorics. However, what do you do when you need to estimate all the numbers in, say, the 100000th row of Pascal's triangle?
Is there any way to estimate the number so that the costly multiplications and divisions of binomials can be avoided? I'm already estimating factorials with Stirling's formula, but it still takes a number of seconds to calculate only one number - and I need about 100000/2 (since a row is symmetric).