I'm playing around with generating rows of Pascal Triangle. I want to know, given a fixed-width integer type, the maximum row I can calculate before any individual element would be too big.
The sum of the elements of a row n of the triangle add up to 2^n. So calculating row 64 on a 64-bit computer would be safe. But how much further? With signed arithmetic, I got to 66 as the last row, and 67 as last for unsigned arithmetic. Is there a way to estimate how big the middle element(s) would be so I know the maximum row r given bit size n?