Pythagorean triples?

Does anyone know if there is already a formula in the literature for expanding the Pythagorean triples, so that one can calculate the following example (space bar and a 2 should mean squared):

3 2+4 2+12 2+84 2 +3612 2+6526884 2 +21300113901612 2+226847426110843688722000884 2 +2572 9877366557343481074291996721923093306518970391612 2+3310132946490399283969363908888 78360035026305412754995683702777533071737279144813617823976263475290370884 2+547849 0061720606284682046858334937256238872873516182925589473588321738405245398726866423 6809164877269859097474567984739516975948612635461161507766858920689912820154069522 660952033478909299656771083000427841612 2=54784900617206062846820468583349372562388 7287351618292558947358832173840524539872686642368091648772698590974745679847395169 7594861263546116150776685892068991282015406952266095203347890929965677108300042784 1613 2