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Net Income Per Share (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Thousands
 12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Net Income Per Share [Abstract]      
Net income $ 394,948 $ 322,160 $ 331,241
Weighted average shares - basic (shares) 59,909 60,274 60,707
Weighted Average Number Diluted Shares Outstanding Adjustment 361 823 1,350
Weighted Average Number of Shares Outstanding, Diluted 60,270 61,097 62,057
Net income per share - basic (USD per share) $ 6.59 $ 5.34 $ 5.46
Net income per share - diluted (USD per share) $ 6.55 $ 5.27 $ 5.34