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Stockholders' Equity (Stock-based Compensation Expense Recognized) (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022
Share Based Compensation [Abstract] |  |  |
Employee stock-based compensation expense | $ 33,052 | $ 23,958 | $ 20,109

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