Nature of Business Prior Year Restated (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended		9 Months Ended
		Jun. 30, 2019	Jun. 30, 2018	Jun. 30, 2019	Jun. 30, 2018	Mar. 31, 2019	Sep. 30, 2018	Mar. 31, 2018	Sep. 30, 2017
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Accounts receivable, net		$ 318,044		$ 318,044			$ 266,742
Deferred income taxes		13,483		13,483			13,805
Other assets		43,179		43,179			36,254
Other accrued liabilities		28,289		28,289			31,025
Deferred revenue		103,270		103,270			103,335
Stockholders’ equity		268,317	$ 336,124	268,317	$ 336,124	$ 247,478	287,437	$ 414,823	$ 466,183
Revenues		314,249	254,993	854,739	743,614
Cost of revenues	[1]	87,215	79,011	248,849	232,936
Selling, general and administrative	[1]	102,906	97,391	308,094	283,858
Provision for income taxes		13,902	8,181	17,644	14,173
Net income		64,152	29,721	137,540	93,769
Comprehensive income		$ 59,963	$ 10,925	$ 133,011	$ 87,169
Basic (in dollars per share)		$ 2.21	$ 1.00	$ 4.74	$ 3.13
Diluted (in dollars per share)		$ 2.12	$ 0.95	$ 4.54	$ 2.99
Deferred income taxes				$ 247	$ (3,643)
Changes in operating assets and liabilities					(3,931)
Previously Reported
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Accounts receivable, net							208,865
Deferred income taxes							20,117
Other assets							12,431
Other accrued liabilities							30,457
Deferred revenue							52,215
Stockholders’ equity							263,737
Revenues			$ 259,505		752,684
Cost of revenues			78,390		231,268
Selling, general and administrative			98,685		286,038
Provision for income taxes			9,380		24,565
Net income			32,361		91,935
Comprehensive income			$ 13,565		$ 85,335
Basic (in dollars per share)			$ 1.09		$ 3.07
Diluted (in dollars per share)			$ 1.04		$ 2.93
Deferred income taxes					$ 6,749
Changes in operating assets and liabilities					(12,489)
Accounting Standards Update 2014-09 | Restatement Adjustment
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Accounts receivable, net							57,877
Deferred income taxes							(6,312)
Other assets							23,823
Other accrued liabilities							568
Deferred revenue							51,120
Stockholders’ equity							$ 23,700
Revenues			$ (4,512)		(9,070)
Cost of revenues			621		1,668
Selling, general and administrative			(1,294)		(2,180)
Provision for income taxes			(1,199)		(10,392)
Net income			(2,640)		1,834
Comprehensive income			$ (2,640)		$ 1,834
Basic (in dollars per share)			$ (0.09)		$ 0.06
Diluted (in dollars per share)			$ (0.09)		$ 0.06
Deferred income taxes					$ (10,392)
Changes in operating assets and liabilities					$ 8,558

[1] Cost of revenues and selling, general and administrative expenses exclude the amortization of intangible assets. See Note 4.