Nature of Business Prior Year Restated (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended
		Dec. 31, 2018	Dec. 31, 2017	Sep. 30, 2018
Error Corrections and Prior Period Adjustments Restatement [Line Items]
Accounts receivable, net		$ 247,566		$ 266,742
Deferred income taxes		14,066		13,805
Other assets		38,262		36,254
Other accrued liabilities		26,079		31,025
Deferred revenue		103,527		103,335
Stockholders’ equity		227,895		287,437
Revenues		262,256	$ 232,361
Cost of revenues	[1]	76,066	74,432
Selling, general and administrative	[1]	100,258	90,342
Provision for income taxes		(2,851)	(2,001)
Net income		40,007	32,879
Comprehensive income		$ 36,742	$ 35,950
Basic (in dollars per share)		$ 1.38	$ 1.09
Diluted (in dollars per share)		$ 1.32	$ 1.04
Deferred income taxes		$ (50)	$ (1,942)
Changes in operating assets and liabilities			(26,320)
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			235,321
Cost of revenues			74,359
Selling, general and administrative			90,296
Provision for income taxes			6,658
Net income			27,299
Comprehensive income			$ 30,370
Basic (in dollars per share)			$ 0.91
Diluted (in dollars per share)			$ 0.86
Deferred income taxes			$ 6,717
Changes in operating assets and liabilities			(29,399)
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			(2,960)
Cost of revenues			73
Selling, general and administrative			46
Provision for income taxes			(8,659)
Net income			5,580
Comprehensive income			$ 5,580
Basic (in dollars per share)			$ 0.18
Diluted (in dollars per share)			$ 0.18
Deferred income taxes			$ (8,659)
Changes in operating assets and liabilities			$ 3,079

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