Revenue from Contracts with Customers (Impact of ASC 606 on Balance Sheet) (Details) - USD ($) $ in Thousands	Mar. 30, 2019	Dec. 29, 2018	Sep. 30, 2018	Mar. 31, 2018	Dec. 30, 2017	Sep. 30, 2017
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Cash and cash equivalents	$ 294,299		$ 259,946
Short-term marketable securities	25,428		25,836
Accounts receivable, net of allowance for doubtful accounts of $719 and $607 at March 30, 2019 and September 30, 2018, respectively	352,217		129,297
Prepaid expenses	66,210		48,997
Other current assets	52,448		169,708
Total current assets	790,602		633,784
Property and equipment, net	106,837		80,613
Goodwill	1,229,541		1,182,457
Acquired intangible assets, net	192,372		200,202
Long-term marketable securities	30,987		30,115
Deferred tax assets	195,884		165,566
Other assets	169,596		36,285
Total assets	2,715,819		2,329,022
Accounts payable	36,685		53,473
Accrued expenses and other current liabilities	100,319		74,388
Accrued compensation and benefits	73,408		101,784
Accrued income taxes	6,579		18,044
Deferred revenue	381,392		487,590
Total current liabilities	598,383		735,279
Long-term debt	738,700		643,268
Deferred tax liabilities	36,326		5,589
Deferred revenue	10,415		11,852
Other liabilities	84,287		58,445
Total liabilities	1,468,111		1,454,433
Preferred stock	0		0
Common stock	1,181		1,180
Additional paid-in capital	1,523,949		1,558,403
Accumulated deficit	(182,298)		(599,409)
Accumulated other comprehensive loss	(95,124)		(85,585)
Total stockholders’ equity	1,247,708	$ 1,321,169	874,589	$ 927,724	$ 889,099	$ 885,436
Total liabilities and stockholders’ equity	2,715,819		$ 2,329,022
Calculated under Revenue Guidance in Effect before Topic 606 [Member]
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Cash and cash equivalents	294,299
Short-term marketable securities	25,428
Accounts receivable, net of allowance for doubtful accounts of $719 and $607 at March 30, 2019 and September 30, 2018, respectively	110,510
Prepaid expenses	66,509
Other current assets	153,687
Total current assets	650,433
Property and equipment, net	106,837
Goodwill	1,229,541
Acquired intangible assets, net	192,372
Long-term marketable securities	30,987
Deferred tax assets	228,776
Other assets	41,750
Total assets	2,480,696
Accounts payable	36,685
Accrued expenses and other current liabilities	73,719
Accrued compensation and benefits	73,408
Accrued income taxes	1,181
Deferred revenue	545,168
Total current liabilities	730,161
Long-term debt	738,700
Deferred tax liabilities	6,079
Deferred revenue	8,541
Other liabilities	84,287
Total liabilities	1,567,768
Preferred stock	0
Common stock	1,181
Additional paid-in capital	1,523,949
Accumulated deficit	(519,930)
Accumulated other comprehensive loss	(92,272)
Total stockholders’ equity	912,928
Total liabilities and stockholders’ equity	$ 2,480,696