Revenue from Contracts with Customers (Impact of ASC 606 on Balance Sheet) (Details) - USD ($) $ in Thousands	Dec. 29, 2018	Sep. 30, 2018	Dec. 30, 2017	Sep. 30, 2017
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Cash and cash equivalents	$ 276,990	$ 259,946
Short-term marketable securities	25,598	25,836
Accounts receivable, net of allowance for doubtful accounts of $564 and $607 at December 29, 2018 and September 30, 2018, respectively	385,670	129,297
Prepaid expenses	63,045	48,997
Other current assets	48,682	169,708
Total current assets	799,985	633,784
Property and equipment, net	107,359	80,613
Goodwill	1,230,901	1,182,457
Acquired intangible assets, net	205,084	200,202
Long-term marketable securities	30,054	30,115
Deferred tax assets	201,149	165,566
Other assets	178,437	36,285
Total assets	2,752,969	2,329,022
Accounts payable	57,249	53,473
Accrued expenses and other current liabilities	83,721	74,388
Accrued compensation and benefits	74,483	101,784
Accrued income taxes	405	18,044
Deferred revenue	325,111	487,590
Total current liabilities	540,969	735,279
Long-term debt	778,484	643,268
Deferred tax liabilities	36,261	5,589
Deferred revenue	10,197	11,852
Other liabilities	65,889	58,445
Total liabilities	1,431,800	1,454,433
Preferred stock	0	0
Common stock	1,187	1,180
Additional paid-in capital	1,553,875	1,558,403
Accumulated deficit	(138,785)	(599,409)
Accumulated other comprehensive loss	(95,108)	(85,585)
Total stockholders’ equity	1,321,169	874,589	$ 889,099	$ 885,436
Total liabilities and stockholders’ equity	2,752,969	$ 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	276,990
Short-term marketable securities	25,598
Accounts receivable, net of allowance for doubtful accounts of $564 and $607 at December 29, 2018 and September 30, 2018, respectively	138,989
Prepaid expenses	63,045
Other current assets	143,104
Total current assets	647,726
Property and equipment, net	107,359
Goodwill	1,230,901
Acquired intangible assets, net	205,084
Long-term marketable securities	30,054
Deferred tax assets	234,558
Other assets	34,328
Total assets	2,490,010
Accounts payable	57,249
Accrued expenses and other current liabilities	56,897
Accrued compensation and benefits	74,483
Accrued income taxes	4,958
Deferred revenue	484,613
Total current liabilities	678,200
Long-term debt	778,484
Deferred tax liabilities	5,731
Deferred revenue	8,324
Other liabilities	65,889
Total liabilities	1,536,628
Preferred stock	0
Common stock	1,187
Additional paid-in capital	1,553,875
Accumulated deficit	(507,900)
Accumulated other comprehensive loss	(93,780)
Total stockholders’ equity	953,382
Total liabilities and stockholders’ equity	$ 2,490,010