What is this loud clacking engine sound from 2001 BMW 325i E46?

After listening to your recorded engine noise, I suspect your alternator bearings are the source. If you have access to a laser temp reader, check the temp of the alternator near the front and rear beariings. Compare that to an alternator on a similar sized car. Yours will significantly hotter. You can also put a wooden dowell on various points to isolate the clatter. Be careful as you put the free end againt you ear. Check pcv for clatter, top of valve cover, ac comp, ps pump, alternator etc. You have a TSB out on the HYDRAULIC BUCKET TAPPETS. (HVA) You can review the TSB at: http://www.bbbind.com/free_tsb.html

[HYDRAULIC BUCKET TAPPETS (HVA) TROUBLESHOOTING TIPS - REVISED TSBID: 138110 Mfg Num: 11 01 01 Issue Date: 2001-06-01]

***Now, if it is your engine, buy a can of "Seafoam" from your local autoparts store. Add it to your oil, it clears clogged oil passages. Carefull not to overfill your oil level. The clatter should clear up within 5 mi of driving.

Sounds like a bearing, BMW TSB says it may be a tappet issue, I am also including a general oiling problem as a possible cause.

Good Luck