A most unusual tree.

We inherited this tree when we moved in 32 years ago. I have no idea what it is, and have never seen another in my travels. My old neighbours called it a date tree, but it ain't. I would love to know; if any of you geniuses could help.
It doesn't do much except produce large clusters of these seeds right through the summer.
Funny day today, lovely cloudless sky and a ferocious wind coming from... well... nowhere.