Have you checked here?
http://www.brandsoftheworld.com

It isn't there sadly :(

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golden ratio of passion. sansogno.coastaldisturbance.com

There are several different versions of these crowns, varying in complexity.

For example,

http://www.sweden.se/templates/cs/FactSheet____14193.aspx

http://www.ngw.nl/int/zwe/se-nat.htm

For vector try www.brandsoftheworld.com and search on say 'Sweden Hockey', 'Swedish Olympic Committee'.

See also

http://en.wikipedia.org/wiki/Coat_of_arms_of_Sweden

and note section on regulated use.

Here's a pdf with it on:
http://www.sweden.se/upload/Sweden_se/english/factsheets/SI/SI_FS38a_Swe...

If you decide to redraw it, I reckon each crown is a 4x3. The lower vertices then appear to fall at the golden section. The whole thing (ie all 3 crowns) fit onto a 12x8 rectangle.

Redrawing it would be unnecessary, since you posted a PDF. You can open that PDF in Illustrator, and copy the logo in vectors from it.

Because I'm so nice, I have done just that. Shall I upload it somewhere?
Or if you want to do it yourself.. :)

edit:
Though I'm not sure if such a thing is allowed, reading that regulations and such.

Nick job wrote: See also
http://en.wikipedia.org/wiki/Coat_of_arms_of_Sweden
and note section on regulated use.

You should look this over, the use of the coat of arms is heavily regulated.

I think Saab used three crowns as part of their logo at some point in their history. Not sure about right now.