Single coil balance

Thanks for posting. That's a 15-180 Pivot Shoe, which uses Series 190 Coil Balances. the stamps are usually found on the coil springs themselves, near the tongue. You will need to remove the coil system from the window to assess this. Alternatively, you can also just give us the exact weight of the window sash that these balances support, and I can work out the spring weights you need. 

The pivot bar does look unusual--does the one on the other side have that same offset? Ultimately I'll need you to remove it so I can have a clear look at it. We should be able to narrow options down from there.

The video below shows how to remove and install a different but similar coil balance system. Take a look and let me know if you have any questions about any of this.