I need help identifying the series of my 3240 block and tackle window balances

Thanks for posting. That stamp isn't an identifier; it just tells us the balance's strength. This looks like either an S380-33 or S385-33 Channel Balance. The only difference between these two balances is the depth of the bottom nylon shoe, or the 'heel-to-toe' measurement. See the diagram below for reference. Compare both with your old hardware to see what matches best. For a new stamp option, choose 3240.

Comparison of the S378, S380 and S385 balance shoes.