Browning Belgium 22 short odd serial number

[killa4rilla]

I inherited this rifle from my father and was trying to date it based on the serial number 3F16040, which is stamped on the bottom of the barrel. I have been unable to find any info related to this series of numbers and the letter F. I know that an E was used in some serial numbers, but still the numerical values don't match. Any help is greatly appreciated! Please see attachments for pics.

 

[Scorch]

According to the numbering scheme explained on Browning's web site, it would have been made in 1963 (seems OK), and was the 16,040th gun made that year (seems not OK). That doesn't seem to make much sense to me, I would think that production would be much lower, and the F doesn't match the numbering and catalog scheme.

 

[Salmoneye]

My bet is a poorly stamped 'E' (.22 Short)...