Given the computed field refresh issue, even if you managed to get a count of rows (eg on a page-scope SSJS variable), it woudln't update the computed field.
It might be easier to to count to rows in the HTML table using clientside javascript ?
something like ..
page onload event :
get the HTML table
get the table rows property (array of rows in the table)
number or rows = that value (1st row = TH (header) row if there is one = row 0)
use javsscript to plug that value into a known DIV