Formulas to calculate total and other bits

SajExcel 

Introduced a few helper columns and used Sergei's formula (made range dynamic) to count unique observations up to the date of observation. This gives you the "All-time sequence" in one column. The same formula (with adjusted ranges) entered from each beginning of the new year gives you the Yearly sequence.

Using the filter buttons I can see that you saw the Carrion Crow 8 times in total. It was the 8th one in 2018, the 11th in 2019 and the 1st in 2020.

Perhaps not the prettiest solution, but it works. And, I believe it's fairly easy to understand and maintain.