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I was able to do it by doing a model and type search for manuals on the Briggs & Stratton site:
http://www.briggsandstratton.com/us/en/support/manuals/engine
On that page, enter the model and type of your engine, and the cover of the resulting operators manual has the series numbers that match. There are 3 or 4 series listed for your model and type. But, they all look different enough that a search on the Briggs and Stratton site should get you pics of each individual series type (the manual does not identify each one, just shows pics and lists all the covered series) and from that find the one that looks like yours.
Basically, the manual cover gets you a short list of series numbers and your engine belongs to one of them. Then use the pics to narrow it down to the correct series.
I'm a little gob smacked that it took this to find out what series the model and type belong to. Suddenly I'm very happy that my snow blower has a Tecumseh engine. lol
Hope that helps!
The series is typically on a decal on the engine or on the Operators Manuel You're best bet for verifying a maintenance kit is to get the Model Type and Trim number from the engine and compare the air filter part number on the illustrated parts list on the Briggs and Stratton site. Or, chat a B and S agent and they can find the info for you.