This name is a synonym of Potentilla bipinnatifida Douglas ex Hook..
The record derives from RJP
(data supplied on 2011-10-18)
which reports it as a synonym (record 3851) with original publication details: A flora of North America A flora of North America; 1838 438 1840.
This name record (from RJP) was not included in version 1 of The Plant List. It is possible the same name was included from a different data source, to check this you can search for Potentilla pensylvanica in version 1 of The Plant List.