The On-Line Encyclopedia of Integer Sequences
oeis.org
oeis.org
Let me give you a concrete example, back from some online puzzle by a Large Internet Search company. You have X items of unique heights, and the question is how many ways you can line them up so that someone looking from one end can see Y distinct non-occluded heights, and someone looking from the other side can see Z distinct heights.
IIRC manually experimenting with small numbers revealed a pattern that OEIS said was Stirling Numbers of the first kind [0]. Simply having this jargon/label available made it possible to access work other people did on it in the past.
[0] https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_...
https://hn.algolia.com/?dateRange=all&query=The%20On-Line%20...