Welcome to the glorious world of series expansions

You may also wish to visit the On-Line Encyclopedia of Integer Sequences (OEIS) , which is an amazing treasure trove of sequences, with lots of information about their origin, references to publications, links to other sites etc. Each series on this site is linked to the OEIS. After the internal link (blue) there is a number Axxxxxx (red) which takes you to the OEIS. When you click it you get the relevant entry, which gives references, cross-refs to other sequences, formulae when available, etc.