It’s time to try writing a blog post every day of November again. This time I’ll really try to make the posts shorter.
This one will consistent entirely of a puzzle. Consider the formal power series
giving the ordinary generating function of the factorials. This power series has zero radius of convergence, but it still makes sense formally. Its logarithm
is another formal power series of the form , where the turn out to be positive integers.
Puzzle: What do the count?
No cheating using the OEIS! That’s no fun anyway.