Number of ways to pick one or more elements from a set of $N$ elements I'm looking for a particular formula in combinatorics, but I don't even know what it would be called.   It is likely related to the Bell Number.
Given a set of $N$ elements, I'd like to know how many different ways I can pick one-or-more elements from the set.
For example: $N = 3$  (set consisting of a, b, and c)

*

*a

*b

*c

*a + b

*a + c

*b + c

*a + b + c
(The Bell Number for a set of size 3 is only 5, so it comes up short of what I'm looking for)
Is there a term for this value, and how can it be calculated?

$\binom{N}{1}+\binom{N}{2}+\cdots+\binom{N}{N}=2^N-1.$ 
