Numbers Expressed as Sums of Binomial Coefficients

Definition
Let $n \in \Z_{> 0}$ be a (strictly) positive integer.

Then for all $k \in \Z_{> 0}$, it is possible to express $k$ in the form:

such that $0 \le k_1 < k_2 < \cdots < k_n$.

Also see

 * Definition:Combinatorial Number System