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Counting Nondecreasing Integer Sequences that Lie Below a Barrier
Given a barrier $0 \leq b_0 \leq b_1 \leq \cdots$, let $f(n)$ be the number of nondecreasing integer sequences $0 \leq a_0 \leq a_1 \leq \cdots \leq a_n$ for which $a_j \leq b_j$ for all $0 \leq j \leq n$. Known formulæ for $f(n)$ include an $n \times n$ determinant …