Number of nondecreasing functions from $\{1,2,\dots,n\}$ to $\{1,2,\dots,n\}$

Question

How many functions $$f: \{1,2,\dots,n\} \to \{1,2,\dots,n\}$$ are there such that for every $i \leq j$ we have $f(i) \leq f(j)$?

The only way I could think of was removing all the "bad" cases from $n^n$, but that wouldn't be very effective. What better way could I use?

http://oeis.org/A001700 – Rodrigo de Azevedo Dec 21 '16 at 10:34 — Rodrigo de Azevedo, Dec 21 '16 at 10:34

score 0 · Accepted Answer · answered Dec 21 '16 at 10:20

0

From here.
Also, removing "bad" cases from total cases is not always a good idea.

answered Dec 21 '16 at 10:20

1 Answers1