Tl;dr the Reflex saving throw to not become entangled.
If we read the Entangle ability, it's no help. It just specifies a few minor, irrelevant things. So let's turn to Animate Rope! Animate Rope says very clearly
Saving throw none
at the top of the spell. This isn't promising, but surely there's some meaning. Nobody ever puts in useless saving throw numbers for no reason, right? Yes, that's a joke. So what could it mean?
Searching for the word DC in the spell, we find a DC 23 Strength check to burst rope, a DC 20 Escape Artist check to escape, and a DC 15+spell level Concentration check to cast while entangled. Could there be an argument that it means one of those? Maybe, maybe not. I'm not motivated to try to figure out the rules there. But wait a second... Concentration check to cast while entangled?
Going back a few sentences, we find a Reflex saving throw!
The rope does not deal damage, but it can be used as a trip line or to cause a single opponent that fails a Reflex saving throw to become entangled.
So it does have a saving throw after all! This must the the thing with DC 20! But why did Animate Rope have that pesky "Saving throw none" at the top of the spell? Maybe they wanted to make it clear that the rope doesn't get a saving throw not to be animated, even if it's sentient or magical? Animate Rope allows you to target even an enemy's Rope of Climbing. Anyway, there's clearly a saving throw in some cases, even if the spell says there's not at first.
