All trees are graceful, probably

A graceful labelling of a (finite) tree with $n$ vertices is a bijection from $\{1,2,\ldots,n\}$ to the vertices of the tree such that each of the numbers in $\{1,2,\ldots,n-1\}$ is the absolute difference of the labels at the ends of some edge.

For example, the path with 5 vertices has graceful labelling 2,5,1,3,4 as the weights of the edges are respectively 3,4,2,1.

It was conjectured long ago (by Alex Rosa?) that every tree has a graceful labelling, but this is still open. There is proof by computer up to something like 30 or 40 vertices, and tons of partial results.

A less known problem concerns the graceful labellings of a path, which are called graceful permutations (see A006967). The number of them grows quickly but nobody knows how quickly. Nor, as far as I know, is there any recurrence or generating function known.