Plotting a tree without specifying all the nodes - Exhaustive search

Hello everyone,
I’m trying to draw a tree to visualize an exhaustive search without specifying all the nodes’ positions in the graph.
For example, I’d like to build a tree so that, given n=4 objects, the nodes with depth 1 are 4 (in the first one there is the object 1, in the second one there is the object 2 and so on; I prefer to visualize only the number inside each node). The nodes children of node 1 and with depth 2 are n-1=3; the node children of node 2 and with depth 3 are n-2=2 and so on.

The function TreePlot seems to have no the option to do what I want without specifying all the nodes.

Thank you in advance.

Crossposted here.