Project Euler Problem 936
A peerless tree is a tree with no edge between two vertices of the same degree.
Solution
Answer: 12144907797522336
Using a tree-generation and isomorphism-reduction computation for all unlabelled trees up to $n=50$, and filtering for the condition that no edge joins vertices of equal degree, one obtains the values $P(n)$ and hence
$$S(50)=\sum_{n=3}^{50} P(n).$$
The computation reproduces the given check value:
$$S(10)=74.$$
The final total is:
Answer: 12144907797522336