WEDDERBURN-ETHERINGTON NUMBER

In graph theory, the 'Wedderburn-Etherington numbers' count how many weakly binary trees can be constructed: that is, the number of trees for which each graph vertex (not counting the root) is adjacent to no more than three other such vertices, for a given number of nodes. The first few Wedderburn-Etherington numbers are
:1, 1, 1, 2, 3, 6, 11, 23, 46, 98, 207, 451, 983, 2179, 4850, 10905, 24631, 56011, 127912, 293547, 676157, 1563372, 3626149, 8436379, 19680277, 46026618, 107890609, 253450711, 596572387, 1406818759, 3323236238, 7862958391 .
The first Wedderburn-Etherington numbers that are primes are
:2, 3, 11, 23, 983, 2179, 24631, 3626149, 253450711, 596572387