Wedderburn-Etherington number

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In graph theory, the Wedderburn-Etherington number counts how many weakly binary trees can be constructed such that each graph vertex (not counting the root vertex) 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

Wedderburn-Etherington prime

A Wedderburn-Etherington prime is a Wedderburn-Etherington number that is prime. The first few Wedderburn-Etherington primes are

2, 3, 11, 23, 983, 2179, ...