Wedderburn-Etherington number

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In graph theory, the Wedderburn-Etherington numbers count 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 (sequence A001190 in OEIS).

The first Wedderburn-Etherington numbers that are primes are

2, 3, 11, 23, 983, 2179, 24631, 3626149, 253450711, 596572387
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